id	sid	tid	token	lemma	pos
cbi-29	1	1	v2018i1	v2018i1	PROPN
cbi-29	1	2	volume	volume	NOUN
cbi-29	1	3	1	1	NUM
cbi-29	1	4	,	,	PUNCT
cbi-29	1	5	issue	issue	VERB
cbi-29	1	6	1	1	NUM
cbi-29	1	7	simplifying	simplify	VERB
cbi-29	1	8	and	and	CCONJ
cbi-29	1	9	refactoring	refactoring	NOUN
cbi-29	1	10	introductory	introductory	PROPN
cbi-29	1	11	calculus	calculus	PROPN
cbi-29	1	12	jonathan	jonathan	PROPN
cbi-29	1	13	bartlett	bartlett	PROPN
cbi-29	1	14	doi	doi	PROPN
cbi-29	1	15	:	:	PUNCT
cbi-29	1	16	10.33014	10.33014	NUM
cbi-29	1	17	/	/	SYM
cbi-29	1	18	issn.2640	issn.2640	ADJ
cbi-29	1	19	-	-	PUNCT
cbi-29	1	20	5652.1.1.bartlett.1	5652.1.1.bartlett.1	ADJ
cbi-29	1	21	abstract	abstract	ADJ
cbi-29	1	22	first	first	ADJ
cbi-29	1	23	year	year	NOUN
cbi-29	1	24	calculus	calculus	NOUN
cbi-29	1	25	is	be	AUX
cbi-29	1	26	often	often	ADV
cbi-29	1	27	taught	teach	VERB
cbi-29	1	28	in	in	ADP
cbi-29	1	29	a	a	DET
cbi-29	1	30	way	way	NOUN
cbi-29	1	31	that	that	PRON
cbi-29	1	32	is	be	AUX
cbi-29	1	33	very	very	ADV
cbi-29	1	34	burdensome	burdensome	ADJ
cbi-29	1	35	to	to	ADP
cbi-29	1	36	the	the	DET
cbi-29	1	37	student	student	NOUN
cbi-29	1	38	.	.	PUNCT
cbi-29	2	1	students	student	NOUN
cbi-29	2	2	have	have	VERB
cbi-29	2	3	to	to	PART
cbi-29	2	4	memorize	memorize	VERB
cbi-29	2	5	a	a	DET
cbi-29	2	6	diversity	diversity	NOUN
cbi-29	2	7	of	of	ADP
cbi-29	2	8	processes	process	NOUN
cbi-29	2	9	for	for	ADP
cbi-29	2	10	essentially	essentially	ADV
cbi-29	2	11	performing	perform	VERB
cbi-29	2	12	the	the	DET
cbi-29	2	13	same	same	ADJ
cbi-29	2	14	task	task	NOUN
cbi-29	2	15	.	.	PUNCT
cbi-29	3	1	however	however	ADV
cbi-29	3	2	,	,	PUNCT
cbi-29	3	3	many	many	ADJ
cbi-29	3	4	calculus	calculus	NOUN
cbi-29	3	5	processes	process	NOUN
cbi-29	3	6	can	can	AUX
cbi-29	3	7	be	be	AUX
cbi-29	3	8	simplified	simplify	VERB
cbi-29	3	9	and	and	CCONJ
cbi-29	3	10	streamlined	streamline	VERB
cbi-29	3	11	so	so	SCONJ
cbi-29	3	12	that	that	SCONJ
cbi-29	3	13	fewer	few	ADJ
cbi-29	3	14	concepts	concept	NOUN
cbi-29	3	15	can	can	AUX
cbi-29	3	16	provide	provide	VERB
cbi-29	3	17	more	more	ADJ
cbi-29	3	18	flexibility	flexibility	NOUN
cbi-29	3	19	and	and	CCONJ
cbi-29	3	20	capability	capability	NOUN
cbi-29	3	21	for	for	ADP
cbi-29	3	22	first	first	ADJ
cbi-29	3	23	-	-	PUNCT
cbi-29	3	24	year	year	NOUN
cbi-29	3	25	students	student	NOUN
cbi-29	3	26	.	.	PUNCT
cbi-29	4	1	1	1	NUM
cbi-29	4	2	introduction	introduction	NOUN
cbi-29	4	3	while	while	SCONJ
cbi-29	4	4	the	the	DET
cbi-29	4	5	exact	exact	ADJ
cbi-29	4	6	set	set	NOUN
cbi-29	4	7	of	of	ADP
cbi-29	4	8	topics	topic	NOUN
cbi-29	4	9	in	in	ADP
cbi-29	4	10	any	any	DET
cbi-29	4	11	particular	particular	ADJ
cbi-29	4	12	calculus	calculus	NOUN
cbi-29	4	13	book	book	NOUN
cbi-29	4	14	or	or	CCONJ
cbi-29	4	15	course	course	NOUN
cbi-29	4	16	may	may	AUX
cbi-29	4	17	vary	vary	VERB
cbi-29	4	18	,	,	PUNCT
cbi-29	4	19	the	the	DET
cbi-29	4	20	general	general	ADJ
cbi-29	4	21	method	method	NOUN
cbi-29	4	22	of	of	ADP
cbi-29	4	23	calculus	calculus	NOUN
cbi-29	4	24	training	training	NOUN
cbi-29	4	25	has	have	AUX
cbi-29	4	26	been	be	AUX
cbi-29	4	27	essentially	essentially	ADV
cbi-29	4	28	set	set	VERB
cbi-29	4	29	in	in	ADP
cbi-29	4	30	stone	stone	NOUN
cbi-29	4	31	for	for	ADP
cbi-29	4	32	the	the	DET
cbi-29	4	33	last	last	ADJ
cbi-29	4	34	hundred	hundred	NUM
cbi-29	4	35	years	year	NOUN
cbi-29	4	36	.	.	PUNCT
cbi-29	5	1	nonetheless	nonetheless	ADV
cbi-29	5	2	,	,	PUNCT
cbi-29	5	3	there	there	PRON
cbi-29	5	4	are	be	VERB
cbi-29	5	5	many	many	ADJ
cbi-29	5	6	issues	issue	NOUN
cbi-29	5	7	with	with	ADP
cbi-29	5	8	this	this	DET
cbi-29	5	9	methodology	methodology	NOUN
cbi-29	5	10	that	that	PRON
cbi-29	5	11	have	have	AUX
cbi-29	5	12	been	be	AUX
cbi-29	5	13	insufficiently	insufficiently	ADV
cbi-29	5	14	addressed	address	VERB
cbi-29	5	15	over	over	ADP
cbi-29	5	16	the	the	DET
cbi-29	5	17	years	year	NOUN
cbi-29	5	18	.	.	PUNCT
cbi-29	6	1	these	these	DET
cbi-29	6	2	issues	issue	NOUN
cbi-29	6	3	range	range	VERB
cbi-29	6	4	from	from	ADP
cbi-29	6	5	the	the	DET
cbi-29	6	6	sequencing	sequencing	NOUN
cbi-29	6	7	of	of	ADP
cbi-29	6	8	topics	topic	NOUN
cbi-29	6	9	to	to	ADP
cbi-29	6	10	the	the	DET
cbi-29	6	11	content	content	NOUN
cbi-29	6	12	of	of	ADP
cbi-29	6	13	the	the	DET
cbi-29	6	14	topics	topic	NOUN
cbi-29	6	15	themselves	themselves	PRON
cbi-29	6	16	.	.	PUNCT
cbi-29	7	1	a	a	DET
cbi-29	7	2	well	well	ADV
cbi-29	7	3	-	-	PUNCT
cbi-29	7	4	recognized	recognize	VERB
cbi-29	7	5	phenomena	phenomena	NOUN
cbi-29	7	6	in	in	ADP
cbi-29	7	7	computer	computer	NOUN
cbi-29	7	8	programming	programming	NOUN
cbi-29	7	9	is	be	AUX
cbi-29	7	10	known	know	VERB
cbi-29	7	11	as	as	ADP
cbi-29	7	12	“	"	PUNCT
cbi-29	7	13	code	code	NOUN
cbi-29	7	14	debt	debt	NOUN
cbi-29	7	15	.	.	PUNCT
cbi-29	7	16	”	"	PUNCT
cbi-29	8	1	code	code	NOUN
cbi-29	8	2	debt	debt	NOUN
cbi-29	8	3	occurs	occur	VERB
cbi-29	8	4	when	when	SCONJ
cbi-29	8	5	new	new	ADJ
cbi-29	8	6	ideas	idea	NOUN
cbi-29	8	7	and	and	CCONJ
cbi-29	8	8	changes	change	NOUN
cbi-29	8	9	get	get	AUX
cbi-29	8	10	incorporated	incorporate	VERB
cbi-29	8	11	into	into	ADP
cbi-29	8	12	a	a	DET
cbi-29	8	13	program	program	NOUN
cbi-29	8	14	,	,	PUNCT
cbi-29	8	15	but	but	CCONJ
cbi-29	8	16	the	the	DET
cbi-29	8	17	rest	rest	NOUN
cbi-29	8	18	of	of	ADP
cbi-29	8	19	the	the	DET
cbi-29	8	20	program	program	NOUN
cbi-29	8	21	does	do	AUX
cbi-29	8	22	n’t	not	PART
cbi-29	8	23	change	change	VERB
cbi-29	8	24	sufficiently	sufficiently	ADV
cbi-29	8	25	to	to	PART
cbi-29	8	26	take	take	VERB
cbi-29	8	27	these	these	DET
cbi-29	8	28	new	new	ADJ
cbi-29	8	29	ideas	idea	NOUN
cbi-29	8	30	and	and	CCONJ
cbi-29	8	31	changes	change	NOUN
cbi-29	8	32	into	into	ADP
cbi-29	8	33	account	account	NOUN
cbi-29	8	34	.	.	PUNCT
cbi-29	9	1	because	because	SCONJ
cbi-29	9	2	of	of	ADP
cbi-29	9	3	this	this	PRON
cbi-29	9	4	,	,	PUNCT
cbi-29	9	5	there	there	ADV
cbi-29	9	6	winds	wind	VERB
cbi-29	9	7	up	up	ADP
cbi-29	9	8	being	be	AUX
cbi-29	9	9	a	a	DET
cbi-29	9	10	lot	lot	NOUN
cbi-29	9	11	of	of	ADP
cbi-29	9	12	duplication	duplication	NOUN
cbi-29	9	13	and	and	CCONJ
cbi-29	9	14	confusion	confusion	NOUN
cbi-29	9	15	over	over	ADP
cbi-29	9	16	the	the	DET
cbi-29	9	17	right	right	ADJ
cbi-29	9	18	ways	way	NOUN
cbi-29	9	19	of	of	ADP
cbi-29	9	20	doing	do	VERB
cbi-29	9	21	things	thing	NOUN
cbi-29	9	22	.	.	PUNCT
cbi-29	10	1	it	it	PRON
cbi-29	10	2	is	be	AUX
cbi-29	10	3	known	know	VERB
cbi-29	10	4	as	as	ADP
cbi-29	10	5	code	code	NOUN
cbi-29	10	6	debt	debt	NOUN
cbi-29	10	7	because	because	SCONJ
cbi-29	10	8	eventually	eventually	ADV
cbi-29	10	9	,	,	PUNCT
cbi-29	10	10	to	to	PART
cbi-29	10	11	relieve	relieve	VERB
cbi-29	10	12	the	the	DET
cbi-29	10	13	tension	tension	NOUN
cbi-29	10	14	,	,	PUNCT
cbi-29	10	15	future	future	ADJ
cbi-29	10	16	work	work	NOUN
cbi-29	10	17	will	will	AUX
cbi-29	10	18	have	have	VERB
cbi-29	10	19	to	to	PART
cbi-29	10	20	be	be	AUX
cbi-29	10	21	done	do	VERB
cbi-29	10	22	to	to	ADP
cbi-29	10	23	the	the	DET
cbi-29	10	24	rest	rest	NOUN
cbi-29	10	25	of	of	ADP
cbi-29	10	26	the	the	DET
cbi-29	10	27	system	system	NOUN
cbi-29	10	28	to	to	PART
cbi-29	10	29	bring	bring	VERB
cbi-29	10	30	it	it	PRON
cbi-29	10	31	back	back	ADV
cbi-29	10	32	into	into	ADP
cbi-29	10	33	alignment	alignment	NOUN
cbi-29	10	34	.	.	PUNCT
cbi-29	11	1	to	to	PART
cbi-29	11	2	relieve	relieve	VERB
cbi-29	11	3	code	code	NOUN
cbi-29	11	4	debt	debt	NOUN
cbi-29	11	5	,	,	PUNCT
cbi-29	11	6	computer	computer	NOUN
cbi-29	11	7	programmers	programmer	NOUN
cbi-29	11	8	engage	engage	VERB
cbi-29	11	9	in	in	ADP
cbi-29	11	10	in	in	ADP
cbi-29	11	11	a	a	DET
cbi-29	11	12	process	process	NOUN
cbi-29	11	13	known	know	VERB
cbi-29	11	14	as	as	ADP
cbi-29	11	15	“	"	PUNCT
cbi-29	11	16	refactoring	refactoring	NOUN
cbi-29	11	17	.	.	PUNCT
cbi-29	11	18	”	"	PUNCT
cbi-29	12	1	the	the	DET
cbi-29	12	2	idea	idea	NOUN
cbi-29	12	3	behind	behind	ADP
cbi-29	12	4	refactoring	refactoring	NOUN
cbi-29	12	5	is	be	AUX
cbi-29	12	6	to	to	PART
cbi-29	12	7	reconceptualize	reconceptualize	VERB
cbi-29	12	8	the	the	DET
cbi-29	12	9	whole	whole	NOUN
cbi-29	12	10	of	of	ADP
cbi-29	12	11	the	the	DET
cbi-29	12	12	computer	computer	NOUN
cbi-29	12	13	program	program	NOUN
cbi-29	12	14	in	in	ADP
cbi-29	12	15	order	order	NOUN
cbi-29	12	16	to	to	PART
cbi-29	12	17	discover	discover	VERB
cbi-29	12	18	which	which	DET
cbi-29	12	19	facilities	facility	NOUN
cbi-29	12	20	are	be	AUX
cbi-29	12	21	the	the	DET
cbi-29	12	22	core	core	NOUN
cbi-29	12	23	,	,	PUNCT
cbi-29	12	24	distinguishable	distinguishable	ADJ
cbi-29	12	25	pieces	piece	NOUN
cbi-29	12	26	and	and	CCONJ
cbi-29	12	27	which	which	DET
cbi-29	12	28	ones	one	NOUN
cbi-29	12	29	are	be	AUX
cbi-29	12	30	merely	merely	ADV
cbi-29	12	31	a	a	DET
cbi-29	12	32	variant	variant	NOUN
cbi-29	12	33	or	or	CCONJ
cbi-29	12	34	permutation	permutation	NOUN
cbi-29	12	35	of	of	ADP
cbi-29	12	36	those	those	DET
cbi-29	12	37	pieces	piece	NOUN
cbi-29	12	38	.	.	PUNCT
cbi-29	13	1	the	the	DET
cbi-29	13	2	present	present	ADJ
cbi-29	13	3	goal	goal	NOUN
cbi-29	13	4	of	of	ADP
cbi-29	13	5	the	the	DET
cbi-29	13	6	paper	paper	NOUN
cbi-29	13	7	is	be	AUX
cbi-29	13	8	to	to	PART
cbi-29	13	9	begin	begin	VERB
cbi-29	13	10	a	a	DET
cbi-29	13	11	similar	similar	ADJ
cbi-29	13	12	process	process	NOUN
cbi-29	13	13	of	of	ADP
cbi-29	13	14	refactoring	refactore	VERB
cbi-29	13	15	the	the	DET
cbi-29	13	16	subject	subject	NOUN
cbi-29	13	17	of	of	ADP
cbi-29	13	18	calculus	calculus	NOUN
cbi-29	13	19	and	and	CCONJ
cbi-29	13	20	the	the	DET
cbi-29	13	21	way	way	NOUN
cbi-29	13	22	that	that	PRON
cbi-29	13	23	it	it	PRON
cbi-29	13	24	is	be	AUX
cbi-29	13	25	taught	teach	VERB
cbi-29	13	26	.	.	PUNCT
cbi-29	14	1	2	2	NUM
cbi-29	14	2	proof	proof	NOUN
cbi-29	14	3	mechanisms	mechanism	NOUN
cbi-29	14	4	and	and	CCONJ
cbi-29	14	5	learning	learn	VERB
cbi-29	14	6	calculus	calculus	NOUN
cbi-29	14	7	calculus	calculus	NOUN
cbi-29	14	8	books	book	NOUN
cbi-29	14	9	and	and	CCONJ
cbi-29	14	10	courses	course	NOUN
cbi-29	14	11	are	be	AUX
cbi-29	14	12	often	often	ADV
cbi-29	14	13	written	write	VERB
cbi-29	14	14	so	so	SCONJ
cbi-29	14	15	that	that	SCONJ
cbi-29	14	16	each	each	DET
cbi-29	14	17	step	step	NOUN
cbi-29	14	18	of	of	ADP
cbi-29	14	19	the	the	DET
cbi-29	14	20	development	development	NOUN
cbi-29	14	21	of	of	ADP
cbi-29	14	22	calculus	calculus	NOUN
cbi-29	14	23	can	can	AUX
cbi-29	14	24	be	be	AUX
cbi-29	14	25	proved	prove	VERB
cbi-29	14	26	.	.	PUNCT
cbi-29	15	1	most	most	ADJ
cbi-29	15	2	books	book	NOUN
cbi-29	15	3	begin	begin	VERB
cbi-29	15	4	with	with	ADP
cbi-29	15	5	limits	limit	NOUN
cbi-29	15	6	,	,	PUNCT
cbi-29	15	7	and	and	CCONJ
cbi-29	15	8	then	then	ADV
cbi-29	15	9	calculus	calculus	NOUN
cbi-29	15	10	is	be	AUX
cbi-29	15	11	then	then	ADV
cbi-29	15	12	proved	prove	VERB
cbi-29	15	13	using	use	VERB
cbi-29	15	14	limits	limit	NOUN
cbi-29	15	15	.	.	PUNCT
cbi-29	16	1	unfortunately	unfortunately	ADV
cbi-29	16	2	,	,	PUNCT
cbi-29	16	3	most	most	ADJ
cbi-29	16	4	calculus	calculus	NOUN
cbi-29	16	5	students	student	NOUN
cbi-29	16	6	are	be	AUX
cbi-29	16	7	not	not	PART
cbi-29	16	8	yet	yet	ADV
cbi-29	16	9	ready	ready	ADJ
cbi-29	16	10	for	for	ADP
cbi-29	16	11	limits	limit	NOUN
cbi-29	16	12	,	,	PUNCT
cbi-29	16	13	and	and	CCONJ
cbi-29	16	14	limits	limit	NOUN
cbi-29	16	15	often	often	ADV
cbi-29	16	16	wind	wind	VERB
cbi-29	16	17	up	up	ADP
cbi-29	16	18	being	be	AUX
cbi-29	16	19	a	a	DET
cbi-29	16	20	confusing	confusing	ADJ
cbi-29	16	21	side	side	NOUN
cbi-29	16	22	-	-	PUNCT
cbi-29	16	23	challenge	challenge	NOUN
cbi-29	16	24	that	that	PRON
cbi-29	16	25	derail	derail	VERB
cbi-29	16	26	students	student	NOUN
cbi-29	16	27	before	before	SCONJ
cbi-29	16	28	they	they	PRON
cbi-29	16	29	have	have	AUX
cbi-29	16	30	even	even	ADV
cbi-29	16	31	begun	begin	VERB
cbi-29	16	32	to	to	PART
cbi-29	16	33	study	study	VERB
cbi-29	16	34	the	the	DET
cbi-29	16	35	subject	subject	NOUN
cbi-29	16	36	in	in	ADP
cbi-29	16	37	depth	depth	NOUN
cbi-29	16	38	.	.	PUNCT
cbi-29	17	1	in	in	ADP
cbi-29	17	2	nearly	nearly	ADV
cbi-29	17	3	any	any	PRON
cbi-29	17	4	subject	subject	NOUN
cbi-29	17	5	,	,	PUNCT
cbi-29	17	6	students	student	NOUN
cbi-29	17	7	do	do	VERB
cbi-29	17	8	best	well	ADV
cbi-29	17	9	when	when	SCONJ
cbi-29	17	10	proofs	proof	NOUN
cbi-29	17	11	occur	occur	VERB
cbi-29	17	12	after	after	SCONJ
cbi-29	17	13	the	the	DET
cbi-29	17	14	core	core	NOUN
cbi-29	17	15	content	content	NOUN
cbi-29	17	16	is	be	AUX
cbi-29	17	17	learned	learn	VERB
cbi-29	17	18	.	.	PUNCT
cbi-29	18	1	as	as	ADP
cbi-29	18	2	an	an	DET
cbi-29	18	3	example	example	NOUN
cbi-29	18	4	,	,	PUNCT
cbi-29	18	5	consider	consider	VERB
cbi-29	18	6	children	child	NOUN
cbi-29	18	7	learning	learn	VERB
cbi-29	18	8	a	a	DET
cbi-29	18	9	language	language	NOUN
cbi-29	18	10	.	.	PUNCT
cbi-29	19	1	children	child	NOUN
cbi-29	19	2	learn	learn	VERB
cbi-29	19	3	english	english	PROPN
cbi-29	19	4	(	(	PUNCT
cbi-29	19	5	or	or	CCONJ
cbi-29	19	6	any	any	DET
cbi-29	19	7	other	other	ADJ
cbi-29	19	8	language	language	NOUN
cbi-29	19	9	)	)	PUNCT
cbi-29	19	10	long	long	ADV
cbi-29	19	11	before	before	SCONJ
cbi-29	19	12	they	they	PRON
cbi-29	19	13	learn	learn	VERB
cbi-29	19	14	the	the	DET
cbi-29	19	15	grammar	grammar	NOUN
cbi-29	19	16	of	of	ADP
cbi-29	19	17	english	english	PROPN
cbi-29	19	18	.	.	PUNCT
cbi-29	20	1	in	in	ADP
cbi-29	20	2	fact	fact	NOUN
cbi-29	20	3	,	,	PUNCT
cbi-29	20	4	most	most	ADJ
cbi-29	20	5	students	student	NOUN
cbi-29	20	6	can	can	AUX
cbi-29	20	7	speak	speak	VERB
cbi-29	20	8	english	english	PROPN
cbi-29	20	9	perfectly	perfectly	ADV
cbi-29	20	10	well	well	ADV
cbi-29	20	11	without	without	ADP
cbi-29	20	12	ever	ever	ADV
cbi-29	20	13	learning	learn	VERB
cbi-29	20	14	the	the	DET
cbi-29	20	15	rules	rule	NOUN
cbi-29	20	16	(	(	PUNCT
cbi-29	20	17	grammar	grammar	NOUN
cbi-29	20	18	)	)	PUNCT
cbi-29	20	19	that	that	PRON
cbi-29	20	20	govern	govern	VERB
cbi-29	20	21	english	english	PROPN
cbi-29	20	22	.	.	PUNCT
cbi-29	21	1	even	even	ADV
cbi-29	21	2	when	when	SCONJ
cbi-29	21	3	learning	learn	VERB
cbi-29	21	4	foreign	foreign	ADJ
cbi-29	21	5	languages	language	NOUN
cbi-29	21	6	,	,	PUNCT
cbi-29	21	7	immersive	immersive	ADJ
cbi-29	21	8	approaches	approach	NOUN
cbi-29	21	9	(	(	PUNCT
cbi-29	21	10	i.e.	i.e.	X
cbi-29	21	11	,	,	PUNCT
cbi-29	21	12	those	those	PRON
cbi-29	21	13	in	in	ADP
cbi-29	21	14	which	which	PRON
cbi-29	21	15	the	the	DET
cbi-29	21	16	language	language	NOUN
cbi-29	21	17	precedes	precede	VERB
cbi-29	21	18	the	the	DET
cbi-29	21	19	grammar	grammar	NOUN
cbi-29	21	20	of	of	ADP
cbi-29	21	21	it	it	PRON
cbi-29	21	22	)	)	PUNCT
cbi-29	21	23	tend	tend	VERB
cbi-29	21	24	to	to	PART
cbi-29	21	25	work	work	VERB
cbi-29	21	26	most	most	ADV
cbi-29	21	27	effectively	effectively	ADV
cbi-29	21	28	(	(	PUNCT
cbi-29	21	29	gonzálezlloret	gonzálezlloret	NOUN
cbi-29	21	30	and	and	CCONJ
cbi-29	21	31	nielson	nielson	PROPN
cbi-29	21	32	,	,	PUNCT
cbi-29	21	33	2015	2015	NUM
cbi-29	21	34	)	)	PUNCT
cbi-29	21	35	.	.	PUNCT
cbi-29	22	1	of	of	ADP
cbi-29	22	2	course	course	ADV
cbi-29	22	3	,	,	PUNCT
cbi-29	22	4	mathematical	mathematical	ADJ
cbi-29	22	5	learning	learning	NOUN
cbi-29	22	6	is	be	AUX
cbi-29	22	7	not	not	PART
cbi-29	22	8	identical	identical	ADJ
cbi-29	22	9	to	to	ADP
cbi-29	22	10	language	language	NOUN
cbi-29	22	11	learning	learning	NOUN
cbi-29	22	12	.	.	PUNCT
cbi-29	23	1	part	part	NOUN
cbi-29	23	2	of	of	ADP
cbi-29	23	3	mathematics	mathematic	NOUN
cbi-29	23	4	is	be	AUX
cbi-29	23	5	proof	proof	ADJ
cbi-29	23	6	,	,	PUNCT
cbi-29	23	7	so	so	ADV
cbi-29	23	8	learning	learn	VERB
cbi-29	23	9	proof	proof	ADJ
cbi-29	23	10	tools	tool	NOUN
cbi-29	23	11	is	be	AUX
cbi-29	23	12	certainly	certainly	ADV
cbi-29	23	13	an	an	DET
cbi-29	23	14	important	important	ADJ
cbi-29	23	15	part	part	NOUN
cbi-29	23	16	of	of	ADP
cbi-29	23	17	mathematics	mathematic	NOUN
cbi-29	23	18	.	.	PUNCT
cbi-29	24	1	additionally	additionally	ADV
cbi-29	24	2	,	,	PUNCT
cbi-29	24	3	with	with	ADP
cbi-29	24	4	most	most	ADJ
cbi-29	24	5	technical	technical	ADJ
cbi-29	24	6	subjects	subject	NOUN
cbi-29	24	7	,	,	PUNCT
cbi-29	24	8	having	have	VERB
cbi-29	24	9	a	a	DET
cbi-29	24	10	grounding	grounding	NOUN
cbi-29	24	11	in	in	ADP
cbi-29	24	12	the	the	DET
cbi-29	24	13	“	"	PUNCT
cbi-29	24	14	why	why	SCONJ
cbi-29	24	15	”	"	PUNCT
cbi-29	24	16	aspects	aspect	NOUN
cbi-29	24	17	certainly	certainly	ADV
cbi-29	24	18	helps	help	VERB
cbi-29	24	19	one	one	NUM
cbi-29	24	20	to	to	PART
cbi-29	24	21	learn	learn	VERB
cbi-29	24	22	the	the	DET
cbi-29	24	23	intuitions	intuition	NOUN
cbi-29	24	24	behind	behind	ADP
cbi-29	24	25	the	the	DET
cbi-29	24	26	“	"	PUNCT
cbi-29	24	27	how	how	SCONJ
cbi-29	24	28	.	.	PUNCT
cbi-29	24	29	”	"	PUNCT
cbi-29	25	1	however	however	ADV
cbi-29	25	2	,	,	PUNCT
cbi-29	25	3	even	even	ADV
cbi-29	25	4	when	when	SCONJ
cbi-29	25	5	the	the	DET
cbi-29	25	6	proofs	proof	NOUN
cbi-29	25	7	help	help	AUX
cbi-29	25	8	build	build	VERB
cbi-29	25	9	an	an	DET
cbi-29	25	10	intuition	intuition	NOUN
cbi-29	25	11	,	,	PUNCT
cbi-29	25	12	there	there	PRON
cbi-29	25	13	is	be	VERB
cbi-29	25	14	a	a	DET
cbi-29	25	15	difference	difference	NOUN
cbi-29	25	16	between	between	ADP
cbi-29	25	17	teaching	teach	VERB
cbi-29	25	18	an	an	DET
cbi-29	25	19	intuition	intuition	NOUN
cbi-29	25	20	behind	behind	ADP
cbi-29	25	21	an	an	DET
cbi-29	25	22	idea	idea	NOUN
cbi-29	25	23	by	by	ADP
cbi-29	25	24	proving	prove	VERB
cbi-29	25	25	its	its	PRON
cbi-29	25	26	truth	truth	NOUN
cbi-29	25	27	and	and	CCONJ
cbi-29	25	28	trying	try	VERB
cbi-29	25	29	to	to	PART
cbi-29	25	30	get	get	VERB
cbi-29	25	31	students	student	NOUN
cbi-29	25	32	to	to	PART
cbi-29	25	33	construct	construct	VERB
cbi-29	25	34	their	their	PRON
cbi-29	25	35	own	own	ADJ
cbi-29	25	36	proofs	proof	NOUN
cbi-29	25	37	ex	ex	PRON
cbi-29	25	38	nihilo	nihilo	ADJ
cbi-29	25	39	.	.	PUNCT
cbi-29	26	1	therefore	therefore	ADV
cbi-29	26	2	,	,	PUNCT
cbi-29	26	3	the	the	DET
cbi-29	26	4	sequencing	sequencing	NOUN
cbi-29	26	5	in	in	ADP
cbi-29	26	6	this	this	DET
cbi-29	26	7	method	method	NOUN
cbi-29	26	8	will	will	AUX
cbi-29	26	9	focus	focus	VERB
cbi-29	26	10	on	on	ADP
cbi-29	26	11	first	first	ADV
cbi-29	26	12	making	make	VERB
cbi-29	26	13	the	the	DET
cbi-29	26	14	intuitive	intuitive	ADJ
cbi-29	26	15	understanding	understanding	NOUN
cbi-29	26	16	work	work	NOUN
cbi-29	26	17	,	,	PUNCT
cbi-29	26	18	and	and	CCONJ
cbi-29	26	19	then	then	ADV
cbi-29	26	20	only	only	ADV
cbi-29	26	21	later	later	ADV
cbi-29	26	22	establish	establish	VERB
cbi-29	26	23	proofs	proof	NOUN
cbi-29	26	24	.	.	PUNCT
cbi-29	27	1	the	the	DET
cbi-29	27	2	primary	primary	ADJ
cbi-29	27	3	target	target	NOUN
cbi-29	27	4	of	of	ADP
cbi-29	27	5	this	this	DET
cbi-29	27	6	reasoning	reasoning	NOUN
cbi-29	27	7	is	be	AUX
cbi-29	27	8	limits	limit	NOUN
cbi-29	27	9	.	.	PUNCT
cbi-29	28	1	most	most	ADJ
cbi-29	28	2	of	of	ADP
cbi-29	28	3	the	the	DET
cbi-29	28	4	time	time	NOUN
cbi-29	28	5	,	,	PUNCT
cbi-29	28	6	limits	limit	NOUN
cbi-29	28	7	are	be	AUX
cbi-29	28	8	introduced	introduce	VERB
cbi-29	28	9	before	before	ADP
cbi-29	28	10	any	any	PRON
cbi-29	28	11	of	of	ADP
cbi-29	28	12	the	the	DET
cbi-29	28	13	problems	problem	NOUN
cbi-29	28	14	it	it	PRON
cbi-29	28	15	is	be	AUX
cbi-29	28	16	intended	intend	VERB
cbi-29	28	17	to	to	PART
cbi-29	28	18	solve	solve	VERB
cbi-29	28	19	,	,	PUNCT
cbi-29	28	20	which	which	PRON
cbi-29	28	21	makes	make	VERB
cbi-29	28	22	the	the	DET
cbi-29	28	23	subject	subject	NOUN
cbi-29	28	24	confusing	confuse	VERB
cbi-29	28	25	in	in	ADP
cbi-29	28	26	the	the	DET
cbi-29	28	27	first	first	ADJ
cbi-29	28	28	place	place	NOUN
cbi-29	28	29	.	.	PUNCT
cbi-29	29	1	if	if	SCONJ
cbi-29	29	2	a	a	DET
cbi-29	29	3	student	student	NOUN
cbi-29	29	4	has	have	AUX
cbi-29	29	5	grown	grow	VERB
cbi-29	29	6	up	up	ADP
cbi-29	29	7	doing	do	VERB
cbi-29	29	8	the	the	DET
cbi-29	29	9	simple	simple	ADJ
cbi-29	29	10	calculation	calculation	NOUN
cbi-29	29	11	f	f	PROPN
cbi-29	29	12	(	(	PUNCT
cbi-29	29	13	3	3	NUM
cbi-29	29	14	)	)	PUNCT
cbi-29	29	15	when	when	SCONJ
cbi-29	29	16	f	f	X
cbi-29	29	17	(	(	PUNCT
cbi-29	29	18	x	x	X
cbi-29	29	19	)	)	PUNCT
cbi-29	29	20	=	=	SYM
cbi-29	29	21	x2	x2	PROPN
cbi-29	29	22	,	,	PUNCT
cbi-29	29	23	it	it	PRON
cbi-29	29	24	makes	make	VERB
cbi-29	29	25	no	no	DET
cbi-29	29	26	sense	sense	NOUN
cbi-29	29	27	to	to	PART
cbi-29	29	28	transform	transform	VERB
cbi-29	29	29	this	this	PRON
cbi-29	29	30	into	into	ADP
cbi-29	29	31	limit	limit	NOUN
cbi-29	29	32	notation	notation	NOUN
cbi-29	29	33	,	,	PUNCT
cbi-29	29	34	lim	lim	PROPN
cbi-29	29	35	x→3	x→3	PUNCT
cbi-29	30	1	x2	x2	INTJ
cbi-29	30	2	.	.	PUNCT
cbi-29	31	1	this	this	PRON
cbi-29	31	2	is	be	AUX
cbi-29	31	3	simply	simply	ADV
cbi-29	31	4	seen	see	VERB
cbi-29	31	5	by	by	ADP
cbi-29	31	6	the	the	DET
cbi-29	31	7	student	student	NOUN
cbi-29	31	8	as	as	ADP
cbi-29	31	9	extra	extra	ADJ
cbi-29	31	10	steps	step	NOUN
cbi-29	31	11	which	which	PRON
cbi-29	31	12	have	have	VERB
cbi-29	31	13	no	no	DET
cbi-29	31	14	perceptible	perceptible	ADJ
cbi-29	31	15	benefit	benefit	NOUN
cbi-29	31	16	.	.	PUNCT
cbi-29	32	1	18	18	NUM
cbi-29	32	2	simplifying	simplify	VERB
cbi-29	32	3	and	and	CCONJ
cbi-29	32	4	refactoring	refactore	VERB
cbi-29	32	5	introductory	introductory	ADJ
cbi-29	32	6	calculus	calculus	NOUN
cbi-29	32	7	students	student	NOUN
cbi-29	32	8	see	see	VERB
cbi-29	32	9	the	the	DET
cbi-29	32	10	new	new	ADJ
cbi-29	32	11	notation	notation	NOUN
cbi-29	32	12	,	,	PUNCT
cbi-29	32	13	a	a	DET
cbi-29	32	14	bunch	bunch	NOUN
cbi-29	32	15	of	of	ADP
cbi-29	32	16	rules	rule	NOUN
cbi-29	32	17	,	,	PUNCT
cbi-29	32	18	and	and	CCONJ
cbi-29	32	19	are	be	AUX
cbi-29	32	20	asked	ask	VERB
cbi-29	32	21	to	to	PART
cbi-29	32	22	put	put	VERB
cbi-29	32	23	them	they	PRON
cbi-29	32	24	together	together	ADV
cbi-29	32	25	to	to	PART
cbi-29	32	26	solve	solve	VERB
cbi-29	32	27	trivial	trivial	ADJ
cbi-29	32	28	problems	problem	NOUN
cbi-29	32	29	that	that	PRON
cbi-29	32	30	they	they	PRON
cbi-29	32	31	could	could	AUX
cbi-29	32	32	solve	solve	VERB
cbi-29	32	33	using	use	VERB
cbi-29	32	34	the	the	DET
cbi-29	32	35	normal	normal	ADJ
cbi-29	32	36	rules	rule	NOUN
cbi-29	32	37	of	of	ADP
cbi-29	32	38	algebra	algebra	NOUN
cbi-29	32	39	.	.	PUNCT
cbi-29	33	1	therefore	therefore	ADV
cbi-29	33	2	,	,	PUNCT
cbi-29	33	3	they	they	PRON
cbi-29	33	4	start	start	VERB
cbi-29	33	5	to	to	PART
cbi-29	33	6	get	get	AUX
cbi-29	33	7	lost	lose	VERB
cbi-29	33	8	because	because	SCONJ
cbi-29	33	9	they	they	PRON
cbi-29	33	10	are	be	AUX
cbi-29	33	11	bombarded	bombard	VERB
cbi-29	33	12	with	with	ADP
cbi-29	33	13	extra	extra	ADJ
cbi-29	33	14	notation	notation	NOUN
cbi-29	33	15	for	for	ADP
cbi-29	33	16	nothing	nothing	PRON
cbi-29	33	17	.	.	PUNCT
cbi-29	34	1	they	they	PRON
cbi-29	34	2	ca	can	AUX
cbi-29	34	3	n’t	not	PART
cbi-29	34	4	grasp	grasp	VERB
cbi-29	34	5	at	at	ADP
cbi-29	34	6	what	what	PRON
cbi-29	34	7	this	this	PRON
cbi-29	34	8	could	could	AUX
cbi-29	34	9	possibly	possibly	ADV
cbi-29	34	10	be	be	AUX
cbi-29	34	11	for	for	ADP
cbi-29	34	12	,	,	PUNCT
cbi-29	34	13	and	and	CCONJ
cbi-29	34	14	are	be	AUX
cbi-29	34	15	lost	lose	VERB
cbi-29	34	16	before	before	SCONJ
cbi-29	34	17	they	they	PRON
cbi-29	34	18	ever	ever	ADV
cbi-29	34	19	really	really	ADV
cbi-29	34	20	start	start	VERB
cbi-29	34	21	.	.	PUNCT
cbi-29	35	1	at	at	ADP
cbi-29	35	2	minimum	minimum	NOUN
cbi-29	35	3	,	,	PUNCT
cbi-29	35	4	the	the	DET
cbi-29	35	5	concept	concept	NOUN
cbi-29	35	6	of	of	ADP
cbi-29	35	7	limits	limit	NOUN
cbi-29	35	8	should	should	AUX
cbi-29	35	9	be	be	AUX
cbi-29	35	10	introduced	introduce	VERB
cbi-29	35	11	to	to	PART
cbi-29	35	12	solve	solve	VERB
cbi-29	35	13	the	the	DET
cbi-29	35	14	problem	problem	NOUN
cbi-29	35	15	of	of	ADP
cbi-29	35	16	having	have	VERB
cbi-29	35	17	“	"	PUNCT
cbi-29	35	18	holes	hole	NOUN
cbi-29	35	19	”	"	PUNCT
cbi-29	35	20	in	in	ADP
cbi-29	35	21	a	a	DET
cbi-29	35	22	graph	graph	NOUN
cbi-29	35	23	rather	rather	ADV
cbi-29	35	24	than	than	ADP
cbi-29	35	25	for	for	ADP
cbi-29	35	26	expressions	expression	NOUN
cbi-29	35	27	that	that	PRON
cbi-29	35	28	are	be	AUX
cbi-29	35	29	easily	easily	ADV
cbi-29	35	30	calculated	calculate	VERB
cbi-29	35	31	without	without	ADP
cbi-29	35	32	limits	limit	NOUN
cbi-29	35	33	.	.	PUNCT
cbi-29	36	1	this	this	PRON
cbi-29	36	2	at	at	ADV
cbi-29	36	3	least	least	ADJ
cbi-29	36	4	provides	provide	VERB
cbi-29	36	5	a	a	DET
cbi-29	36	6	good	good	ADJ
cbi-29	36	7	context	context	NOUN
cbi-29	36	8	for	for	ADP
cbi-29	36	9	why	why	SCONJ
cbi-29	36	10	students	student	NOUN
cbi-29	36	11	should	should	AUX
cbi-29	36	12	bother	bother	VERB
cbi-29	36	13	with	with	ADP
cbi-29	36	14	them	they	PRON
cbi-29	36	15	.	.	PUNCT
cbi-29	37	1	in	in	ADP
cbi-29	37	2	my	my	PRON
cbi-29	37	3	own	own	ADJ
cbi-29	37	4	classes	class	NOUN
cbi-29	37	5	,	,	PUNCT
cbi-29	37	6	i	i	PRON
cbi-29	37	7	have	have	AUX
cbi-29	37	8	moved	move	VERB
cbi-29	37	9	limits	limit	NOUN
cbi-29	37	10	to	to	ADP
cbi-29	37	11	the	the	DET
cbi-29	37	12	end	end	NOUN
cbi-29	37	13	of	of	ADP
cbi-29	37	14	the	the	DET
cbi-29	37	15	course	course	NOUN
cbi-29	37	16	altogether	altogether	ADV
cbi-29	37	17	.	.	PUNCT
cbi-29	38	1	some	some	PRON
cbi-29	38	2	want	want	VERB
cbi-29	38	3	to	to	PART
cbi-29	38	4	introduce	introduce	VERB
cbi-29	38	5	limits	limit	NOUN
cbi-29	38	6	to	to	PART
cbi-29	38	7	establish	establish	VERB
cbi-29	38	8	a	a	DET
cbi-29	38	9	formal	formal	ADJ
cbi-29	38	10	definition	definition	NOUN
cbi-29	38	11	of	of	ADP
cbi-29	38	12	continuity	continuity	NOUN
cbi-29	38	13	.	.	PUNCT
cbi-29	39	1	however	however	ADV
cbi-29	39	2	,	,	PUNCT
cbi-29	39	3	it	it	PRON
cbi-29	39	4	is	be	AUX
cbi-29	39	5	much	much	ADV
cbi-29	39	6	more	more	ADV
cbi-29	39	7	straightforward	straightforward	ADJ
cbi-29	39	8	to	to	ADP
cbi-29	39	9	new	new	ADJ
cbi-29	39	10	students	student	NOUN
cbi-29	39	11	to	to	PART
cbi-29	39	12	introduce	introduce	VERB
cbi-29	39	13	continuity	continuity	NOUN
cbi-29	39	14	as	as	ADP
cbi-29	39	15	“	"	PUNCT
cbi-29	39	16	being	be	AUX
cbi-29	39	17	able	able	ADJ
cbi-29	39	18	to	to	PART
cbi-29	39	19	draw	draw	VERB
cbi-29	39	20	a	a	DET
cbi-29	39	21	graph	graph	NOUN
cbi-29	39	22	without	without	ADP
cbi-29	39	23	picking	pick	VERB
cbi-29	39	24	up	up	ADP
cbi-29	39	25	your	your	PRON
cbi-29	39	26	pencil	pencil	NOUN
cbi-29	39	27	”	"	PUNCT
cbi-29	39	28	than	than	SCONJ
cbi-29	39	29	to	to	PART
cbi-29	39	30	talk	talk	VERB
cbi-29	39	31	about	about	ADP
cbi-29	39	32	limits	limit	NOUN
cbi-29	39	33	.	.	PUNCT
cbi-29	40	1	students	student	NOUN
cbi-29	40	2	understand	understand	VERB
cbi-29	40	3	drawing	draw	VERB
cbi-29	40	4	without	without	ADP
cbi-29	40	5	picking	pick	VERB
cbi-29	40	6	up	up	ADP
cbi-29	40	7	your	your	PRON
cbi-29	40	8	pencil	pencil	NOUN
cbi-29	40	9	much	much	ADV
cbi-29	40	10	better	well	ADJ
cbi-29	40	11	than	than	ADP
cbi-29	40	12	limits	limit	NOUN
cbi-29	40	13	.	.	PUNCT
cbi-29	41	1	after	after	ADP
cbi-29	41	2	a	a	DET
cbi-29	41	3	whole	whole	ADJ
cbi-29	41	4	year	year	NOUN
cbi-29	41	5	of	of	ADP
cbi-29	41	6	talking	talk	VERB
cbi-29	41	7	about	about	ADP
cbi-29	41	8	continuity	continuity	NOUN
cbi-29	41	9	in	in	ADP
cbi-29	41	10	terms	term	NOUN
cbi-29	41	11	of	of	ADP
cbi-29	41	12	whether	whether	SCONJ
cbi-29	41	13	or	or	CCONJ
cbi-29	41	14	not	not	PART
cbi-29	41	15	you	you	PRON
cbi-29	41	16	pick	pick	VERB
cbi-29	41	17	up	up	ADP
cbi-29	41	18	your	your	PRON
cbi-29	41	19	pencil	pencil	NOUN
cbi-29	41	20	(	(	PUNCT
cbi-29	41	21	and	and	CCONJ
cbi-29	41	22	why	why	SCONJ
cbi-29	41	23	that	that	PRON
cbi-29	41	24	is	be	AUX
cbi-29	41	25	important	important	ADJ
cbi-29	41	26	to	to	PART
cbi-29	41	27	calculus	calculus	VERB
cbi-29	41	28	)	)	PUNCT
cbi-29	41	29	,	,	PUNCT
cbi-29	41	30	you	you	PRON
cbi-29	41	31	can	can	AUX
cbi-29	41	32	say	say	VERB
cbi-29	41	33	that	that	SCONJ
cbi-29	41	34	,	,	PUNCT
cbi-29	41	35	as	as	ADP
cbi-29	41	36	another	another	DET
cbi-29	41	37	benefit	benefit	NOUN
cbi-29	41	38	of	of	ADP
cbi-29	41	39	limits	limit	NOUN
cbi-29	41	40	,	,	PUNCT
cbi-29	41	41	we	we	PRON
cbi-29	41	42	get	get	VERB
cbi-29	41	43	a	a	DET
cbi-29	41	44	more	more	ADV
cbi-29	41	45	formal	formal	ADJ
cbi-29	41	46	definition	definition	NOUN
cbi-29	41	47	of	of	ADP
cbi-29	41	48	what	what	PRON
cbi-29	41	49	it	it	PRON
cbi-29	41	50	means	mean	VERB
cbi-29	41	51	to	to	PART
cbi-29	41	52	have	have	VERB
cbi-29	41	53	a	a	DET
cbi-29	41	54	continuous	continuous	ADJ
cbi-29	41	55	graph	graph	NOUN
cbi-29	41	56	.	.	PUNCT
cbi-29	42	1	thus	thus	ADV
cbi-29	42	2	,	,	PUNCT
cbi-29	42	3	the	the	DET
cbi-29	42	4	explicit	explicit	ADJ
cbi-29	42	5	justification	justification	NOUN
cbi-29	42	6	for	for	ADP
cbi-29	42	7	the	the	DET
cbi-29	42	8	derivative	derivative	ADJ
cbi-29	42	9	using	using	NOUN
cbi-29	42	10	limits	limit	NOUN
cbi-29	42	11	occurs	occur	VERB
cbi-29	42	12	long	long	ADV
cbi-29	42	13	after	after	SCONJ
cbi-29	42	14	the	the	DET
cbi-29	42	15	students	student	NOUN
cbi-29	42	16	learn	learn	VERB
cbi-29	42	17	the	the	DET
cbi-29	42	18	derivative	derivative	NOUN
cbi-29	42	19	and	and	CCONJ
cbi-29	42	20	learn	learn	VERB
cbi-29	42	21	to	to	PART
cbi-29	42	22	use	use	VERB
cbi-29	42	23	it	it	PRON
cbi-29	42	24	well	well	ADV
cbi-29	42	25	.	.	PUNCT
cbi-29	43	1	this	this	PRON
cbi-29	43	2	has	have	VERB
cbi-29	43	3	the	the	DET
cbi-29	43	4	additional	additional	ADJ
cbi-29	43	5	advantage	advantage	NOUN
cbi-29	43	6	of	of	ADP
cbi-29	43	7	including	include	VERB
cbi-29	43	8	l’hospital	l’hospital	PROPN
cbi-29	43	9	’s	’s	PART
cbi-29	43	10	rule	rule	NOUN
cbi-29	43	11	as	as	ADP
cbi-29	43	12	part	part	NOUN
cbi-29	43	13	of	of	ADP
cbi-29	43	14	the	the	DET
cbi-29	43	15	general	general	ADJ
cbi-29	43	16	discussion	discussion	NOUN
cbi-29	43	17	of	of	ADP
cbi-29	43	18	limit	limit	NOUN
cbi-29	43	19	behavior	behavior	NOUN
cbi-29	43	20	,	,	PUNCT
cbi-29	43	21	rather	rather	ADV
cbi-29	43	22	than	than	ADP
cbi-29	43	23	having	have	VERB
cbi-29	43	24	to	to	PART
cbi-29	43	25	revisit	revisit	VERB
cbi-29	43	26	limits	limit	NOUN
cbi-29	43	27	again	again	ADV
cbi-29	43	28	after	after	ADP
cbi-29	43	29	derivatives	derivative	NOUN
cbi-29	43	30	.	.	PUNCT
cbi-29	44	1	3	3	NUM
cbi-29	44	2	introducing	introduce	VERB
cbi-29	44	3	the	the	DET
cbi-29	44	4	derivative	derivative	NOUN
cbi-29	44	5	in	in	ADP
cbi-29	44	6	this	this	DET
cbi-29	44	7	method	method	NOUN
cbi-29	44	8	,	,	PUNCT
cbi-29	44	9	derivatives	derivative	NOUN
cbi-29	44	10	are	be	AUX
cbi-29	44	11	introduced	introduce	VERB
cbi-29	44	12	through	through	ADP
cbi-29	44	13	extensive	extensive	ADJ
cbi-29	44	14	practical	practical	ADJ
cbi-29	44	15	work	work	NOUN
cbi-29	44	16	on	on	ADP
cbi-29	44	17	evaluating	evaluate	VERB
cbi-29	44	18	slopes	slope	NOUN
cbi-29	44	19	between	between	ADP
cbi-29	44	20	two	two	NUM
cbi-29	44	21	points	point	NOUN
cbi-29	44	22	on	on	ADP
cbi-29	44	23	a	a	DET
cbi-29	44	24	graph	graph	NOUN
cbi-29	44	25	.	.	PUNCT
cbi-29	45	1	given	give	VERB
cbi-29	45	2	a	a	DET
cbi-29	45	3	graph	graph	NOUN
cbi-29	45	4	of	of	ADP
cbi-29	45	5	,	,	PUNCT
cbi-29	45	6	say	say	INTJ
cbi-29	45	7	,	,	PUNCT
cbi-29	45	8	y	y	PROPN
cbi-29	45	9	=	=	SYM
cbi-29	45	10	x2	x2	PROPN
cbi-29	45	11	,	,	PUNCT
cbi-29	45	12	what	what	PRON
cbi-29	45	13	is	be	AUX
cbi-29	45	14	the	the	DET
cbi-29	45	15	slope	slope	NOUN
cbi-29	45	16	between	between	ADP
cbi-29	45	17	the	the	DET
cbi-29	45	18	points	point	NOUN
cbi-29	45	19	x	x	PUNCT
cbi-29	45	20	=	=	SYM
cbi-29	45	21	1	1	NUM
cbi-29	45	22	and	and	CCONJ
cbi-29	45	23	x	x	SYM
cbi-29	45	24	=	=	SYM
cbi-29	45	25	2	2	X
cbi-29	45	26	?	?	SYM
cbi-29	45	27	basic	basic	ADJ
cbi-29	45	28	algebra	algebra	NOUN
cbi-29	45	29	is	be	AUX
cbi-29	45	30	used	use	VERB
cbi-29	45	31	to	to	PART
cbi-29	45	32	to	to	PART
cbi-29	45	33	find	find	VERB
cbi-29	45	34	the	the	DET
cbi-29	45	35	slope	slope	NOUN
cbi-29	45	36	from	from	ADP
cbi-29	45	37	two	two	NUM
cbi-29	45	38	points	point	NOUN
cbi-29	45	39	,	,	PUNCT
cbi-29	45	40	using	use	VERB
cbi-29	45	41	the	the	DET
cbi-29	45	42	standard	standard	ADJ
cbi-29	45	43	formula	formula	NOUN
cbi-29	45	44	m	m	NOUN
cbi-29	45	45	=	=	NOUN
cbi-29	45	46	y1	y1	NOUN
cbi-29	45	47	−	−	PROPN
cbi-29	45	48	y0	y0	NOUN
cbi-29	45	49	x1	x1	NOUN
cbi-29	46	1	−	−	NOUN
cbi-29	46	2	x0	x0	PROPN
cbi-29	46	3	.	.	PUNCT
cbi-29	47	1	next	next	ADV
cbi-29	47	2	,	,	PUNCT
cbi-29	47	3	we	we	PRON
cbi-29	47	4	discuss	discuss	VERB
cbi-29	47	5	what	what	PRON
cbi-29	47	6	it	it	PRON
cbi-29	47	7	means	mean	VERB
cbi-29	47	8	to	to	PART
cbi-29	47	9	find	find	VERB
cbi-29	47	10	the	the	DET
cbi-29	47	11	slope	slope	NOUN
cbi-29	47	12	at	at	ADP
cbi-29	47	13	a	a	DET
cbi-29	47	14	point	point	NOUN
cbi-29	47	15	.	.	PUNCT
cbi-29	48	1	we	we	PRON
cbi-29	48	2	talk	talk	VERB
cbi-29	48	3	about	about	ADP
cbi-29	48	4	the	the	DET
cbi-29	48	5	problems	problem	NOUN
cbi-29	48	6	of	of	ADP
cbi-29	48	7	finding	find	VERB
cbi-29	48	8	a	a	DET
cbi-29	48	9	slope	slope	NOUN
cbi-29	48	10	at	at	ADP
cbi-29	48	11	a	a	DET
cbi-29	48	12	single	single	ADJ
cbi-29	48	13	point	point	NOUN
cbi-29	48	14	(	(	PUNCT
cbi-29	48	15	the	the	DET
cbi-29	48	16	formula	formula	NOUN
cbi-29	48	17	we	we	PRON
cbi-29	48	18	have	have	AUX
cbi-29	48	19	reduces	reduce	VERB
cbi-29	48	20	to	to	ADP
cbi-29	48	21	0	0	NUM
cbi-29	48	22	0	0	NUM
cbi-29	48	23	)	)	PUNCT
cbi-29	48	24	,	,	PUNCT
cbi-29	48	25	and	and	CCONJ
cbi-29	48	26	then	then	ADV
cbi-29	48	27	discuss	discuss	VERB
cbi-29	48	28	methods	method	NOUN
cbi-29	48	29	of	of	ADP
cbi-29	48	30	getting	get	VERB
cbi-29	48	31	around	around	ADP
cbi-29	48	32	that	that	PRON
cbi-29	48	33	.	.	PUNCT
cbi-29	49	1	i	i	PRON
cbi-29	49	2	suggest	suggest	AUX
cbi-29	49	3	estimating	estimate	VERB
cbi-29	49	4	the	the	DET
cbi-29	49	5	slope	slope	NOUN
cbi-29	49	6	at	at	ADP
cbi-29	49	7	the	the	DET
cbi-29	49	8	point	point	NOUN
cbi-29	49	9	using	use	VERB
cbi-29	49	10	two	two	NUM
cbi-29	49	11	points	point	NOUN
cbi-29	49	12	that	that	PRON
cbi-29	49	13	are	be	AUX
cbi-29	49	14	close	close	ADJ
cbi-29	49	15	together	together	ADV
cbi-29	49	16	.	.	PUNCT
cbi-29	50	1	several	several	ADJ
cbi-29	50	2	problems	problem	NOUN
cbi-29	50	3	are	be	AUX
cbi-29	50	4	worked	work	VERB
cbi-29	50	5	for	for	ADP
cbi-29	50	6	getting	get	VERB
cbi-29	50	7	the	the	DET
cbi-29	50	8	distance	distance	NOUN
cbi-29	50	9	between	between	ADP
cbi-29	50	10	the	the	DET
cbi-29	50	11	two	two	NUM
cbi-29	50	12	x	x	PROPN
cbi-29	50	13	locations	location	NOUN
cbi-29	50	14	closer	close	ADJ
cbi-29	50	15	and	and	CCONJ
cbi-29	50	16	closer	close	ADJ
cbi-29	50	17	(	(	PUNCT
cbi-29	50	18	x	x	SYM
cbi-29	50	19	=	=	SYM
cbi-29	50	20	1	1	NUM
cbi-29	50	21	and	and	CCONJ
cbi-29	50	22	x	x	SYM
cbi-29	50	23	=	=	SYM
cbi-29	50	24	1.1	1.1	NUM
cbi-29	50	25	,	,	PUNCT
cbi-29	50	26	then	then	ADV
cbi-29	50	27	move	move	VERB
cbi-29	50	28	to	to	ADP
cbi-29	50	29	x	x	PUNCT
cbi-29	50	30	=	=	SYM
cbi-29	50	31	1	1	NUM
cbi-29	50	32	and	and	CCONJ
cbi-29	50	33	x	x	SYM
cbi-29	50	34	=	=	SYM
cbi-29	50	35	1.0001	1.0001	NUM
cbi-29	50	36	)	)	PUNCT
cbi-29	50	37	.	.	PUNCT
cbi-29	51	1	eventually	eventually	ADV
cbi-29	51	2	,	,	PUNCT
cbi-29	51	3	we	we	PRON
cbi-29	51	4	try	try	VERB
cbi-29	51	5	to	to	PART
cbi-29	51	6	make	make	VERB
cbi-29	51	7	a	a	DET
cbi-29	51	8	formula	formula	NOUN
cbi-29	51	9	that	that	PRON
cbi-29	51	10	expresses	express	VERB
cbi-29	51	11	the	the	DET
cbi-29	51	12	“	"	PUNCT
cbi-29	51	13	general	general	ADJ
cbi-29	51	14	idea	idea	NOUN
cbi-29	51	15	”	"	PUNCT
cbi-29	51	16	of	of	ADP
cbi-29	51	17	a	a	DET
cbi-29	51	18	slope	slope	NOUN
cbi-29	51	19	between	between	ADP
cbi-29	51	20	two	two	NUM
cbi-29	51	21	points	point	NOUN
cbi-29	51	22	on	on	ADP
cbi-29	51	23	a	a	DET
cbi-29	51	24	given	give	VERB
cbi-29	51	25	line	line	NOUN
cbi-29	51	26	.	.	PUNCT
cbi-29	52	1	if	if	SCONJ
cbi-29	52	2	we	we	PRON
cbi-29	52	3	are	be	AUX
cbi-29	52	4	looking	look	VERB
cbi-29	52	5	at	at	ADP
cbi-29	52	6	two	two	NUM
cbi-29	52	7	points	point	NOUN
cbi-29	52	8	where	where	SCONJ
cbi-29	52	9	the	the	DET
cbi-29	52	10	x	x	PROPN
cbi-29	52	11	values	value	NOUN
cbi-29	52	12	are	be	AUX
cbi-29	52	13	0.01	0.01	NUM
cbi-29	52	14	away	away	ADV
cbi-29	52	15	from	from	ADP
cbi-29	52	16	each	each	DET
cbi-29	52	17	other	other	ADJ
cbi-29	52	18	,	,	PUNCT
cbi-29	52	19	we	we	PRON
cbi-29	52	20	eventually	eventually	ADV
cbi-29	52	21	come	come	VERB
cbi-29	52	22	up	up	ADP
cbi-29	52	23	with	with	ADP
cbi-29	52	24	the	the	DET
cbi-29	52	25	formula	formula	NOUN
cbi-29	52	26	m	m	VERB
cbi-29	52	27	=	=	PUNCT
cbi-29	52	28	(	(	PUNCT
cbi-29	52	29	x+0.01)2−x2	x+0.01)2−x2	X
cbi-29	52	30	(	(	PUNCT
cbi-29	52	31	x+0.01)−x	x+0.01)−x	NOUN
cbi-29	52	32	to	to	PART
cbi-29	52	33	match	match	VERB
cbi-29	52	34	their	their	PRON
cbi-29	52	35	existing	exist	VERB
cbi-29	52	36	knowledge	knowledge	NOUN
cbi-29	52	37	of	of	ADP
cbi-29	52	38	the	the	DET
cbi-29	52	39	slope	slope	NOUN
cbi-29	52	40	formula	formula	NOUN
cbi-29	52	41	.	.	PUNCT
cbi-29	53	1	after	after	ADP
cbi-29	53	2	solving	solve	VERB
cbi-29	53	3	a	a	DET
cbi-29	53	4	few	few	ADJ
cbi-29	53	5	of	of	ADP
cbi-29	53	6	these	these	PRON
cbi-29	53	7	,	,	PUNCT
cbi-29	53	8	i	i	PRON
cbi-29	53	9	then	then	ADV
cbi-29	53	10	suggest	suggest	VERB
cbi-29	53	11	that	that	SCONJ
cbi-29	53	12	we	we	PRON
cbi-29	53	13	introduce	introduce	VERB
cbi-29	53	14	a	a	DET
cbi-29	53	15	parameter	parameter	NOUN
cbi-29	53	16	to	to	PART
cbi-29	53	17	represent	represent	VERB
cbi-29	53	18	the	the	DET
cbi-29	53	19	distance	distance	NOUN
cbi-29	53	20	.	.	PUNCT
cbi-29	54	1	this	this	DET
cbi-29	54	2	way	way	NOUN
cbi-29	54	3	,	,	PUNCT
cbi-29	54	4	we	we	PRON
cbi-29	54	5	can	can	AUX
cbi-29	54	6	decide	decide	VERB
cbi-29	54	7	later	later	ADV
cbi-29	54	8	how	how	SCONJ
cbi-29	54	9	close	close	ADV
cbi-29	54	10	we	we	PRON
cbi-29	54	11	want	want	VERB
cbi-29	54	12	the	the	DET
cbi-29	54	13	points	point	NOUN
cbi-29	54	14	to	to	PART
cbi-29	54	15	be	be	AUX
cbi-29	54	16	.	.	PUNCT
cbi-29	55	1	if	if	SCONJ
cbi-29	55	2	we	we	PRON
cbi-29	55	3	call	call	VERB
cbi-29	55	4	our	our	PRON
cbi-29	55	5	parameter	parameter	NOUN
cbi-29	55	6	h	h	NOUN
cbi-29	55	7	,	,	PUNCT
cbi-29	55	8	then	then	ADV
cbi-29	55	9	the	the	DET
cbi-29	55	10	formula	formula	NOUN
cbi-29	55	11	becomes	become	VERB
cbi-29	55	12	m	m	NOUN
cbi-29	55	13	=	=	PUNCT
cbi-29	55	14	(	(	PUNCT
cbi-29	55	15	x+h)2−x2	x+h)2−x2	X
cbi-29	55	16	(	(	PUNCT
cbi-29	55	17	x+h)−x	x+h)−x	PROPN
cbi-29	55	18	.	.	PUNCT
cbi-29	56	1	this	this	DET
cbi-29	56	2	simplifies	simplifie	NOUN
cbi-29	56	3	to	to	ADP
cbi-29	56	4	m	m	PROPN
cbi-29	56	5	=	=	SYM
cbi-29	56	6	2x	2x	NOUN
cbi-29	56	7	+	+	CCONJ
cbi-29	56	8	h.	h.	PROPN
cbi-29	57	1	so	so	ADV
cbi-29	57	2	,	,	PUNCT
cbi-29	57	3	to	to	PART
cbi-29	57	4	find	find	VERB
cbi-29	57	5	the	the	DET
cbi-29	57	6	slope	slope	NOUN
cbi-29	57	7	between	between	ADP
cbi-29	57	8	any	any	DET
cbi-29	57	9	two	two	NUM
cbi-29	57	10	points	point	NOUN
cbi-29	57	11	that	that	PRON
cbi-29	57	12	are	be	AUX
cbi-29	57	13	h	h	NOUN
cbi-29	57	14	=	=	NOUN
cbi-29	57	15	0.01	0.01	NUM
cbi-29	57	16	away	away	ADV
cbi-29	57	17	from	from	ADP
cbi-29	57	18	each	each	DET
cbi-29	57	19	other	other	ADJ
cbi-29	57	20	,	,	PUNCT
cbi-29	57	21	we	we	PRON
cbi-29	57	22	simply	simply	ADV
cbi-29	57	23	use	use	VERB
cbi-29	57	24	the	the	DET
cbi-29	57	25	formula	formula	NOUN
cbi-29	57	26	.	.	PUNCT
cbi-29	58	1	we	we	PRON
cbi-29	58	2	then	then	ADV
cbi-29	58	3	make	make	VERB
cbi-29	58	4	h	h	NOUN
cbi-29	58	5	smaller	small	ADJ
cbi-29	58	6	and	and	CCONJ
cbi-29	58	7	smaller	small	ADJ
cbi-29	58	8	and	and	CCONJ
cbi-29	58	9	smaller	small	ADJ
cbi-29	58	10	to	to	PART
cbi-29	58	11	get	get	VERB
cbi-29	58	12	a	a	DET
cbi-29	58	13	“	"	PUNCT
cbi-29	58	14	more	more	ADV
cbi-29	58	15	exact	exact	ADJ
cbi-29	58	16	”	"	PUNCT
cbi-29	58	17	value	value	NOUN
cbi-29	58	18	of	of	ADP
cbi-29	58	19	the	the	DET
cbi-29	58	20	slope	slope	NOUN
cbi-29	58	21	at	at	ADP
cbi-29	58	22	a	a	DET
cbi-29	58	23	point	point	NOUN
cbi-29	58	24	.	.	PUNCT
cbi-29	59	1	i	i	PRON
cbi-29	59	2	then	then	ADV
cbi-29	59	3	ask	ask	VERB
cbi-29	59	4	them	they	PRON
cbi-29	59	5	to	to	PART
cbi-29	59	6	think	think	VERB
cbi-29	59	7	about	about	ADP
cbi-29	59	8	if	if	SCONJ
cbi-29	59	9	there	there	PRON
cbi-29	59	10	is	be	VERB
cbi-29	59	11	any	any	DET
cbi-29	59	12	way	way	NOUN
cbi-29	59	13	to	to	PART
cbi-29	59	14	abuse	abuse	VERB
cbi-29	59	15	this	this	DET
cbi-29	59	16	formula	formula	NOUN
cbi-29	59	17	in	in	ADP
cbi-29	59	18	order	order	NOUN
cbi-29	59	19	to	to	PART
cbi-29	59	20	find	find	VERB
cbi-29	59	21	a	a	DET
cbi-29	59	22	formula	formula	NOUN
cbi-29	59	23	for	for	ADP
cbi-29	59	24	the	the	DET
cbi-29	59	25	slope	slope	NOUN
cbi-29	59	26	at	at	ADP
cbi-29	59	27	a	a	DET
cbi-29	59	28	single	single	ADJ
cbi-29	59	29	point	point	NOUN
cbi-29	59	30	.	.	PUNCT
cbi-29	60	1	at	at	ADP
cbi-29	60	2	this	this	DET
cbi-29	60	3	point	point	NOUN
cbi-29	60	4	,	,	PUNCT
cbi-29	60	5	students	student	NOUN
cbi-29	60	6	are	be	AUX
cbi-29	60	7	ready	ready	ADJ
cbi-29	60	8	to	to	PART
cbi-29	60	9	understand	understand	VERB
cbi-29	60	10	that	that	SCONJ
cbi-29	60	11	if	if	SCONJ
cbi-29	60	12	i	i	PRON
cbi-29	60	13	set	set	VERB
cbi-29	60	14	h	h	NOUN
cbi-29	60	15	to	to	ADP
cbi-29	60	16	0	0	NUM
cbi-29	60	17	that	that	SCONJ
cbi-29	60	18	the	the	DET
cbi-29	60	19	slope	slope	NOUN
cbi-29	60	20	is	be	AUX
cbi-29	60	21	equivalent	equivalent	ADJ
cbi-29	60	22	to	to	ADP
cbi-29	60	23	the	the	DET
cbi-29	60	24	slope	slope	NOUN
cbi-29	60	25	at	at	ADP
cbi-29	60	26	a	a	DET
cbi-29	60	27	particular	particular	ADJ
cbi-29	60	28	point	point	NOUN
cbi-29	60	29	.	.	PUNCT
cbi-29	61	1	i	i	PRON
cbi-29	61	2	then	then	ADV
cbi-29	61	3	generalize	generalize	VERB
cbi-29	61	4	this	this	PRON
cbi-29	61	5	with	with	ADP
cbi-29	61	6	functions	function	NOUN
cbi-29	61	7	,	,	PUNCT
cbi-29	61	8	using	use	VERB
cbi-29	61	9	f	f	PROPN
cbi-29	61	10	(	(	PUNCT
cbi-29	61	11	x	x	X
cbi-29	61	12	)	)	PUNCT
cbi-29	61	13	to	to	PART
cbi-29	61	14	represent	represent	VERB
cbi-29	61	15	the	the	DET
cbi-29	61	16	function	function	NOUN
cbi-29	61	17	we	we	PRON
cbi-29	61	18	want	want	VERB
cbi-29	61	19	the	the	DET
cbi-29	61	20	slope	slope	NOUN
cbi-29	61	21	of	of	ADP
cbi-29	61	22	,	,	PUNCT
cbi-29	61	23	and	and	CCONJ
cbi-29	61	24	show	show	VERB
cbi-29	61	25	that	that	SCONJ
cbi-29	61	26	basic	basic	ADJ
cbi-29	61	27	simplifications	simplification	NOUN
cbi-29	61	28	give	give	VERB
cbi-29	61	29	us	we	PRON
cbi-29	61	30	the	the	DET
cbi-29	61	31	formulat	formulat	NOUN
cbi-29	61	32	for	for	ADP
cbi-29	61	33	the	the	DET
cbi-29	61	34	derivative	derivative	NOUN
cbi-29	61	35	,	,	PUNCT
cbi-29	61	36	y′	y′	PUNCT
cbi-29	62	1	=	=	SYM
cbi-29	62	2	f	f	X
cbi-29	62	3	(	(	PUNCT
cbi-29	62	4	x	x	PROPN
cbi-29	62	5	+	+	NUM
cbi-29	62	6	h	h	NOUN
cbi-29	62	7	)	)	PUNCT
cbi-29	62	8	−	−	PROPN
cbi-29	62	9	f	f	PROPN
cbi-29	62	10	(	(	PUNCT
cbi-29	62	11	x	x	NOUN
cbi-29	62	12	)	)	PUNCT
cbi-29	62	13	h	h	NOUN
cbi-29	62	14	.	.	PUNCT
cbi-29	63	1	i	i	PRON
cbi-29	63	2	then	then	ADV
cbi-29	63	3	say	say	VERB
cbi-29	63	4	that	that	SCONJ
cbi-29	63	5	,	,	PUNCT
cbi-29	63	6	for	for	ADP
cbi-29	63	7	any	any	DET
cbi-29	63	8	particular	particular	ADJ
cbi-29	63	9	f	f	X
cbi-29	63	10	(	(	PUNCT
cbi-29	63	11	)	)	PUNCT
cbi-29	63	12	,	,	PUNCT
cbi-29	63	13	after	after	ADP
cbi-29	63	14	getting	getting	AUX
cbi-29	63	15	rid	rid	VERB
cbi-29	63	16	of	of	ADP
cbi-29	63	17	h	h	NOUN
cbi-29	63	18	in	in	ADP
cbi-29	63	19	the	the	DET
cbi-29	63	20	denominator	denominator	NOUN
cbi-29	63	21	through	through	ADP
cbi-29	63	22	simplification	simplification	NOUN
cbi-29	63	23	,	,	PUNCT
cbi-29	63	24	we	we	PRON
cbi-29	63	25	can	can	AUX
cbi-29	63	26	simply	simply	ADV
cbi-29	63	27	substitute	substitute	VERB
cbi-29	63	28	0	0	NUM
cbi-29	63	29	for	for	ADP
cbi-29	63	30	h	h	NOUN
cbi-29	63	31	in	in	ADP
cbi-29	63	32	the	the	DET
cbi-29	63	33	resulting	result	VERB
cbi-29	63	34	expression	expression	NOUN
cbi-29	63	35	.	.	PUNCT
cbi-29	64	1	i	i	PRON
cbi-29	64	2	do	do	AUX
cbi-29	64	3	mention	mention	VERB
cbi-29	64	4	that	that	SCONJ
cbi-29	64	5	h	h	NOUN
cbi-29	64	6	is	be	AUX
cbi-29	64	7	not	not	PART
cbi-29	64	8	really	really	ADV
cbi-29	64	9	zero	zero	NUM
cbi-29	64	10	,	,	PUNCT
cbi-29	64	11	but	but	CCONJ
cbi-29	64	12	in	in	ADP
cbi-29	64	13	fact	fact	NOUN
cbi-29	64	14	really	really	ADV
cbi-29	64	15	close	close	ADJ
cbi-29	64	16	to	to	ADP
cbi-29	64	17	it	it	PRON
cbi-29	64	18	.	.	PUNCT
cbi-29	65	1	nonetheless	nonetheless	ADV
cbi-29	65	2	,	,	PUNCT
cbi-29	65	3	i	i	PRON
cbi-29	65	4	tell	tell	VERB
cbi-29	65	5	them	they	PRON
cbi-29	65	6	that	that	SCONJ
cbi-29	65	7	the	the	DET
cbi-29	65	8	formal	formal	ADJ
cbi-29	65	9	justification	justification	NOUN
cbi-29	65	10	for	for	ADP
cbi-29	65	11	treating	treat	VERB
cbi-29	65	12	h	h	NOUN
cbi-29	65	13	as	as	SCONJ
cbi-29	65	14	zero	zero	NUM
cbi-29	65	15	will	will	AUX
cbi-29	65	16	come	come	VERB
cbi-29	65	17	later	later	ADV
cbi-29	65	18	in	in	ADP
cbi-29	65	19	the	the	DET
cbi-29	65	20	course	course	NOUN
cbi-29	65	21	,	,	PUNCT
cbi-29	65	22	and	and	CCONJ
cbi-29	65	23	that	that	SCONJ
cbi-29	65	24	for	for	ADP
cbi-29	65	25	now	now	ADV
cbi-29	65	26	they	they	PRON
cbi-29	65	27	should	should	AUX
cbi-29	65	28	treat	treat	VERB
cbi-29	65	29	it	it	PRON
cbi-29	65	30	as	as	ADP
cbi-29	65	31	a	a	DET
cbi-29	65	32	value	value	NOUN
cbi-29	65	33	that	that	PRON
cbi-29	65	34	is	be	AUX
cbi-29	65	35	sufficiently	sufficiently	ADV
cbi-29	65	36	close	close	ADJ
cbi-29	65	37	to	to	ADP
cbi-29	65	38	zero	zero	NUM
cbi-29	65	39	that	that	SCONJ
cbi-29	65	40	it	it	PRON
cbi-29	65	41	can	can	AUX
cbi-29	65	42	be	be	AUX
cbi-29	65	43	treated	treat	VERB
cbi-29	65	44	as	as	ADP
cbi-29	65	45	such	such	ADJ
cbi-29	65	46	,	,	PUNCT
cbi-29	65	47	but	but	CCONJ
cbi-29	65	48	sufficiently	sufficiently	ADV
cbi-29	65	49	far	far	ADV
cbi-29	65	50	away	away	ADV
cbi-29	65	51	from	from	ADP
cbi-29	65	52	zero	zero	NUM
cbi-29	65	53	that	that	SCONJ
cbi-29	65	54	it	it	PRON
cbi-29	65	55	does	do	AUX
cbi-29	65	56	n’t	not	PART
cbi-29	65	57	produce	produce	VERB
cbi-29	65	58	divide	divide	NOUN
cbi-29	65	59	-	-	PUNCT
cbi-29	65	60	by	by	ADP
cbi-29	65	61	-	-	PUNCT
cbi-29	65	62	zero	zero	NUM
cbi-29	65	63	errors	error	NOUN
cbi-29	65	64	.	.	PUNCT
cbi-29	66	1	doing	do	VERB
cbi-29	66	2	this	this	PRON
cbi-29	66	3	helps	help	VERB
cbi-29	66	4	students	student	NOUN
cbi-29	66	5	start	start	VERB
cbi-29	66	6	building	build	VERB
cbi-29	66	7	intuitions	intuition	NOUN
cbi-29	66	8	around	around	ADP
cbi-29	66	9	these	these	DET
cbi-29	66	10	types	type	NOUN
cbi-29	66	11	of	of	ADP
cbi-29	66	12	situations	situation	NOUN
cbi-29	66	13	,	,	PUNCT
cbi-29	66	14	which	which	PRON
cbi-29	66	15	will	will	AUX
cbi-29	66	16	help	help	VERB
cbi-29	66	17	us	we	PRON
cbi-29	66	18	refine	refine	VERB
cbi-29	66	19	them	they	PRON
cbi-29	66	20	in	in	ADP
cbi-29	66	21	our	our	PRON
cbi-29	66	22	formal	formal	ADJ
cbi-29	66	23	discussions	discussion	NOUN
cbi-29	66	24	of	of	ADP
cbi-29	66	25	limits	limit	NOUN
cbi-29	66	26	later	later	ADV
cbi-29	66	27	on	on	ADV
cbi-29	66	28	.	.	PUNCT
cbi-29	67	1	4	4	NUM
cbi-29	67	2	derivatives	derivative	NOUN
cbi-29	67	3	vs.	vs.	ADP
cbi-29	67	4	differentials	differential	NOUN
cbi-29	67	5	there	there	PRON
cbi-29	67	6	are	be	VERB
cbi-29	67	7	two	two	NUM
cbi-29	67	8	potential	potential	ADJ
cbi-29	67	9	operators	operator	NOUN
cbi-29	67	10	to	to	PART
cbi-29	67	11	use	use	VERB
cbi-29	67	12	for	for	ADP
cbi-29	67	13	teaching	teach	VERB
cbi-29	67	14	differential	differential	ADJ
cbi-29	67	15	calculus	calculus	NOUN
cbi-29	67	16	.	.	PUNCT
cbi-29	68	1	the	the	DET
cbi-29	68	2	first	first	ADJ
cbi-29	68	3	,	,	PUNCT
cbi-29	68	4	and	and	CCONJ
cbi-29	68	5	more	more	ADV
cbi-29	68	6	commonly	commonly	ADV
cbi-29	68	7	used	use	VERB
cbi-29	68	8	,	,	PUNCT
cbi-29	68	9	is	be	AUX
cbi-29	68	10	the	the	DET
cbi-29	68	11	derivative	derivative	ADJ
cbi-29	68	12	operator	operator	NOUN
cbi-29	68	13	,	,	PUNCT
cbi-29	68	14	which	which	PRON
cbi-29	68	15	can	can	AUX
cbi-29	68	16	be	be	AUX
cbi-29	68	17	written	write	VERB
cbi-29	68	18	as	as	ADP
cbi-29	68	19	dx	dx	PROPN
cbi-29	68	20	(	(	PUNCT
cbi-29	68	21	)	)	PUNCT
cbi-29	68	22	or	or	CCONJ
cbi-29	68	23	as	as	ADP
cbi-29	68	24	d	d	PROPN
cbi-29	68	25	dx	dx	PROPN
cbi-29	68	26	(	(	PUNCT
cbi-29	68	27	)	)	PUNCT
cbi-29	68	28	.	.	PUNCT
cbi-29	69	1	this	this	PRON
cbi-29	69	2	is	be	AUX
cbi-29	69	3	commonly	commonly	ADV
cbi-29	69	4	spoken	speak	VERB
cbi-29	69	5	of	of	ADP
cbi-29	69	6	as	as	ADP
cbi-29	69	7	“	"	PUNCT
cbi-29	69	8	taking	take	VERB
cbi-29	69	9	the	the	DET
cbi-29	69	10	derivative	derivative	NOUN
cbi-29	69	11	with	with	ADP
cbi-29	69	12	respect	respect	NOUN
cbi-29	69	13	to	to	ADP
cbi-29	69	14	x.	x.	NOUN
cbi-29	69	15	”	"	PUNCT
cbi-29	70	1	the	the	DET
cbi-29	70	2	problem	problem	NOUN
cbi-29	70	3	with	with	ADP
cbi-29	70	4	this	this	DET
cbi-29	70	5	operator	operator	NOUN
cbi-29	70	6	is	be	AUX
cbi-29	70	7	that	that	SCONJ
cbi-29	70	8	it	it	PRON
cbi-29	70	9	becomes	become	VERB
cbi-29	70	10	very	very	ADV
cbi-29	70	11	volume	volume	NOUN
cbi-29	70	12	1	1	NUM
cbi-29	70	13	,	,	PUNCT
cbi-29	70	14	issue	issue	VERB
cbi-29	70	15	1	1	NUM
cbi-29	70	16	4	4	NUM
cbi-29	70	17	.	.	PUNCT
cbi-29	70	18	derivatives	derivative	NOUN
cbi-29	70	19	vs.	vs.	ADP
cbi-29	70	20	differentials	differential	NOUN
cbi-29	70	21	19	19	NUM
cbi-29	70	22	confusing	confuse	VERB
cbi-29	70	23	for	for	ADP
cbi-29	70	24	students	student	NOUN
cbi-29	70	25	when	when	SCONJ
cbi-29	70	26	they	they	PRON
cbi-29	70	27	get	get	VERB
cbi-29	70	28	to	to	ADP
cbi-29	70	29	derivatives	derivative	NOUN
cbi-29	70	30	of	of	ADP
cbi-29	70	31	implicit	implicit	ADJ
cbi-29	70	32	functions	function	NOUN
cbi-29	70	33	.	.	PUNCT
cbi-29	71	1	the	the	DET
cbi-29	71	2	reason	reason	NOUN
cbi-29	71	3	for	for	ADP
cbi-29	71	4	this	this	PRON
cbi-29	71	5	is	be	AUX
cbi-29	71	6	that	that	SCONJ
cbi-29	71	7	,	,	PUNCT
cbi-29	71	8	when	when	SCONJ
cbi-29	71	9	applied	apply	VERB
cbi-29	71	10	to	to	ADP
cbi-29	71	11	implicit	implicit	ADJ
cbi-29	71	12	functions	function	NOUN
cbi-29	71	13	,	,	PUNCT
cbi-29	71	14	derivatives	derivative	NOUN
cbi-29	71	15	are	be	AUX
cbi-29	71	16	spitting	spit	VERB
cbi-29	71	17	out	out	ADP
cbi-29	71	18	other	other	ADJ
cbi-29	71	19	derivatives	derivative	NOUN
cbi-29	71	20	rather	rather	ADV
cbi-29	71	21	than	than	ADP
cbi-29	71	22	simple	simple	ADJ
cbi-29	71	23	answers	answer	NOUN
cbi-29	71	24	.	.	PUNCT
cbi-29	72	1	and	and	CCONJ
cbi-29	72	2	,	,	PUNCT
cbi-29	72	3	in	in	ADP
cbi-29	72	4	fact	fact	NOUN
cbi-29	72	5	,	,	PUNCT
cbi-29	72	6	it	it	PRON
cbi-29	72	7	does	do	VERB
cbi-29	72	8	this	this	PRON
cbi-29	72	9	for	for	ADP
cbi-29	72	10	some	some	DET
cbi-29	72	11	variables	variable	NOUN
cbi-29	72	12	and	and	CCONJ
cbi-29	72	13	not	not	PART
cbi-29	72	14	others	other	NOUN
cbi-29	72	15	.	.	PUNCT
cbi-29	73	1	for	for	ADP
cbi-29	73	2	instance	instance	NOUN
cbi-29	73	3	,	,	PUNCT
cbi-29	73	4	the	the	DET
cbi-29	73	5	derivative	derivative	NOUN
cbi-29	73	6	x	x	PUNCT
cbi-29	73	7	with	with	ADP
cbi-29	73	8	respect	respect	NOUN
cbi-29	73	9	to	to	ADP
cbi-29	73	10	x	x	SYM
cbi-29	73	11	is	be	AUX
cbi-29	73	12	1	1	NUM
cbi-29	73	13	,	,	PUNCT
cbi-29	73	14	but	but	CCONJ
cbi-29	73	15	the	the	DET
cbi-29	73	16	derivative	derivative	NOUN
cbi-29	73	17	of	of	ADP
cbi-29	73	18	y	y	PROPN
cbi-29	73	19	with	with	ADP
cbi-29	73	20	respect	respect	NOUN
cbi-29	73	21	to	to	ADP
cbi-29	73	22	x	x	SYM
cbi-29	73	23	is	be	AUX
cbi-29	73	24	dy	dy	X
cbi-29	73	25	dx	dx	PROPN
cbi-29	73	26	.	.	PUNCT
cbi-29	74	1	this	this	DET
cbi-29	74	2	assymetry	assymetry	NOUN
cbi-29	74	3	causes	cause	VERB
cbi-29	74	4	confusion	confusion	NOUN
cbi-29	74	5	.	.	PUNCT
cbi-29	75	1	while	while	SCONJ
cbi-29	75	2	the	the	DET
cbi-29	75	3	derivative	derivative	ADJ
cbi-29	75	4	operation	operation	NOUN
cbi-29	75	5	is	be	AUX
cbi-29	75	6	perfectly	perfectly	ADV
cbi-29	75	7	consistent	consistent	ADJ
cbi-29	75	8	and	and	CCONJ
cbi-29	75	9	solves	solve	VERB
cbi-29	75	10	the	the	DET
cbi-29	75	11	necessary	necessary	ADJ
cbi-29	75	12	problems	problem	NOUN
cbi-29	75	13	,	,	PUNCT
cbi-29	75	14	a	a	DET
cbi-29	75	15	much	much	ADV
cbi-29	75	16	clearer	clear	ADJ
cbi-29	75	17	way	way	NOUN
cbi-29	75	18	to	to	PART
cbi-29	75	19	teach	teach	VERB
cbi-29	75	20	students	student	NOUN
cbi-29	75	21	all	all	DET
cbi-29	75	22	types	type	NOUN
cbi-29	75	23	of	of	ADP
cbi-29	75	24	derivatives	derivative	NOUN
cbi-29	75	25	is	be	AUX
cbi-29	75	26	to	to	PART
cbi-29	75	27	instead	instead	ADV
cbi-29	75	28	focus	focus	VERB
cbi-29	75	29	on	on	ADP
cbi-29	75	30	the	the	DET
cbi-29	75	31	differential	differential	ADJ
cbi-29	75	32	operator	operator	NOUN
cbi-29	75	33	,	,	PUNCT
cbi-29	75	34	d	d	X
cbi-29	75	35	(	(	PUNCT
cbi-29	75	36	)	)	PUNCT
cbi-29	75	37	.	.	PUNCT
cbi-29	76	1	the	the	DET
cbi-29	76	2	differential	differential	ADJ
cbi-29	76	3	operator	operator	NOUN
cbi-29	76	4	is	be	AUX
cbi-29	76	5	similar	similar	ADJ
cbi-29	76	6	to	to	ADP
cbi-29	76	7	the	the	DET
cbi-29	76	8	derivative	derivative	NOUN
cbi-29	76	9	,	,	PUNCT
cbi-29	76	10	but	but	CCONJ
cbi-29	76	11	it	it	PRON
cbi-29	76	12	does	do	AUX
cbi-29	76	13	not	not	PART
cbi-29	76	14	treat	treat	VERB
cbi-29	76	15	any	any	DET
cbi-29	76	16	variable	variable	NOUN
cbi-29	76	17	specially	specially	ADV
cbi-29	76	18	.	.	PUNCT
cbi-29	77	1	there	there	PRON
cbi-29	77	2	is	be	VERB
cbi-29	77	3	no	no	DET
cbi-29	77	4	variable	variable	NOUN
cbi-29	77	5	that	that	SCONJ
cbi-29	77	6	the	the	DET
cbi-29	77	7	derivative	derivative	NOUN
cbi-29	77	8	is	be	AUX
cbi-29	77	9	being	be	AUX
cbi-29	77	10	taken	take	VERB
cbi-29	77	11	with	with	ADP
cbi-29	77	12	respect	respect	NOUN
cbi-29	77	13	to	to	ADP
cbi-29	77	14	.	.	PUNCT
cbi-29	78	1	instead	instead	ADV
cbi-29	78	2	,	,	PUNCT
cbi-29	78	3	whichever	whichever	DET
cbi-29	78	4	variable(s	variable(s	NOUN
cbi-29	78	5	)	)	PUNCT
cbi-29	78	6	are	be	AUX
cbi-29	78	7	in	in	ADP
cbi-29	78	8	the	the	DET
cbi-29	78	9	expression	expression	NOUN
cbi-29	78	10	always	always	ADV
cbi-29	78	11	comes	come	VERB
cbi-29	78	12	out	out	ADP
cbi-29	78	13	at	at	ADP
cbi-29	78	14	the	the	DET
cbi-29	78	15	end	end	NOUN
cbi-29	78	16	as	as	ADP
cbi-29	78	17	a	a	DET
cbi-29	78	18	differential	differential	NOUN
cbi-29	78	19	.	.	PUNCT
cbi-29	79	1	to	to	PART
cbi-29	79	2	understand	understand	VERB
cbi-29	79	3	the	the	DET
cbi-29	79	4	differences	difference	NOUN
cbi-29	79	5	,	,	PUNCT
cbi-29	79	6	we	we	PRON
cbi-29	79	7	will	will	AUX
cbi-29	79	8	apply	apply	VERB
cbi-29	79	9	the	the	DET
cbi-29	79	10	operators	operator	NOUN
cbi-29	79	11	to	to	ADP
cbi-29	79	12	both	both	CCONJ
cbi-29	79	13	an	an	DET
cbi-29	79	14	explicit	explicit	ADJ
cbi-29	79	15	and	and	CCONJ
cbi-29	79	16	an	an	DET
cbi-29	79	17	implicit	implicit	ADJ
cbi-29	79	18	function	function	NOUN
cbi-29	79	19	.	.	PUNCT
cbi-29	80	1	the	the	DET
cbi-29	80	2	explicit	explicit	ADJ
cbi-29	80	3	function	function	NOUN
cbi-29	80	4	will	will	AUX
cbi-29	80	5	be	be	AUX
cbi-29	80	6	y	y	NOUN
cbi-29	80	7	=	=	PUNCT
cbi-29	80	8	x3	x3	ADJ
cbi-29	80	9	and	and	CCONJ
cbi-29	80	10	the	the	DET
cbi-29	80	11	implicit	implicit	ADJ
cbi-29	80	12	function	function	NOUN
cbi-29	80	13	will	will	AUX
cbi-29	80	14	be	be	AUX
cbi-29	80	15	xy	xy	NOUN
cbi-29	80	16	=	=	NOUN
cbi-29	80	17	5	5	X
cbi-29	80	18	.	.	PUNCT
cbi-29	80	19	using	use	VERB
cbi-29	80	20	the	the	DET
cbi-29	80	21	d	d	PROPN
cbi-29	80	22	dx	dx	PROPN
cbi-29	80	23	(	(	PUNCT
cbi-29	80	24	)	)	PUNCT
cbi-29	80	25	operator	operator	NOUN
cbi-29	80	26	,	,	PUNCT
cbi-29	80	27	the	the	DET
cbi-29	80	28	explicit	explicit	ADJ
cbi-29	80	29	function	function	NOUN
cbi-29	80	30	is	be	AUX
cbi-29	80	31	straightforward	straightforward	ADJ
cbi-29	80	32	.	.	PUNCT
cbi-29	81	1	d	d	X
cbi-29	81	2	dx	dx	PROPN
cbi-29	81	3	(	(	PUNCT
cbi-29	81	4	y	y	NOUN
cbi-29	81	5	)	)	PUNCT
cbi-29	81	6	=	=	PUNCT
cbi-29	82	1	d	d	X
cbi-29	82	2	dx	dx	PROPN
cbi-29	82	3	(	(	PUNCT
cbi-29	82	4	x3	x3	PROPN
cbi-29	82	5	)	)	PUNCT
cbi-29	82	6	dy	dy	NOUN
cbi-29	82	7	dx	dx	PROPN
cbi-29	82	8	=	=	SYM
cbi-29	82	9	3x2	3x2	NUM
cbi-29	82	10	.	.	PUNCT
cbi-29	83	1	however	however	ADV
cbi-29	83	2	,	,	PUNCT
cbi-29	83	3	the	the	DET
cbi-29	83	4	implicit	implicit	ADJ
cbi-29	83	5	function	function	NOUN
cbi-29	83	6	is	be	AUX
cbi-29	83	7	unintuitive	unintuitive	ADJ
cbi-29	83	8	for	for	ADP
cbi-29	83	9	students	student	NOUN
cbi-29	83	10	.	.	PUNCT
cbi-29	84	1	d	d	X
cbi-29	84	2	dx	dx	PROPN
cbi-29	84	3	(	(	PUNCT
cbi-29	84	4	xy	xy	PROPN
cbi-29	84	5	)	)	PUNCT
cbi-29	84	6	=	=	SYM
cbi-29	84	7	5	5	NUM
cbi-29	84	8	x	x	SYM
cbi-29	84	9	dy	dy	X
cbi-29	84	10	dx	dx	PROPN
cbi-29	84	11	+	+	PROPN
cbi-29	84	12	y	y	PROPN
cbi-29	84	13	=	=	PUNCT
cbi-29	84	14	0	0	PROPN
cbi-29	85	1	the	the	DET
cbi-29	85	2	product	product	NOUN
cbi-29	85	3	rule	rule	NOUN
cbi-29	85	4	,	,	PUNCT
cbi-29	85	5	which	which	PRON
cbi-29	85	6	is	be	AUX
cbi-29	85	7	supposed	suppose	VERB
cbi-29	85	8	to	to	PART
cbi-29	85	9	have	have	VERB
cbi-29	85	10	some	some	DET
cbi-29	85	11	amount	amount	NOUN
cbi-29	85	12	of	of	ADP
cbi-29	85	13	symmetry	symmetry	NOUN
cbi-29	85	14	to	to	ADP
cbi-29	85	15	it	it	PRON
cbi-29	85	16	,	,	PUNCT
cbi-29	85	17	now	now	ADV
cbi-29	85	18	seems	seem	VERB
cbi-29	85	19	to	to	PART
cbi-29	85	20	have	have	VERB
cbi-29	85	21	no	no	DET
cbi-29	85	22	symmetry	symmetry	NOUN
cbi-29	85	23	whatsoever	whatsoever	ADV
cbi-29	85	24	.	.	PUNCT
cbi-29	86	1	however	however	ADV
cbi-29	86	2	,	,	PUNCT
cbi-29	86	3	when	when	SCONJ
cbi-29	86	4	taking	take	VERB
cbi-29	86	5	differentials	differential	NOUN
cbi-29	86	6	,	,	PUNCT
cbi-29	86	7	the	the	DET
cbi-29	86	8	operations	operation	NOUN
cbi-29	86	9	are	be	AUX
cbi-29	86	10	much	much	ADV
cbi-29	86	11	more	more	ADV
cbi-29	86	12	straightforward	straightforward	ADJ
cbi-29	86	13	.	.	PUNCT
cbi-29	87	1	first	first	ADV
cbi-29	87	2	,	,	PUNCT
cbi-29	87	3	the	the	DET
cbi-29	87	4	explicit	explicit	ADJ
cbi-29	87	5	function	function	NOUN
cbi-29	87	6	.	.	PUNCT
cbi-29	88	1	d(y	d(y	NOUN
cbi-29	88	2	)	)	PUNCT
cbi-29	88	3	=	=	PUNCT
cbi-29	88	4	d(x3	d(x3	NOUN
cbi-29	88	5	)	)	PUNCT
cbi-29	88	6	dy	dy	NOUN
cbi-29	88	7	=	=	SYM
cbi-29	88	8	3x2	3x2	NUM
cbi-29	88	9	dx	dx	PROPN
cbi-29	88	10	as	as	SCONJ
cbi-29	88	11	you	you	PRON
cbi-29	88	12	can	can	AUX
cbi-29	88	13	see	see	VERB
cbi-29	88	14	,	,	PUNCT
cbi-29	88	15	this	this	PRON
cbi-29	88	16	is	be	AUX
cbi-29	88	17	identical	identical	ADJ
cbi-29	88	18	to	to	ADP
cbi-29	88	19	the	the	DET
cbi-29	88	20	d	d	PROPN
cbi-29	88	21	dx	dx	PROPN
cbi-29	88	22	(	(	PUNCT
cbi-29	88	23	)	)	PUNCT
cbi-29	88	24	operation	operation	NOUN
cbi-29	88	25	except	except	SCONJ
cbi-29	88	26	that	that	SCONJ
cbi-29	88	27	the	the	DET
cbi-29	88	28	result	result	NOUN
cbi-29	88	29	is	be	AUX
cbi-29	88	30	not	not	PART
cbi-29	88	31	divided	divide	VERB
cbi-29	88	32	by	by	ADP
cbi-29	88	33	dx	dx	PROPN
cbi-29	88	34	.	.	PUNCT
cbi-29	89	1	this	this	PRON
cbi-29	89	2	localizes	localize	VERB
cbi-29	89	3	the	the	DET
cbi-29	89	4	differentials	differential	NOUN
cbi-29	89	5	to	to	ADP
cbi-29	89	6	the	the	DET
cbi-29	89	7	contexts	context	NOUN
cbi-29	89	8	where	where	SCONJ
cbi-29	89	9	they	they	PRON
cbi-29	89	10	occur	occur	VERB
cbi-29	89	11	.	.	PUNCT
cbi-29	90	1	as	as	SCONJ
cbi-29	90	2	we	we	PRON
cbi-29	90	3	will	will	AUX
cbi-29	90	4	see	see	VERB
cbi-29	90	5	shortly	shortly	ADV
cbi-29	90	6	,	,	PUNCT
cbi-29	90	7	this	this	PRON
cbi-29	90	8	simplifies	simplify	VERB
cbi-29	90	9	a	a	DET
cbi-29	90	10	lot	lot	NOUN
cbi-29	90	11	of	of	ADP
cbi-29	90	12	reasoning	reasoning	NOUN
cbi-29	90	13	about	about	ADP
cbi-29	90	14	complicated	complicated	ADJ
cbi-29	90	15	derivatives	derivative	NOUN
cbi-29	90	16	.	.	PUNCT
cbi-29	91	1	here	here	ADV
cbi-29	91	2	is	be	AUX
cbi-29	91	3	the	the	DET
cbi-29	91	4	differentiation	differentiation	NOUN
cbi-29	91	5	of	of	ADP
cbi-29	91	6	the	the	DET
cbi-29	91	7	implicit	implicit	ADJ
cbi-29	91	8	function	function	NOUN
cbi-29	91	9	.	.	PUNCT
cbi-29	92	1	d(xy	d(xy	NUM
cbi-29	92	2	)	)	PUNCT
cbi-29	92	3	=	=	SYM
cbi-29	92	4	d(5	d(5	PROPN
cbi-29	92	5	)	)	PUNCT
cbi-29	92	6	x	x	SYM
cbi-29	93	1	dy	dy	NOUN
cbi-29	94	1	+	+	CCONJ
cbi-29	94	2	y	y	PROPN
cbi-29	94	3	dx	dx	PROPN
cbi-29	95	1	=	=	SYM
cbi-29	95	2	0	0	PROPN
cbi-29	96	1	this	this	PRON
cbi-29	96	2	is	be	AUX
cbi-29	96	3	functionally	functionally	ADV
cbi-29	96	4	identical	identical	ADJ
cbi-29	96	5	to	to	ADP
cbi-29	96	6	the	the	DET
cbi-29	96	7	implicit	implicit	ADJ
cbi-29	96	8	derivative	derivative	NOUN
cbi-29	96	9	.	.	PUNCT
cbi-29	97	1	however	however	ADV
cbi-29	97	2	,	,	PUNCT
cbi-29	97	3	it	it	PRON
cbi-29	97	4	maintains	maintain	VERB
cbi-29	97	5	the	the	DET
cbi-29	97	6	symmetry	symmetry	NOUN
cbi-29	97	7	of	of	ADP
cbi-29	97	8	the	the	DET
cbi-29	97	9	product	product	NOUN
cbi-29	97	10	rule	rule	VERB
cbi-29	97	11	itself	itself	PRON
cbi-29	97	12	.	.	PUNCT
cbi-29	98	1	additionally	additionally	ADV
cbi-29	98	2	,	,	PUNCT
cbi-29	98	3	it	it	PRON
cbi-29	98	4	required	require	VERB
cbi-29	98	5	no	no	DET
cbi-29	98	6	extra	extra	ADJ
cbi-29	98	7	rules	rule	NOUN
cbi-29	98	8	for	for	ADP
cbi-29	98	9	the	the	DET
cbi-29	98	10	student	student	NOUN
cbi-29	98	11	for	for	ADP
cbi-29	98	12	the	the	DET
cbi-29	98	13	handling	handling	NOUN
cbi-29	98	14	of	of	ADP
cbi-29	98	15	y	y	PROPN
cbi-29	98	16	vs.	vs.	ADP
cbi-29	98	17	x.	x.	NOUN
cbi-29	98	18	they	they	PRON
cbi-29	98	19	are	be	AUX
cbi-29	98	20	both	both	PRON
cbi-29	98	21	treated	treat	VERB
cbi-29	98	22	identically	identically	ADV
cbi-29	98	23	in	in	ADP
cbi-29	98	24	the	the	DET
cbi-29	98	25	differentiation	differentiation	NOUN
cbi-29	98	26	step	step	NOUN
cbi-29	98	27	.	.	PUNCT
cbi-29	99	1	to	to	PART
cbi-29	99	2	convert	convert	VERB
cbi-29	99	3	the	the	DET
cbi-29	99	4	result	result	NOUN
cbi-29	99	5	of	of	ADP
cbi-29	99	6	differentiation	differentiation	NOUN
cbi-29	99	7	into	into	ADP
cbi-29	99	8	a	a	DET
cbi-29	99	9	derivative	derivative	NOUN
cbi-29	99	10	,	,	PUNCT
cbi-29	99	11	the	the	DET
cbi-29	99	12	student	student	NOUN
cbi-29	99	13	merely	merely	ADV
cbi-29	99	14	needs	need	VERB
cbi-29	99	15	to	to	PART
cbi-29	99	16	solve	solve	VERB
cbi-29	99	17	for	for	ADP
cbi-29	99	18	dy	dy	PROPN
cbi-29	99	19	dx	dx	PROPN
cbi-29	99	20	using	use	VERB
cbi-29	99	21	normal	normal	ADJ
cbi-29	99	22	algebra	algebra	NOUN
cbi-29	99	23	rules	rule	NOUN
cbi-29	99	24	.	.	PUNCT
cbi-29	100	1	therefore	therefore	ADV
cbi-29	100	2	,	,	PUNCT
cbi-29	100	3	all	all	DET
cbi-29	100	4	derivatives	derivative	NOUN
cbi-29	100	5	become	become	VERB
cbi-29	100	6	a	a	DET
cbi-29	100	7	two	two	NUM
cbi-29	100	8	-	-	PUNCT
cbi-29	100	9	step	step	NOUN
cbi-29	100	10	process	process	NOUN
cbi-29	100	11	:	:	PUNCT
cbi-29	100	12	1	1	X
cbi-29	100	13	.	.	X
cbi-29	100	14	find	find	VERB
cbi-29	100	15	the	the	DET
cbi-29	100	16	differential	differential	NOUN
cbi-29	100	17	of	of	ADP
cbi-29	100	18	the	the	DET
cbi-29	100	19	equation	equation	NOUN
cbi-29	100	20	.	.	PUNCT
cbi-29	101	1	2	2	X
cbi-29	101	2	.	.	X
cbi-29	101	3	solve	solve	VERB
cbi-29	101	4	for	for	ADP
cbi-29	101	5	the	the	DET
cbi-29	101	6	derivative	derivative	NOUN
cbi-29	101	7	you	you	PRON
cbi-29	101	8	are	be	AUX
cbi-29	101	9	interested	interested	ADJ
cbi-29	101	10	in	in	ADP
cbi-29	101	11	.	.	PUNCT
cbi-29	102	1	this	this	DET
cbi-29	102	2	way	way	NOUN
cbi-29	102	3	,	,	PUNCT
cbi-29	102	4	the	the	DET
cbi-29	102	5	process	process	NOUN
cbi-29	102	6	for	for	ADP
cbi-29	102	7	finding	find	VERB
cbi-29	102	8	dy	dy	NOUN
cbi-29	102	9	dx	dx	PROPN
cbi-29	102	10	is	be	AUX
cbi-29	102	11	the	the	DET
cbi-29	102	12	same	same	ADJ
cbi-29	102	13	as	as	ADP
cbi-29	102	14	for	for	ADP
cbi-29	102	15	finding	find	VERB
cbi-29	102	16	dx	dx	PROPN
cbi-29	102	17	dy	dy	NOUN
cbi-29	102	18	.	.	PUNCT
cbi-29	103	1	there	there	PRON
cbi-29	103	2	are	be	VERB
cbi-29	103	3	no	no	DET
cbi-29	103	4	funny	funny	ADJ
cbi-29	103	5	steps	step	NOUN
cbi-29	103	6	.	.	PUNCT
cbi-29	104	1	you	you	PRON
cbi-29	104	2	merely	merely	ADV
cbi-29	104	3	differentiate	differentiate	VERB
cbi-29	104	4	both	both	DET
cbi-29	104	5	sides	side	NOUN
cbi-29	104	6	and	and	CCONJ
cbi-29	104	7	then	then	ADV
cbi-29	104	8	solve	solve	VERB
cbi-29	104	9	for	for	ADP
cbi-29	104	10	the	the	DET
cbi-29	104	11	particular	particular	ADJ
cbi-29	104	12	derivative	derivative	NOUN
cbi-29	104	13	(	(	PUNCT
cbi-29	104	14	ratio	ratio	NOUN
cbi-29	104	15	of	of	ADP
cbi-29	104	16	differentials	differential	NOUN
cbi-29	104	17	)	)	PUNCT
cbi-29	104	18	that	that	PRON
cbi-29	104	19	you	you	PRON
cbi-29	104	20	want	want	VERB
cbi-29	104	21	.	.	PUNCT
cbi-29	105	1	it	it	PRON
cbi-29	105	2	does	do	AUX
cbi-29	105	3	not	not	PART
cbi-29	105	4	matter	matter	VERB
cbi-29	105	5	if	if	SCONJ
cbi-29	105	6	the	the	DET
cbi-29	105	7	equation	equation	NOUN
cbi-29	105	8	is	be	AUX
cbi-29	105	9	implicit	implicit	ADJ
cbi-29	105	10	,	,	PUNCT
cbi-29	105	11	explicit	explicit	ADJ
cbi-29	105	12	,	,	PUNCT
cbi-29	105	13	or	or	CCONJ
cbi-29	105	14	,	,	PUNCT
cbi-29	105	15	as	as	SCONJ
cbi-29	105	16	we	we	PRON
cbi-29	105	17	will	will	AUX
cbi-29	105	18	see	see	VERB
cbi-29	105	19	shortly	shortly	ADV
cbi-29	105	20	,	,	PUNCT
cbi-29	105	21	multivariate	multivariate	NOUN
cbi-29	105	22	,	,	PUNCT
cbi-29	105	23	the	the	DET
cbi-29	105	24	process	process	NOUN
cbi-29	105	25	is	be	AUX
cbi-29	105	26	identical	identical	ADJ
cbi-29	105	27	.	.	PUNCT
cbi-29	106	1	even	even	ADV
cbi-29	106	2	though	though	SCONJ
cbi-29	106	3	going	go	VERB
cbi-29	106	4	through	through	ADP
cbi-29	106	5	the	the	DET
cbi-29	106	6	differential	differential	NOUN
cbi-29	106	7	is	be	AUX
cbi-29	106	8	slightly	slightly	ADV
cbi-29	106	9	more	more	ADV
cbi-29	106	10	complicated	complicated	ADJ
cbi-29	106	11	for	for	ADP
cbi-29	106	12	simple	simple	ADJ
cbi-29	106	13	equations	equation	NOUN
cbi-29	106	14	,	,	PUNCT
cbi-29	106	15	overall	overall	ADV
cbi-29	106	16	i	i	PRON
cbi-29	106	17	have	have	AUX
cbi-29	106	18	found	find	VERB
cbi-29	106	19	that	that	SCONJ
cbi-29	106	20	students	student	NOUN
cbi-29	106	21	find	find	VERB
cbi-29	106	22	the	the	DET
cbi-29	106	23	separation	separation	NOUN
cbi-29	106	24	of	of	ADP
cbi-29	106	25	finding	find	VERB
cbi-29	106	26	differentials	differential	NOUN
cbi-29	106	27	and	and	CCONJ
cbi-29	106	28	then	then	ADV
cbi-29	106	29	finding	find	VERB
cbi-29	106	30	derivatives	derivative	NOUN
cbi-29	106	31	to	to	PART
cbi-29	106	32	be	be	AUX
cbi-29	106	33	much	much	ADV
cbi-29	106	34	easier	easy	ADJ
cbi-29	106	35	to	to	PART
cbi-29	106	36	process	process	VERB
cbi-29	106	37	over	over	ADP
cbi-29	106	38	a	a	DET
cbi-29	106	39	wider	wide	ADJ
cbi-29	106	40	variety	variety	NOUN
cbi-29	106	41	of	of	ADP
cbi-29	106	42	problems	problem	NOUN
cbi-29	106	43	.	.	PUNCT
cbi-29	107	1	interestingly	interestingly	ADV
cbi-29	107	2	,	,	PUNCT
cbi-29	107	3	this	this	PRON
cbi-29	107	4	is	be	AUX
cbi-29	107	5	the	the	DET
cbi-29	107	6	way	way	NOUN
cbi-29	107	7	the	the	DET
cbi-29	107	8	original	original	ADJ
cbi-29	107	9	leibnizian	leibnizian	ADJ
cbi-29	107	10	calculus	calculus	NOUN
cbi-29	107	11	was	be	AUX
cbi-29	107	12	developed	develop	VERB
cbi-29	107	13	.	.	PUNCT
cbi-29	108	1	the	the	DET
cbi-29	108	2	process	process	NOUN
cbi-29	108	3	focused	focus	VERB
cbi-29	108	4	on	on	ADP
cbi-29	108	5	differentials	differential	NOUN
cbi-29	108	6	rather	rather	ADV
cbi-29	108	7	than	than	ADP
cbi-29	108	8	derivatives	derivative	NOUN
cbi-29	108	9	,	,	PUNCT
cbi-29	108	10	and	and	CCONJ
cbi-29	108	11	did	do	AUX
cbi-29	108	12	not	not	PART
cbi-29	108	13	focus	focus	VERB
cbi-29	108	14	on	on	ADP
cbi-29	108	15	finding	find	VERB
cbi-29	108	16	ratios	ratio	NOUN
cbi-29	108	17	of	of	ADP
cbi-29	108	18	differentials	differential	NOUN
cbi-29	108	19	or	or	CCONJ
cbi-29	108	20	worrying	worry	VERB
cbi-29	108	21	about	about	ADP
cbi-29	108	22	identifying	identify	VERB
cbi-29	108	23	independent	independent	ADJ
cbi-29	108	24	variables	variable	NOUN
cbi-29	108	25	(	(	PUNCT
cbi-29	108	26	bos	bos	PROPN
cbi-29	108	27	,	,	PUNCT
cbi-29	108	28	1974	1974	NUM
cbi-29	108	29	)	)	PUNCT
cbi-29	108	30	.	.	PUNCT
cbi-29	109	1	as	as	SCONJ
cbi-29	109	2	mentioned	mention	VERB
cbi-29	109	3	in	in	ADP
cbi-29	109	4	section	section	NOUN
cbi-29	109	5	3	3	NUM
cbi-29	109	6	,	,	PUNCT
cbi-29	109	7	i	i	PRON
cbi-29	109	8	do	do	AUX
cbi-29	109	9	start	start	VERB
cbi-29	109	10	with	with	ADP
cbi-29	109	11	the	the	DET
cbi-29	109	12	traditional	traditional	ADJ
cbi-29	109	13	derivative	derivative	NOUN
cbi-29	109	14	,	,	PUNCT
cbi-29	109	15	as	as	SCONJ
cbi-29	109	16	it	it	PRON
cbi-29	109	17	is	be	AUX
cbi-29	109	18	much	much	ADV
cbi-29	109	19	more	more	ADV
cbi-29	109	20	concrete	concrete	ADJ
cbi-29	109	21	.	.	PUNCT
cbi-29	110	1	however	however	ADV
cbi-29	110	2	,	,	PUNCT
cbi-29	110	3	i	i	PRON
cbi-29	110	4	do	do	AUX
cbi-29	110	5	attempt	attempt	VERB
cbi-29	110	6	to	to	PART
cbi-29	110	7	pivot	pivot	VERB
cbi-29	110	8	very	very	ADV
cbi-29	110	9	quickly	quickly	ADV
cbi-29	110	10	from	from	ADP
cbi-29	110	11	derivatives	derivative	NOUN
cbi-29	110	12	to	to	ADP
cbi-29	110	13	differentials	differential	NOUN
cbi-29	110	14	.	.	PUNCT
cbi-29	111	1	another	another	DET
cbi-29	111	2	possible	possible	ADJ
cbi-29	111	3	mechanism	mechanism	NOUN
cbi-29	111	4	for	for	ADP
cbi-29	111	5	doing	do	VERB
cbi-29	111	6	this	this	PRON
cbi-29	111	7	was	be	AUX
cbi-29	111	8	pioneered	pioneer	VERB
cbi-29	111	9	by	by	ADP
cbi-29	111	10	thomson	thomson	PROPN
cbi-29	111	11	(	(	PUNCT
cbi-29	111	12	1910	1910	NUM
cbi-29	111	13	)	)	PUNCT
cbi-29	111	14	.	.	PUNCT
cbi-29	112	1	in	in	ADP
cbi-29	112	2	this	this	DET
cbi-29	112	3	method	method	NOUN
cbi-29	112	4	,	,	PUNCT
cbi-29	112	5	differentials	differential	NOUN
cbi-29	112	6	are	be	AUX
cbi-29	112	7	introduced	introduce	VERB
cbi-29	112	8	first	first	ADV
cbi-29	112	9	,	,	PUNCT
cbi-29	112	10	basically	basically	ADV
cbi-29	112	11	as	as	ADP
cbi-29	112	12	almost	almost	ADV
cbi-29	112	13	-	-	PUNCT
cbi-29	112	14	discrete	discrete	ADJ
cbi-29	112	15	differences	difference	NOUN
cbi-29	112	16	.	.	PUNCT
cbi-29	113	1	essentially	essentially	ADV
cbi-29	113	2	,	,	PUNCT
cbi-29	113	3	the	the	DET
cbi-29	113	4	question	question	NOUN
cbi-29	113	5	is	be	AUX
cbi-29	113	6	asked	ask	VERB
cbi-29	113	7	,	,	PUNCT
cbi-29	113	8	given	give	VERB
cbi-29	113	9	,	,	PUNCT
cbi-29	113	10	say	say	INTJ
cbi-29	113	11	,	,	PUNCT
cbi-29	113	12	y	y	PROPN
cbi-29	113	13	=	=	SYM
cbi-29	113	14	x2	x2	PROPN
cbi-29	113	15	,	,	PUNCT
cbi-29	113	16	if	if	SCONJ
cbi-29	113	17	i	i	PRON
cbi-29	113	18	added	add	VERB
cbi-29	113	19	a	a	DET
cbi-29	113	20	number	number	NOUN
cbi-29	113	21	named	name	VERB
cbi-29	113	22	dy	dy	NOUN
cbi-29	113	23	to	to	ADP
cbi-29	113	24	all	all	DET
cbi-29	113	25	the	the	DET
cbi-29	113	26	y	y	PROPN
cbi-29	113	27	variables	variable	NOUN
cbi-29	113	28	,	,	PUNCT
cbi-29	113	29	i	i	PRON
cbi-29	113	30	would	would	AUX
cbi-29	113	31	have	have	VERB
cbi-29	113	32	to	to	PART
cbi-29	113	33	compensate	compensate	VERB
cbi-29	113	34	by	by	ADP
cbi-29	113	35	adding	add	VERB
cbi-29	113	36	some	some	DET
cbi-29	113	37	other	other	ADJ
cbi-29	113	38	number	number	NOUN
cbi-29	113	39	dx	dx	PROPN
cbi-29	113	40	to	to	ADP
cbi-29	113	41	all	all	DET
cbi-29	113	42	the	the	DET
cbi-29	113	43	x	x	ADJ
cbi-29	113	44	variables	variable	NOUN
cbi-29	113	45	.	.	PUNCT
cbi-29	114	1	this	this	DET
cbi-29	114	2	possibility	possibility	NOUN
cbi-29	114	3	is	be	AUX
cbi-29	114	4	also	also	ADV
cbi-29	114	5	explored	explore	VERB
cbi-29	114	6	,	,	PUNCT
cbi-29	114	7	but	but	CCONJ
cbi-29	114	8	not	not	PART
cbi-29	114	9	very	very	ADV
cbi-29	114	10	fully	fully	ADV
cbi-29	114	11	,	,	PUNCT
cbi-29	114	12	by	by	ADP
cbi-29	114	13	dray	dray	NOUN
cbi-29	114	14	and	and	CCONJ
cbi-29	114	15	manogue	manogue	PROPN
cbi-29	114	16	(	(	PUNCT
cbi-29	114	17	2010	2010	NUM
cbi-29	114	18	)	)	PUNCT
cbi-29	114	19	.	.	PUNCT
cbi-29	115	1	future	future	ADJ
cbi-29	115	2	work	work	NOUN
cbi-29	115	3	may	may	AUX
cbi-29	115	4	entail	entail	VERB
cbi-29	115	5	discovering	discovering	NOUN
cbi-29	115	6	which	which	DET
cbi-29	115	7	approach	approach	NOUN
cbi-29	115	8	is	be	AUX
cbi-29	115	9	more	more	ADV
cbi-29	115	10	beneficial	beneficial	ADJ
cbi-29	115	11	to	to	ADP
cbi-29	115	12	students	student	NOUN
cbi-29	115	13	—	—	PUNCT
cbi-29	115	14	starting	start	VERB
cbi-29	115	15	with	with	ADP
cbi-29	115	16	slopes	slope	NOUN
cbi-29	115	17	as	as	ADP
cbi-29	115	18	a	a	DET
cbi-29	115	19	concrete	concrete	ADJ
cbi-29	115	20	tie	tie	NOUN
cbi-29	115	21	-	-	PUNCT
cbi-29	115	22	in	in	NOUN
cbi-29	115	23	to	to	ADP
cbi-29	115	24	algebra	algebra	NOUN
cbi-29	115	25	and	and	CCONJ
cbi-29	115	26	then	then	ADV
cbi-29	115	27	pivoting	pivot	VERB
cbi-29	115	28	to	to	ADP
cbi-29	115	29	differentials	differential	NOUN
cbi-29	115	30	,	,	PUNCT
cbi-29	115	31	or	or	CCONJ
cbi-29	115	32	starting	start	VERB
cbi-29	115	33	more	more	ADV
cbi-29	115	34	directly	directly	ADV
cbi-29	115	35	with	with	ADP
cbi-29	115	36	differentials	differential	NOUN
cbi-29	115	37	at	at	ADP
cbi-29	115	38	the	the	DET
cbi-29	115	39	very	very	ADJ
cbi-29	115	40	beginning	beginning	NOUN
cbi-29	115	41	.	.	PUNCT
cbi-29	116	1	20	20	NUM
cbi-29	116	2	simplifying	simplify	VERB
cbi-29	116	3	and	and	CCONJ
cbi-29	116	4	refactoring	refactoring	NOUN
cbi-29	116	5	introductory	introductory	ADJ
cbi-29	116	6	calculus	calculus	NOUN
cbi-29	116	7	5	5	NUM
cbi-29	116	8	treating	treat	VERB
cbi-29	116	9	differentials	differential	NOUN
cbi-29	116	10	algebraically	algebraically	ADV
cbi-29	116	11	because	because	SCONJ
cbi-29	116	12	we	we	PRON
cbi-29	116	13	are	be	AUX
cbi-29	116	14	solving	solve	VERB
cbi-29	116	15	for	for	ADP
cbi-29	116	16	the	the	DET
cbi-29	116	17	derivative	derivative	NOUN
cbi-29	116	18	instead	instead	ADV
cbi-29	116	19	of	of	ADP
cbi-29	116	20	calculating	calculate	VERB
cbi-29	116	21	it	it	PRON
cbi-29	116	22	directly	directly	ADV
cbi-29	116	23	,	,	PUNCT
cbi-29	116	24	we	we	PRON
cbi-29	116	25	must	must	AUX
cbi-29	116	26	be	be	AUX
cbi-29	116	27	willing	willing	ADJ
cbi-29	116	28	to	to	PART
cbi-29	116	29	treat	treat	VERB
cbi-29	116	30	differentials	differential	NOUN
cbi-29	116	31	algebraically	algebraically	ADV
cbi-29	116	32	.	.	PUNCT
cbi-29	117	1	although	although	SCONJ
cbi-29	117	2	in	in	ADP
cbi-29	117	3	the	the	DET
cbi-29	117	4	19th	19th	ADJ
cbi-29	117	5	century	century	NOUN
cbi-29	117	6	this	this	PRON
cbi-29	117	7	was	be	AUX
cbi-29	117	8	frowned	frown	VERB
cbi-29	117	9	upon	upon	SCONJ
cbi-29	117	10	,	,	PUNCT
cbi-29	117	11	developments	development	NOUN
cbi-29	117	12	in	in	ADP
cbi-29	117	13	the	the	DET
cbi-29	117	14	20th	20th	ADJ
cbi-29	117	15	century	century	NOUN
cbi-29	117	16	have	have	AUX
cbi-29	117	17	shown	show	VERB
cbi-29	117	18	that	that	SCONJ
cbi-29	117	19	differentials	differential	NOUN
cbi-29	117	20	can	can	AUX
cbi-29	117	21	be	be	AUX
cbi-29	117	22	thought	think	VERB
cbi-29	117	23	of	of	ADP
cbi-29	117	24	as	as	ADP
cbi-29	117	25	algebraic	algebraic	ADJ
cbi-29	117	26	units	unit	NOUN
cbi-29	117	27	.	.	PUNCT
cbi-29	118	1	abraham	abraham	PROPN
cbi-29	118	2	robinson	robinson	PROPN
cbi-29	118	3	’s	’s	PART
cbi-29	118	4	formal	formal	ADJ
cbi-29	118	5	description	description	NOUN
cbi-29	118	6	of	of	ADP
cbi-29	118	7	the	the	DET
cbi-29	118	8	hyperreals	hyperreal	NOUN
cbi-29	118	9	and	and	CCONJ
cbi-29	118	10	the	the	DET
cbi-29	118	11	introduction	introduction	NOUN
cbi-29	118	12	of	of	ADP
cbi-29	118	13	non	non	ADJ
cbi-29	118	14	-	-	ADJ
cbi-29	118	15	standard	standard	ADJ
cbi-29	118	16	analysis	analysis	NOUN
cbi-29	118	17	provides	provide	VERB
cbi-29	118	18	sufficient	sufficient	ADJ
cbi-29	118	19	justification	justification	NOUN
cbi-29	118	20	for	for	ADP
cbi-29	118	21	treating	treat	VERB
cbi-29	118	22	differentials	differential	NOUN
cbi-29	118	23	algebraically	algebraically	ADV
cbi-29	118	24	(	(	PUNCT
cbi-29	118	25	robinson	robinson	PROPN
cbi-29	118	26	,	,	PUNCT
cbi-29	118	27	1974	1974	NUM
cbi-29	118	28	;	;	PUNCT
cbi-29	118	29	henle	henle	PROPN
cbi-29	118	30	and	and	CCONJ
cbi-29	118	31	kleinberg	kleinberg	PROPN
cbi-29	118	32	,	,	PUNCT
cbi-29	118	33	2003	2003	NUM
cbi-29	118	34	;	;	PUNCT
cbi-29	118	35	keisler	keisler	NOUN
cbi-29	118	36	,	,	PUNCT
cbi-29	118	37	2012	2012	NUM
cbi-29	118	38	)	)	PUNCT
cbi-29	118	39	.	.	PUNCT
cbi-29	119	1	essentially	essentially	ADV
cbi-29	119	2	,	,	PUNCT
cbi-29	119	3	differentials	differential	NOUN
cbi-29	119	4	are	be	AUX
cbi-29	119	5	treated	treat	VERB
cbi-29	119	6	as	as	ADP
cbi-29	119	7	hyperreal	hyperreal	ADJ
cbi-29	119	8	values	value	NOUN
cbi-29	119	9	—	—	PUNCT
cbi-29	119	10	values	value	NOUN
cbi-29	119	11	which	which	PRON
cbi-29	119	12	exist	exist	VERB
cbi-29	119	13	on	on	ADP
cbi-29	119	14	the	the	DET
cbi-29	119	15	number	number	NOUN
cbi-29	119	16	line	line	NOUN
cbi-29	119	17	but	but	CCONJ
cbi-29	119	18	which	which	PRON
cbi-29	119	19	are	be	AUX
cbi-29	119	20	not	not	PART
cbi-29	119	21	contained	contain	VERB
cbi-29	119	22	by	by	ADP
cbi-29	119	23	the	the	DET
cbi-29	119	24	reals	real	NOUN
cbi-29	119	25	.	.	PUNCT
cbi-29	120	1	although	although	SCONJ
cbi-29	120	2	differentials	differential	NOUN
cbi-29	120	3	can	can	AUX
cbi-29	120	4	be	be	AUX
cbi-29	120	5	treated	treat	VERB
cbi-29	120	6	algebraically	algebraically	ADV
cbi-29	120	7	,	,	PUNCT
cbi-29	120	8	they	they	PRON
cbi-29	120	9	ca	can	AUX
cbi-29	120	10	n’t	not	PART
cbi-29	120	11	actually	actually	ADV
cbi-29	120	12	be	be	AUX
cbi-29	120	13	solved	solve	VERB
cbi-29	120	14	for	for	ADP
cbi-29	120	15	as	as	ADV
cbi-29	120	16	specific	specific	ADJ
cbi-29	120	17	numbers	number	NOUN
cbi-29	120	18	.	.	PUNCT
cbi-29	121	1	eventually	eventually	ADV
cbi-29	121	2	,	,	PUNCT
cbi-29	121	3	to	to	PART
cbi-29	121	4	get	get	VERB
cbi-29	121	5	a	a	DET
cbi-29	121	6	number	number	NOUN
cbi-29	121	7	that	that	PRON
cbi-29	121	8	can	can	AUX
cbi-29	121	9	be	be	AUX
cbi-29	121	10	evaluated	evaluate	VERB
cbi-29	121	11	or	or	CCONJ
cbi-29	121	12	calculated	calculate	VERB
cbi-29	121	13	,	,	PUNCT
cbi-29	121	14	the	the	DET
cbi-29	121	15	differentials	differential	NOUN
cbi-29	121	16	have	have	VERB
cbi-29	121	17	to	to	PART
cbi-29	121	18	be	be	AUX
cbi-29	121	19	in	in	ADP
cbi-29	121	20	ratio	ratio	NOUN
cbi-29	121	21	with	with	ADP
cbi-29	121	22	each	each	DET
cbi-29	121	23	other	other	ADJ
cbi-29	121	24	.	.	PUNCT
cbi-29	122	1	however	however	ADV
cbi-29	122	2	,	,	PUNCT
cbi-29	122	3	for	for	ADP
cbi-29	122	4	intermediate	intermediate	ADJ
cbi-29	122	5	steps	step	NOUN
cbi-29	122	6	,	,	PUNCT
cbi-29	122	7	there	there	PRON
cbi-29	122	8	is	be	VERB
cbi-29	122	9	no	no	DET
cbi-29	122	10	problem	problem	NOUN
cbi-29	122	11	with	with	ADP
cbi-29	122	12	treating	treat	VERB
cbi-29	122	13	differentials	differential	NOUN
cbi-29	122	14	such	such	ADJ
cbi-29	122	15	as	as	ADP
cbi-29	122	16	dx	dx	PROPN
cbi-29	122	17	and	and	CCONJ
cbi-29	122	18	dy	dy	VERB
cbi-29	122	19	exactly	exactly	ADV
cbi-29	122	20	as	as	SCONJ
cbi-29	122	21	you	you	PRON
cbi-29	122	22	would	would	AUX
cbi-29	122	23	the	the	DET
cbi-29	122	24	variables	variable	NOUN
cbi-29	122	25	x	x	PUNCT
cbi-29	122	26	and	and	CCONJ
cbi-29	122	27	y.	y.	NOUN
cbi-29	122	28	they	they	PRON
cbi-29	122	29	can	can	AUX
cbi-29	122	30	be	be	AUX
cbi-29	122	31	multiplied	multiply	VERB
cbi-29	122	32	,	,	PUNCT
cbi-29	122	33	divided	divide	VERB
cbi-29	122	34	,	,	PUNCT
cbi-29	122	35	cancelled	cancel	VERB
cbi-29	122	36	,	,	PUNCT
cbi-29	122	37	etc	etc	X
cbi-29	122	38	.	.	X
cbi-29	123	1	treating	treat	VERB
cbi-29	123	2	differentials	differential	NOUN
cbi-29	123	3	as	as	SCONJ
cbi-29	123	4	algebraic	algebraic	ADJ
cbi-29	123	5	units	unit	NOUN
cbi-29	123	6	is	be	AUX
cbi-29	123	7	very	very	ADV
cbi-29	123	8	intuitive	intuitive	ADJ
cbi-29	123	9	for	for	ADP
cbi-29	123	10	students	student	NOUN
cbi-29	123	11	who	who	PRON
cbi-29	123	12	have	have	AUX
cbi-29	123	13	studied	study	VERB
cbi-29	123	14	and	and	CCONJ
cbi-29	123	15	practiced	practice	VERB
cbi-29	123	16	the	the	DET
cbi-29	123	17	algebraic	algebraic	ADJ
cbi-29	123	18	treatment	treatment	NOUN
cbi-29	123	19	of	of	ADP
cbi-29	123	20	unknowns	unknown	NOUN
cbi-29	123	21	for	for	ADP
cbi-29	123	22	quite	quite	DET
cbi-29	123	23	some	some	DET
cbi-29	123	24	time	time	NOUN
cbi-29	123	25	.	.	PUNCT
cbi-29	124	1	additionally	additionally	ADV
cbi-29	124	2	,	,	PUNCT
cbi-29	124	3	the	the	DET
cbi-29	124	4	ability	ability	NOUN
cbi-29	124	5	to	to	PART
cbi-29	124	6	treat	treat	VERB
cbi-29	124	7	differentials	differential	NOUN
cbi-29	124	8	algebraically	algebraically	ADV
cbi-29	124	9	improves	improve	VERB
cbi-29	124	10	the	the	DET
cbi-29	124	11	comprehension	comprehension	NOUN
cbi-29	124	12	of	of	ADP
cbi-29	124	13	topics	topic	NOUN
cbi-29	124	14	such	such	ADJ
cbi-29	124	15	as	as	ADP
cbi-29	124	16	related	relate	VERB
cbi-29	124	17	rate	rate	NOUN
cbi-29	124	18	problems	problem	NOUN
cbi-29	124	19	.	.	PUNCT
cbi-29	125	1	in	in	ADP
cbi-29	125	2	related	relate	VERB
cbi-29	125	3	rate	rate	NOUN
cbi-29	125	4	problems	problem	NOUN
cbi-29	125	5	,	,	PUNCT
cbi-29	125	6	dt	dt	PUNCT
cbi-29	125	7	springs	spring	NOUN
cbi-29	125	8	up	up	ADP
cbi-29	125	9	as	as	ADV
cbi-29	125	10	if	if	SCONJ
cbi-29	125	11	from	from	ADP
cbi-29	125	12	nowhere	nowhere	ADV
cbi-29	125	13	.	.	PUNCT
cbi-29	126	1	books	book	NOUN
cbi-29	126	2	often	often	ADV
cbi-29	126	3	teach	teach	VERB
cbi-29	126	4	this	this	PRON
cbi-29	126	5	as	as	ADP
cbi-29	126	6	“	"	PUNCT
cbi-29	126	7	taking	take	VERB
cbi-29	126	8	the	the	DET
cbi-29	126	9	derivative	derivative	NOUN
cbi-29	126	10	with	with	ADP
cbi-29	126	11	respect	respect	NOUN
cbi-29	126	12	to	to	ADP
cbi-29	126	13	t	t	PROPN
cbi-29	126	14	,	,	PUNCT
cbi-29	126	15	”	"	PUNCT
cbi-29	126	16	but	but	CCONJ
cbi-29	126	17	this	this	PRON
cbi-29	126	18	is	be	AUX
cbi-29	126	19	confusing	confusing	ADJ
cbi-29	126	20	since	since	SCONJ
cbi-29	126	21	there	there	PRON
cbi-29	126	22	is	be	VERB
cbi-29	126	23	no	no	DET
cbi-29	126	24	t.	t.	NOUN
cbi-29	126	25	i	i	PRON
cbi-29	126	26	have	have	AUX
cbi-29	126	27	found	find	VERB
cbi-29	126	28	that	that	SCONJ
cbi-29	126	29	students	student	NOUN
cbi-29	126	30	are	be	AUX
cbi-29	126	31	much	much	ADV
cbi-29	126	32	less	less	ADV
cbi-29	126	33	confused	confuse	VERB
cbi-29	126	34	by	by	ADP
cbi-29	126	35	an	an	DET
cbi-29	126	36	algebraic	algebraic	ADJ
cbi-29	126	37	approach	approach	NOUN
cbi-29	126	38	.	.	PUNCT
cbi-29	127	1	we	we	PRON
cbi-29	127	2	simply	simply	ADV
cbi-29	127	3	take	take	VERB
cbi-29	127	4	the	the	DET
cbi-29	127	5	differential	differential	NOUN
cbi-29	127	6	the	the	DET
cbi-29	127	7	same	same	ADJ
cbi-29	127	8	way	way	NOUN
cbi-29	127	9	we	we	PRON
cbi-29	127	10	always	always	ADV
cbi-29	127	11	have	have	VERB
cbi-29	127	12	,	,	PUNCT
cbi-29	127	13	but	but	CCONJ
cbi-29	127	14	then	then	ADV
cbi-29	127	15	we	we	PRON
cbi-29	127	16	divide	divide	VERB
cbi-29	127	17	both	both	DET
cbi-29	127	18	sides	side	NOUN
cbi-29	127	19	of	of	ADP
cbi-29	127	20	the	the	DET
cbi-29	127	21	equation	equation	NOUN
cbi-29	127	22	by	by	ADP
cbi-29	127	23	dt	dt	PROPN
cbi-29	127	24	.	.	PUNCT
cbi-29	128	1	this	this	PRON
cbi-29	128	2	works	work	VERB
cbi-29	128	3	simply	simply	ADV
cbi-29	128	4	because	because	SCONJ
cbi-29	128	5	,	,	PUNCT
cbi-29	128	6	algebraically	algebraically	ADV
cbi-29	128	7	,	,	PUNCT
cbi-29	128	8	we	we	PRON
cbi-29	128	9	can	can	AUX
cbi-29	128	10	divide	divide	VERB
cbi-29	128	11	by	by	ADP
cbi-29	128	12	any	any	DET
cbi-29	128	13	value	value	NOUN
cbi-29	128	14	we	we	PRON
cbi-29	128	15	wish	wish	VERB
cbi-29	128	16	as	as	ADV
cbi-29	128	17	long	long	ADV
cbi-29	128	18	as	as	SCONJ
cbi-29	128	19	we	we	PRON
cbi-29	128	20	divide	divide	VERB
cbi-29	128	21	by	by	ADP
cbi-29	128	22	the	the	DET
cbi-29	128	23	same	same	ADJ
cbi-29	128	24	thing	thing	NOUN
cbi-29	128	25	on	on	ADP
cbi-29	128	26	both	both	DET
cbi-29	128	27	sides	side	NOUN
cbi-29	128	28	of	of	ADP
cbi-29	128	29	the	the	DET
cbi-29	128	30	equation	equation	NOUN
cbi-29	128	31	,	,	PUNCT
cbi-29	128	32	even	even	ADV
cbi-29	128	33	if	if	SCONJ
cbi-29	128	34	it	it	PRON
cbi-29	128	35	is	be	AUX
cbi-29	128	36	a	a	DET
cbi-29	128	37	new	new	ADJ
cbi-29	128	38	unknown	unknown	NOUN
cbi-29	128	39	.	.	PUNCT
cbi-29	129	1	again	again	ADV
cbi-29	129	2	,	,	PUNCT
cbi-29	129	3	by	by	ADP
cbi-29	129	4	using	use	VERB
cbi-29	129	5	differentials	differential	NOUN
cbi-29	129	6	instead	instead	ADV
cbi-29	129	7	of	of	ADP
cbi-29	129	8	derivatives	derivative	NOUN
cbi-29	129	9	,	,	PUNCT
cbi-29	129	10	we	we	PRON
cbi-29	129	11	have	have	AUX
cbi-29	129	12	transformed	transform	VERB
cbi-29	129	13	a	a	DET
cbi-29	129	14	number	number	NOUN
cbi-29	129	15	of	of	ADP
cbi-29	129	16	processes	process	NOUN
cbi-29	129	17	that	that	PRON
cbi-29	129	18	students	student	NOUN
cbi-29	129	19	find	find	VERB
cbi-29	129	20	unintuitive	unintuitive	ADJ
cbi-29	129	21	into	into	ADP
cbi-29	129	22	a	a	DET
cbi-29	129	23	single	single	ADJ
cbi-29	129	24	process	process	NOUN
cbi-29	129	25	where	where	SCONJ
cbi-29	129	26	the	the	DET
cbi-29	129	27	intuition	intuition	NOUN
cbi-29	129	28	is	be	AUX
cbi-29	129	29	supplied	supply	VERB
cbi-29	129	30	by	by	ADP
cbi-29	129	31	the	the	DET
cbi-29	129	32	student	student	NOUN
cbi-29	129	33	’s	’s	PART
cbi-29	129	34	knowledge	knowledge	NOUN
cbi-29	129	35	of	of	ADP
cbi-29	129	36	algebra	algebra	NOUN
cbi-29	129	37	.	.	PUNCT
cbi-29	130	1	6	6	NUM
cbi-29	130	2	multivariable	multivariable	ADJ
cbi-29	130	3	calculus	calculus	NOUN
cbi-29	130	4	this	this	DET
cbi-29	130	5	method	method	NOUN
cbi-29	130	6	of	of	ADP
cbi-29	130	7	using	use	VERB
cbi-29	130	8	differentials	differential	NOUN
cbi-29	130	9	instead	instead	ADV
cbi-29	130	10	of	of	ADP
cbi-29	130	11	derivatives	derivative	NOUN
cbi-29	130	12	also	also	ADV
cbi-29	130	13	simplifies	simplify	VERB
cbi-29	130	14	some	some	DET
cbi-29	130	15	aspects	aspect	NOUN
cbi-29	130	16	of	of	ADP
cbi-29	130	17	multivariable	multivariable	ADJ
cbi-29	130	18	calculus	calculus	NOUN
cbi-29	130	19	.	.	PUNCT
cbi-29	131	1	take	take	VERB
cbi-29	131	2	the	the	DET
cbi-29	131	3	equation	equation	NOUN
cbi-29	131	4	z2	z2	NOUN
cbi-29	131	5	=	=	PUNCT
cbi-29	132	1	xy	xy	PROPN
cbi-29	132	2	.	.	PUNCT
cbi-29	133	1	this	this	PRON
cbi-29	133	2	can	can	AUX
cbi-29	133	3	be	be	AUX
cbi-29	133	4	easily	easily	ADV
cbi-29	133	5	converted	convert	VERB
cbi-29	133	6	into	into	ADP
cbi-29	133	7	differentials	differential	NOUN
cbi-29	133	8	.	.	PUNCT
cbi-29	134	1	d(z2	d(z2	NOUN
cbi-29	134	2	)	)	PUNCT
cbi-29	134	3	=	=	SYM
cbi-29	135	1	d(xy	d(xy	NUM
cbi-29	135	2	)	)	PUNCT
cbi-29	135	3	2z	2z	NOUN
cbi-29	135	4	dz	dz	NOUN
cbi-29	135	5	=	=	PUNCT
cbi-29	135	6	x	x	PUNCT
cbi-29	135	7	dy	dy	NOUN
cbi-29	136	1	+	+	CCONJ
cbi-29	136	2	y	y	PROPN
cbi-29	136	3	dx	dx	PROPN
cbi-29	136	4	this	this	PRON
cbi-29	136	5	can	can	AUX
cbi-29	136	6	then	then	ADV
cbi-29	136	7	be	be	AUX
cbi-29	136	8	solved	solve	VERB
cbi-29	136	9	algebraically	algebraically	ADV
cbi-29	136	10	for	for	ADP
cbi-29	136	11	any	any	DET
cbi-29	136	12	derivative	derivative	NOUN
cbi-29	136	13	that	that	PRON
cbi-29	136	14	is	be	AUX
cbi-29	136	15	desired	desire	VERB
cbi-29	136	16	.	.	PUNCT
cbi-29	137	1	for	for	ADP
cbi-29	137	2	instance	instance	NOUN
cbi-29	137	3	,	,	PUNCT
cbi-29	137	4	dy	dy	PROPN
cbi-29	137	5	dz	dz	PROPN
cbi-29	137	6	can	can	AUX
cbi-29	137	7	be	be	AUX
cbi-29	137	8	found	find	VERB
cbi-29	137	9	.	.	PUNCT
cbi-29	138	1	2z	2z	NOUN
cbi-29	138	2	dz	dz	X
cbi-29	138	3	=	=	PUNCT
cbi-29	138	4	x	x	PUNCT
cbi-29	138	5	dy	dy	NOUN
cbi-29	139	1	+	+	CCONJ
cbi-29	139	2	y	y	PROPN
cbi-29	139	3	dx	dx	PROPN
cbi-29	139	4	2z	2z	PROPN
cbi-29	139	5	dz	dz	X
cbi-29	139	6	−	−	PROPN
cbi-29	140	1	y	y	PROPN
cbi-29	140	2	dx	dx	PROPN
cbi-29	141	1	=	=	PUNCT
cbi-29	142	1	x	x	X
cbi-29	143	1	dy	dy	NOUN
cbi-29	144	1	2z	2z	NUM
cbi-29	144	2	x	x	SYM
cbi-29	144	3	dz	dz	ADP
cbi-29	144	4	−	−	PROPN
cbi-29	144	5	y	y	PROPN
cbi-29	144	6	x	x	X
cbi-29	144	7	dx	dx	PROPN
cbi-29	144	8	=	=	PROPN
cbi-29	144	9	dy	dy	NOUN
cbi-29	144	10	2z	2z	NUM
cbi-29	144	11	x	x	PUNCT
cbi-29	144	12	−	−	NOUN
cbi-29	145	1	y	y	NOUN
cbi-29	145	2	x	x	PUNCT
cbi-29	145	3	dx	dx	PROPN
cbi-29	145	4	dz	dz	PROPN
cbi-29	145	5	=	=	PROPN
cbi-29	145	6	dy	dy	NOUN
cbi-29	145	7	dz	dz	X
cbi-29	145	8	what	what	PRON
cbi-29	145	9	this	this	PRON
cbi-29	145	10	means	mean	VERB
cbi-29	145	11	is	be	AUX
cbi-29	145	12	that	that	SCONJ
cbi-29	145	13	the	the	DET
cbi-29	145	14	rate	rate	NOUN
cbi-29	145	15	at	at	ADP
cbi-29	145	16	which	which	PRON
cbi-29	145	17	y	y	PROPN
cbi-29	145	18	changes	change	VERB
cbi-29	145	19	with	with	ADP
cbi-29	145	20	respect	respect	NOUN
cbi-29	145	21	to	to	ADP
cbi-29	145	22	z	z	NOUN
cbi-29	145	23	not	not	PART
cbi-29	145	24	only	only	ADV
cbi-29	145	25	depends	depend	VERB
cbi-29	145	26	on	on	ADP
cbi-29	145	27	the	the	DET
cbi-29	145	28	actual	actual	ADJ
cbi-29	145	29	values	value	NOUN
cbi-29	145	30	of	of	ADP
cbi-29	145	31	x	x	PROPN
cbi-29	145	32	,	,	PUNCT
cbi-29	145	33	y	y	PROPN
cbi-29	145	34	,	,	PUNCT
cbi-29	145	35	and	and	CCONJ
cbi-29	145	36	z	z	NOUN
cbi-29	145	37	,	,	PUNCT
cbi-29	145	38	but	but	CCONJ
cbi-29	145	39	that	that	SCONJ
cbi-29	145	40	it	it	PRON
cbi-29	145	41	also	also	ADV
cbi-29	145	42	depends	depend	VERB
cbi-29	145	43	on	on	ADP
cbi-29	145	44	the	the	DET
cbi-29	145	45	rate	rate	NOUN
cbi-29	145	46	at	at	ADP
cbi-29	145	47	which	which	PRON
cbi-29	145	48	x	x	PUNCT
cbi-29	145	49	changes	change	VERB
cbi-29	145	50	with	with	ADP
cbi-29	145	51	respect	respect	NOUN
cbi-29	145	52	to	to	ADP
cbi-29	145	53	z.	z.	PROPN
cbi-29	145	54	many	many	ADJ
cbi-29	145	55	calculus	calculus	NOUN
cbi-29	145	56	books	book	NOUN
cbi-29	145	57	skip	skip	VERB
cbi-29	145	58	over	over	ADP
cbi-29	145	59	this	this	DET
cbi-29	145	60	idea	idea	NOUN
cbi-29	145	61	,	,	PUNCT
cbi-29	145	62	probably	probably	ADV
cbi-29	145	63	because	because	SCONJ
cbi-29	145	64	when	when	SCONJ
cbi-29	145	65	differentials	differential	NOUN
cbi-29	145	66	are	be	AUX
cbi-29	145	67	not	not	PART
cbi-29	145	68	treated	treat	VERB
cbi-29	145	69	independently	independently	ADV
cbi-29	145	70	,	,	PUNCT
cbi-29	145	71	these	these	DET
cbi-29	145	72	processes	process	NOUN
cbi-29	145	73	are	be	AUX
cbi-29	145	74	very	very	ADV
cbi-29	145	75	complicated	complicated	ADJ
cbi-29	145	76	.	.	PUNCT
cbi-29	146	1	however	however	ADV
cbi-29	146	2	,	,	PUNCT
cbi-29	146	3	with	with	ADP
cbi-29	146	4	dealing	deal	VERB
cbi-29	146	5	with	with	ADP
cbi-29	146	6	differentials	differential	NOUN
cbi-29	146	7	instead	instead	ADV
cbi-29	146	8	of	of	ADP
cbi-29	146	9	derivatives	derivative	NOUN
cbi-29	146	10	,	,	PUNCT
cbi-29	146	11	these	these	DET
cbi-29	146	12	ideas	idea	NOUN
cbi-29	146	13	arise	arise	VERB
cbi-29	146	14	very	very	ADV
cbi-29	146	15	naturally	naturally	ADV
cbi-29	146	16	from	from	ADP
cbi-29	146	17	the	the	DET
cbi-29	146	18	notation	notation	NOUN
cbi-29	146	19	.	.	PUNCT
cbi-29	147	1	7	7	NUM
cbi-29	147	2	partial	partial	ADJ
cbi-29	147	3	derivatives	derivative	NOUN
cbi-29	147	4	/	/	SYM
cbi-29	147	5	differentials	differential	NOUN
cbi-29	147	6	this	this	DET
cbi-29	147	7	treatment	treatment	NOUN
cbi-29	147	8	of	of	ADP
cbi-29	147	9	differentials	differential	NOUN
cbi-29	147	10	also	also	ADV
cbi-29	147	11	leads	lead	VERB
cbi-29	147	12	to	to	ADP
cbi-29	147	13	a	a	DET
cbi-29	147	14	very	very	ADV
cbi-29	147	15	straightforward	straightforward	ADJ
cbi-29	147	16	way	way	NOUN
cbi-29	147	17	of	of	ADP
cbi-29	147	18	defining	define	VERB
cbi-29	147	19	partial	partial	ADJ
cbi-29	147	20	differentials	differential	NOUN
cbi-29	147	21	and	and	CCONJ
cbi-29	147	22	derivatives	derivative	NOUN
cbi-29	147	23	.	.	PUNCT
cbi-29	148	1	total	total	ADJ
cbi-29	148	2	derivatives	derivative	NOUN
cbi-29	148	3	define	define	VERB
cbi-29	148	4	the	the	DET
cbi-29	148	5	relationships	relationship	NOUN
cbi-29	148	6	between	between	ADP
cbi-29	148	7	changes	change	NOUN
cbi-29	148	8	in	in	ADP
cbi-29	148	9	all	all	DET
cbi-29	148	10	parts	part	NOUN
cbi-29	148	11	of	of	ADP
cbi-29	148	12	the	the	DET
cbi-29	148	13	system	system	NOUN
cbi-29	148	14	.	.	PUNCT
cbi-29	149	1	but	but	CCONJ
cbi-29	149	2	what	what	PRON
cbi-29	149	3	happens	happen	VERB
cbi-29	149	4	if	if	SCONJ
cbi-29	149	5	you	you	PRON
cbi-29	149	6	want	want	VERB
cbi-29	149	7	to	to	PART
cbi-29	149	8	hold	hold	VERB
cbi-29	149	9	some	some	DET
cbi-29	149	10	pieces	piece	NOUN
cbi-29	149	11	still	still	ADV
cbi-29	149	12	,	,	PUNCT
cbi-29	149	13	and	and	CCONJ
cbi-29	149	14	only	only	ADV
cbi-29	149	15	find	find	VERB
cbi-29	149	16	the	the	DET
cbi-29	149	17	way	way	NOUN
cbi-29	149	18	that	that	PRON
cbi-29	149	19	one	one	NUM
cbi-29	149	20	variable	variable	ADJ
cbi-29	149	21	influences	influence	VERB
cbi-29	149	22	another	another	PRON
cbi-29	149	23	when	when	SCONJ
cbi-29	149	24	treated	treat	VERB
cbi-29	149	25	by	by	ADP
cbi-29	149	26	itself	itself	PRON
cbi-29	149	27	?	?	PUNCT
cbi-29	150	1	in	in	ADP
cbi-29	150	2	order	order	NOUN
cbi-29	150	3	to	to	PART
cbi-29	150	4	do	do	AUX
cbi-29	150	5	that	that	PRON
cbi-29	150	6	,	,	PUNCT
cbi-29	150	7	we	we	PRON
cbi-29	150	8	would	would	AUX
cbi-29	150	9	say	say	VERB
cbi-29	150	10	that	that	SCONJ
cbi-29	150	11	the	the	DET
cbi-29	150	12	other	other	ADJ
cbi-29	150	13	variables	variable	NOUN
cbi-29	150	14	do	do	AUX
cbi-29	150	15	n’t	not	PART
cbi-29	150	16	change	change	VERB
cbi-29	150	17	.	.	PUNCT
cbi-29	151	1	another	another	DET
cbi-29	151	2	way	way	NOUN
cbi-29	151	3	of	of	ADP
cbi-29	151	4	saying	say	VERB
cbi-29	151	5	that	that	SCONJ
cbi-29	151	6	these	these	DET
cbi-29	151	7	variables	variable	NOUN
cbi-29	151	8	do	do	AUX
cbi-29	151	9	n’t	not	PART
cbi-29	151	10	change	change	VERB
cbi-29	151	11	is	be	AUX
cbi-29	151	12	to	to	PART
cbi-29	151	13	say	say	VERB
cbi-29	151	14	that	that	SCONJ
cbi-29	151	15	their	their	PRON
cbi-29	151	16	differentials	differential	NOUN
cbi-29	151	17	are	be	AUX
cbi-29	151	18	zero	zero	NUM
cbi-29	151	19	.	.	PUNCT
cbi-29	152	1	in	in	ADP
cbi-29	152	2	other	other	ADJ
cbi-29	152	3	words	word	NOUN
cbi-29	152	4	,	,	PUNCT
cbi-29	152	5	to	to	PART
cbi-29	152	6	convert	convert	VERB
cbi-29	152	7	from	from	ADP
cbi-29	152	8	a	a	DET
cbi-29	152	9	multivariable	multivariable	ADJ
cbi-29	152	10	differential	differential	NOUN
cbi-29	152	11	(	(	PUNCT
cbi-29	152	12	as	as	ADP
cbi-29	152	13	in	in	ADP
cbi-29	152	14	section	section	NOUN
cbi-29	152	15	6	6	NUM
cbi-29	152	16	)	)	PUNCT
cbi-29	152	17	to	to	ADP
cbi-29	152	18	a	a	DET
cbi-29	152	19	partial	partial	ADJ
cbi-29	152	20	differential	differential	NOUN
cbi-29	152	21	is	be	AUX
cbi-29	152	22	to	to	PART
cbi-29	152	23	merely	merely	ADV
cbi-29	152	24	set	set	VERB
cbi-29	152	25	the	the	DET
cbi-29	152	26	other	other	ADJ
cbi-29	152	27	differentials	differential	NOUN
cbi-29	152	28	which	which	PRON
cbi-29	152	29	are	be	AUX
cbi-29	152	30	n’t	not	PART
cbi-29	152	31	under	under	ADP
cbi-29	152	32	consideration	consideration	NOUN
cbi-29	152	33	to	to	ADP
cbi-29	152	34	zero	zero	NUM
cbi-29	152	35	.	.	PUNCT
cbi-29	153	1	for	for	ADP
cbi-29	153	2	instance	instance	NOUN
cbi-29	153	3	,	,	PUNCT
cbi-29	153	4	section	section	NOUN
cbi-29	153	5	6	6	NUM
cbi-29	153	6	ended	end	VERB
cbi-29	153	7	with	with	ADP
cbi-29	153	8	the	the	DET
cbi-29	153	9	equation	equation	NOUN
cbi-29	153	10	dy	dy	NOUN
cbi-29	154	1	dz	dz	NOUN
cbi-29	154	2	=	=	PUNCT
cbi-29	154	3	2z	2z	NOUN
cbi-29	154	4	x	x	PUNCT
cbi-29	154	5	−	−	PUNCT
cbi-29	155	1	y	y	NOUN
cbi-29	155	2	x	x	X
cbi-29	155	3	dx	dx	PROPN
cbi-29	155	4	dz	dz	PROPN
cbi-29	155	5	.	.	PUNCT
cbi-29	156	1	to	to	PART
cbi-29	156	2	understand	understand	VERB
cbi-29	156	3	the	the	DET
cbi-29	156	4	relationship	relationship	NOUN
cbi-29	156	5	between	between	ADP
cbi-29	156	6	the	the	DET
cbi-29	156	7	changes	change	NOUN
cbi-29	156	8	in	in	ADP
cbi-29	156	9	y	y	PROPN
cbi-29	156	10	and	and	CCONJ
cbi-29	156	11	z	z	PROPN
cbi-29	156	12	if	if	SCONJ
cbi-29	156	13	everything	everything	PRON
cbi-29	156	14	else	else	ADV
cbi-29	156	15	is	be	AUX
cbi-29	156	16	kept	keep	VERB
cbi-29	156	17	constant	constant	ADJ
cbi-29	156	18	,	,	PUNCT
cbi-29	156	19	we	we	PRON
cbi-29	156	20	merely	merely	ADV
cbi-29	156	21	need	need	VERB
cbi-29	156	22	to	to	PART
cbi-29	156	23	set	set	VERB
cbi-29	156	24	the	the	DET
cbi-29	156	25	differentials	differential	NOUN
cbi-29	156	26	of	of	ADP
cbi-29	156	27	everything	everything	PRON
cbi-29	156	28	else	else	ADV
cbi-29	156	29	(	(	PUNCT
cbi-29	156	30	dx	dx	PROPN
cbi-29	156	31	in	in	ADP
cbi-29	156	32	this	this	DET
cbi-29	156	33	case	case	NOUN
cbi-29	156	34	)	)	PUNCT
cbi-29	156	35	to	to	PART
cbi-29	156	36	volume	volume	VERB
cbi-29	156	37	1	1	NUM
cbi-29	156	38	,	,	PUNCT
cbi-29	156	39	issue	issue	NOUN
cbi-29	156	40	1	1	NUM
cbi-29	156	41	8	8	NUM
cbi-29	156	42	.	.	PUNCT
cbi-29	157	1	higher	high	ADJ
cbi-29	157	2	order	order	NOUN
cbi-29	157	3	differentials	differential	NOUN
cbi-29	157	4	and	and	CCONJ
cbi-29	157	5	derivatives	derivative	NOUN
cbi-29	157	6	21	21	NUM
cbi-29	157	7	zero	zero	NUM
cbi-29	157	8	.	.	PUNCT
cbi-29	158	1	doing	do	VERB
cbi-29	158	2	this	this	DET
cbi-29	158	3	results	result	NOUN
cbi-29	158	4	in	in	ADP
cbi-29	158	5	the	the	DET
cbi-29	158	6	equation	equation	NOUN
cbi-29	158	7	dy	dy	AUX
cbi-29	158	8	dz	dz	NOUN
cbi-29	158	9	=	=	PUNCT
cbi-29	158	10	2z	2z	NOUN
cbi-29	158	11	x	x	PUNCT
cbi-29	158	12	−	−	PUNCT
cbi-29	159	1	y	y	NOUN
cbi-29	159	2	x	x	PUNCT
cbi-29	159	3	dx	dx	PROPN
cbi-29	159	4	dz	dz	PROPN
cbi-29	159	5	∂y	∂y	X
cbi-29	159	6	∂z	∂z	PROPN
cbi-29	159	7	=	=	PUNCT
cbi-29	160	1	2z	2z	NOUN
cbi-29	160	2	x	x	PUNCT
cbi-29	161	1	−	−	PUNCT
cbi-29	161	2	y	y	NOUN
cbi-29	161	3	x	x	SYM
cbi-29	161	4	0	0	NUM
cbi-29	161	5	dz	dz	X
cbi-29	161	6	=	=	PUNCT
cbi-29	161	7	2z	2z	NUM
cbi-29	161	8	x	x	PUNCT
cbi-29	162	1	−	−	NOUN
cbi-29	162	2	0	0	NUM
cbi-29	163	1	=	=	SYM
cbi-29	163	2	2z	2z	NOUN
cbi-29	163	3	x	x	X
cbi-29	163	4	therefore	therefore	ADV
cbi-29	163	5	,	,	PUNCT
cbi-29	163	6	the	the	DET
cbi-29	163	7	partial	partial	ADJ
cbi-29	163	8	derivative	derivative	NOUN
cbi-29	163	9	of	of	ADP
cbi-29	163	10	y	y	PROPN
cbi-29	163	11	with	with	ADP
cbi-29	163	12	respect	respect	NOUN
cbi-29	163	13	to	to	ADP
cbi-29	163	14	z	z	PROPN
cbi-29	163	15	is	be	AUX
cbi-29	163	16	2z	2z	NUM
cbi-29	163	17	x	x	X
cbi-29	163	18	.	.	PUNCT
cbi-29	164	1	note	note	NOUN
cbi-29	164	2	,	,	PUNCT
cbi-29	164	3	however	however	ADV
cbi-29	164	4	,	,	PUNCT
cbi-29	164	5	that	that	SCONJ
cbi-29	164	6	partial	partial	ADJ
cbi-29	164	7	differentials	differential	NOUN
cbi-29	164	8	can	can	AUX
cbi-29	164	9	not	not	PART
cbi-29	164	10	always	always	ADV
cbi-29	164	11	be	be	AUX
cbi-29	164	12	treated	treat	VERB
cbi-29	164	13	algebraically	algebraically	ADV
cbi-29	164	14	.	.	PUNCT
cbi-29	165	1	this	this	PRON
cbi-29	165	2	is	be	AUX
cbi-29	165	3	not	not	PART
cbi-29	165	4	due	due	ADJ
cbi-29	165	5	to	to	ADP
cbi-29	165	6	a	a	DET
cbi-29	165	7	failing	failing	NOUN
cbi-29	165	8	of	of	ADP
cbi-29	165	9	the	the	DET
cbi-29	165	10	concept	concept	NOUN
cbi-29	165	11	of	of	ADP
cbi-29	165	12	partial	partial	ADJ
cbi-29	165	13	derivatives	derivative	NOUN
cbi-29	165	14	,	,	PUNCT
cbi-29	165	15	but	but	CCONJ
cbi-29	165	16	merely	merely	ADV
cbi-29	165	17	of	of	ADP
cbi-29	165	18	their	their	PRON
cbi-29	165	19	notation	notation	NOUN
cbi-29	165	20	.	.	PUNCT
cbi-29	166	1	for	for	ADP
cbi-29	166	2	our	our	PRON
cbi-29	166	3	original	original	ADJ
cbi-29	166	4	equation	equation	NOUN
cbi-29	166	5	,	,	PUNCT
cbi-29	166	6	∂y	∂y	PRON
cbi-29	166	7	can	can	AUX
cbi-29	166	8	refer	refer	VERB
cbi-29	166	9	to	to	ADP
cbi-29	166	10	two	two	NUM
cbi-29	166	11	different	different	ADJ
cbi-29	166	12	entities	entity	NOUN
cbi-29	166	13	in	in	ADP
cbi-29	166	14	the	the	DET
cbi-29	166	15	ratios	ratio	NOUN
cbi-29	166	16	∂y	∂y	X
cbi-29	166	17	∂z	∂z	PROPN
cbi-29	166	18	(	(	PUNCT
cbi-29	166	19	where	where	SCONJ
cbi-29	166	20	dx	dx	PROPN
cbi-29	166	21	=	=	NOUN
cbi-29	166	22	0	0	NUM
cbi-29	166	23	)	)	PUNCT
cbi-29	166	24	and	and	CCONJ
cbi-29	166	25	∂y	∂y	PROPN
cbi-29	166	26	∂x	∂x	PROPN
cbi-29	166	27	(	(	PUNCT
cbi-29	166	28	where	where	SCONJ
cbi-29	166	29	dy	dy	X
cbi-29	166	30	=	=	NOUN
cbi-29	166	31	0	0	NUM
cbi-29	166	32	)	)	PUNCT
cbi-29	166	33	.	.	PUNCT
cbi-29	167	1	information	information	NOUN
cbi-29	167	2	about	about	ADP
cbi-29	167	3	which	which	PRON
cbi-29	167	4	particular	particular	ADJ
cbi-29	167	5	∂y	∂y	NOUN
cbi-29	167	6	is	be	AUX
cbi-29	167	7	being	be	AUX
cbi-29	167	8	spoken	speak	VERB
cbi-29	167	9	about	about	ADP
cbi-29	167	10	is	be	AUX
cbi-29	167	11	contained	contain	VERB
cbi-29	167	12	in	in	ADP
cbi-29	167	13	the	the	DET
cbi-29	167	14	denominator	denominator	NOUN
cbi-29	167	15	,	,	PUNCT
cbi-29	167	16	and	and	CCONJ
cbi-29	167	17	therefore	therefore	ADV
cbi-29	167	18	splitting	split	VERB
cbi-29	167	19	the	the	DET
cbi-29	167	20	numerator	numerator	NOUN
cbi-29	167	21	from	from	ADP
cbi-29	167	22	the	the	DET
cbi-29	167	23	denominator	denominator	NOUN
cbi-29	167	24	results	result	NOUN
cbi-29	167	25	in	in	ADP
cbi-29	167	26	a	a	DET
cbi-29	167	27	loss	loss	NOUN
cbi-29	167	28	of	of	ADP
cbi-29	167	29	information.1	information.1	NUM
cbi-29	167	30	8	8	NUM
cbi-29	167	31	higher	high	ADJ
cbi-29	167	32	order	order	NOUN
cbi-29	167	33	differentials	differential	NOUN
cbi-29	167	34	and	and	CCONJ
cbi-29	167	35	derivatives	derivative	NOUN
cbi-29	167	36	performing	perform	VERB
cbi-29	167	37	derivatives	derivative	NOUN
cbi-29	167	38	by	by	ADP
cbi-29	167	39	taking	take	VERB
cbi-29	167	40	differentials	differential	NOUN
cbi-29	167	41	first	first	ADV
cbi-29	167	42	also	also	ADV
cbi-29	167	43	has	have	VERB
cbi-29	167	44	benefits	benefit	NOUN
cbi-29	167	45	down	down	ADP
cbi-29	167	46	the	the	DET
cbi-29	167	47	road	road	NOUN
cbi-29	167	48	,	,	PUNCT
cbi-29	167	49	as	as	SCONJ
cbi-29	167	50	it	it	PRON
cbi-29	167	51	allows	allow	VERB
cbi-29	167	52	students	student	NOUN
cbi-29	167	53	to	to	PART
cbi-29	167	54	understand	understand	VERB
cbi-29	167	55	other	other	ADJ
cbi-29	167	56	notations	notation	NOUN
cbi-29	167	57	more	more	ADV
cbi-29	167	58	fully	fully	ADV
cbi-29	167	59	.	.	PUNCT
cbi-29	168	1	the	the	DET
cbi-29	168	2	liebniz	liebniz	NOUN
cbi-29	168	3	notation	notation	NOUN
cbi-29	168	4	for	for	ADP
cbi-29	168	5	the	the	DET
cbi-29	168	6	second	second	ADJ
cbi-29	168	7	derivative	derivative	NOUN
cbi-29	168	8	!	!	PUNCT
cbi-29	169	1	d2y	d2y	PROPN
cbi-29	169	2	dx2	dx2	PROPN
cbi-29	169	3	"	"	PUNCT
cbi-29	169	4	has	have	AUX
cbi-29	169	5	long	long	ADV
cbi-29	169	6	baffled	baffle	VERB
cbi-29	169	7	many	many	ADJ
cbi-29	169	8	students	student	NOUN
cbi-29	169	9	.	.	PUNCT
cbi-29	170	1	most	most	ADJ
cbi-29	170	2	books	book	NOUN
cbi-29	170	3	take	take	VERB
cbi-29	170	4	a	a	DET
cbi-29	170	5	“	"	PUNCT
cbi-29	170	6	just	just	ADV
cbi-29	170	7	use	use	VERB
cbi-29	170	8	it	it	PRON
cbi-29	170	9	and	and	CCONJ
cbi-29	170	10	do	do	AUX
cbi-29	170	11	n’t	not	PART
cbi-29	170	12	ask	ask	VERB
cbi-29	170	13	questions	question	NOUN
cbi-29	170	14	”	"	PUNCT
cbi-29	170	15	approach.2	approach.2	ADP
cbi-29	170	16	however	however	ADV
cbi-29	170	17	,	,	PUNCT
cbi-29	170	18	recent	recent	ADJ
cbi-29	170	19	advances	advance	NOUN
cbi-29	170	20	have	have	AUX
cbi-29	170	21	shown	show	VERB
cbi-29	170	22	that	that	SCONJ
cbi-29	170	23	the	the	DET
cbi-29	170	24	standard	standard	ADJ
cbi-29	170	25	notation	notation	NOUN
cbi-29	170	26	for	for	ADP
cbi-29	170	27	higher	high	ADJ
cbi-29	170	28	-	-	PUNCT
cbi-29	170	29	order	order	NOUN
cbi-29	170	30	derivatives	derivative	NOUN
cbi-29	170	31	is	be	AUX
cbi-29	170	32	not	not	PART
cbi-29	170	33	only	only	ADV
cbi-29	170	34	baffling	baffling	ADJ
cbi-29	170	35	,	,	PUNCT
cbi-29	170	36	it	it	PRON
cbi-29	170	37	is	be	AUX
cbi-29	170	38	in	in	ADP
cbi-29	170	39	a	a	DET
cbi-29	170	40	very	very	ADV
cbi-29	170	41	real	real	ADJ
cbi-29	170	42	sense	sense	NOUN
cbi-29	170	43	incorrect	incorrect	ADJ
cbi-29	170	44	(	(	PUNCT
cbi-29	170	45	bartlett	bartlett	PROPN
cbi-29	170	46	and	and	CCONJ
cbi-29	170	47	khurshudyan	khurshudyan	PROPN
cbi-29	170	48	,	,	PUNCT
cbi-29	170	49	2018	2018	NUM
cbi-29	170	50	)	)	PUNCT
cbi-29	170	51	.	.	PUNCT
cbi-29	171	1	to	to	PART
cbi-29	171	2	understand	understand	VERB
cbi-29	171	3	the	the	DET
cbi-29	171	4	issues	issue	NOUN
cbi-29	171	5	,	,	PUNCT
cbi-29	171	6	first	first	ADV
cbi-29	171	7	recognize	recognize	VERB
cbi-29	171	8	that	that	SCONJ
cbi-29	171	9	differentials	differential	NOUN
cbi-29	171	10	are	be	AUX
cbi-29	171	11	actually	actually	ADV
cbi-29	171	12	a	a	DET
cbi-29	171	13	shorthand	shorthand	NOUN
cbi-29	171	14	.	.	PUNCT
cbi-29	172	1	when	when	SCONJ
cbi-29	172	2	you	you	PRON
cbi-29	172	3	take	take	VERB
cbi-29	172	4	the	the	DET
cbi-29	172	5	differential	differential	NOUN
cbi-29	172	6	of	of	ADP
cbi-29	172	7	a	a	DET
cbi-29	172	8	composite	composite	ADJ
cbi-29	172	9	function	function	NOUN
cbi-29	172	10	,	,	PUNCT
cbi-29	172	11	you	you	PRON
cbi-29	172	12	always	always	ADV
cbi-29	172	13	wind	wind	VERB
cbi-29	172	14	up	up	ADP
cbi-29	172	15	with	with	ADP
cbi-29	172	16	a	a	DET
cbi-29	172	17	differential	differential	NOUN
cbi-29	172	18	of	of	ADP
cbi-29	172	19	the	the	DET
cbi-29	172	20	inner	inner	ADJ
cbi-29	172	21	function	function	NOUN
cbi-29	172	22	.	.	PUNCT
cbi-29	173	1	for	for	ADP
cbi-29	173	2	instance	instance	NOUN
cbi-29	173	3	,	,	PUNCT
cbi-29	173	4	d(sin(x2	d(sin(x2	NOUN
cbi-29	173	5	)	)	PUNCT
cbi-29	173	6	)	)	PUNCT
cbi-29	173	7	=	=	SYM
cbi-29	173	8	cos(x2	cos(x2	NOUN
cbi-29	173	9	)	)	PUNCT
cbi-29	173	10	d(x2	d(x2	NOUN
cbi-29	173	11	)	)	PUNCT
cbi-29	173	12	=	=	SYM
cbi-29	173	13	cos(x2	cos(x2	NOUN
cbi-29	173	14	)	)	PUNCT
cbi-29	173	15	2x	2x	NUM
cbi-29	173	16	dx	dx	PROPN
cbi-29	173	17	.	.	PUNCT
cbi-29	173	18	1a	1a	PROPN
cbi-29	173	19	possible	possible	ADJ
cbi-29	173	20	solution	solution	NOUN
cbi-29	173	21	to	to	ADP
cbi-29	173	22	this	this	DET
cbi-29	173	23	problem	problem	NOUN
cbi-29	173	24	would	would	AUX
cbi-29	173	25	be	be	AUX
cbi-29	173	26	to	to	PART
cbi-29	173	27	subscript	subscript	VERB
cbi-29	173	28	partial	partial	ADJ
cbi-29	173	29	differentials	differential	NOUN
cbi-29	173	30	with	with	ADP
cbi-29	173	31	the	the	DET
cbi-29	173	32	list	list	NOUN
cbi-29	173	33	of	of	ADP
cbi-29	173	34	differentials	differential	NOUN
cbi-29	173	35	which	which	PRON
cbi-29	173	36	were	be	AUX
cbi-29	173	37	allowed	allow	VERB
cbi-29	173	38	to	to	PART
cbi-29	173	39	change	change	VERB
cbi-29	173	40	.	.	PUNCT
cbi-29	174	1	this	this	PRON
cbi-29	174	2	is	be	AUX
cbi-29	174	3	cumbersome	cumbersome	ADJ
cbi-29	174	4	,	,	PUNCT
cbi-29	174	5	but	but	CCONJ
cbi-29	174	6	allows	allow	VERB
cbi-29	174	7	for	for	ADP
cbi-29	174	8	an	an	DET
cbi-29	174	9	algebraic	algebraic	ADJ
cbi-29	174	10	treatment	treatment	NOUN
cbi-29	174	11	of	of	ADP
cbi-29	174	12	partial	partial	ADJ
cbi-29	174	13	differentials	differential	NOUN
cbi-29	174	14	.	.	PUNCT
cbi-29	175	1	so	so	ADV
cbi-29	175	2	,	,	PUNCT
cbi-29	175	3	for	for	ADP
cbi-29	175	4	instance	instance	NOUN
cbi-29	175	5	,	,	PUNCT
cbi-29	175	6	∂y	∂y	PROPN
cbi-29	175	7	∂z	∂z	PROPN
cbi-29	175	8	would	would	AUX
cbi-29	175	9	be	be	AUX
cbi-29	175	10	written	write	VERB
cbi-29	175	11	as	as	SCONJ
cbi-29	175	12	∂yz	∂yz	PROPN
cbi-29	175	13	y	y	PROPN
cbi-29	175	14	∂yz	∂yz	PROPN
cbi-29	175	15	z	z	PROPN
cbi-29	175	16	and	and	CCONJ
cbi-29	175	17	∂y	∂y	PROPN
cbi-29	175	18	∂x	∂x	PROPN
cbi-29	175	19	would	would	AUX
cbi-29	175	20	be	be	AUX
cbi-29	175	21	written	write	VERB
cbi-29	175	22	as	as	ADP
cbi-29	175	23	∂yx	∂yx	PROPN
cbi-29	175	24	y	y	PROPN
cbi-29	175	25	∂yx	∂yx	PROPN
cbi-29	175	26	x	x	X
cbi-29	175	27	.	.	PUNCT
cbi-29	176	1	doing	do	VERB
cbi-29	176	2	this	this	PRON
cbi-29	176	3	makes	make	VERB
cbi-29	176	4	it	it	PRON
cbi-29	176	5	clear	clear	ADJ
cbi-29	176	6	∂yz	∂yz	PROPN
cbi-29	176	7	y	y	PROPN
cbi-29	176	8	is	be	AUX
cbi-29	176	9	a	a	DET
cbi-29	176	10	distinct	distinct	ADJ
cbi-29	176	11	algebraic	algebraic	ADJ
cbi-29	176	12	entity	entity	NOUN
cbi-29	176	13	from	from	ADP
cbi-29	176	14	∂yx	∂yx	PROPN
cbi-29	176	15	y.	y.	NOUN
cbi-29	176	16	this	this	PRON
cbi-29	176	17	is	be	AUX
cbi-29	176	18	the	the	DET
cbi-29	176	19	subject	subject	NOUN
cbi-29	176	20	of	of	ADP
cbi-29	176	21	a	a	DET
cbi-29	176	22	current	current	ADJ
cbi-29	176	23	paper	paper	NOUN
cbi-29	176	24	in	in	ADP
cbi-29	176	25	progress	progress	NOUN
cbi-29	176	26	from	from	ADP
cbi-29	176	27	the	the	DET
cbi-29	176	28	present	present	ADJ
cbi-29	176	29	author	author	NOUN
cbi-29	176	30	.	.	PUNCT
cbi-29	177	1	2bartlett	2bartlett	NUM
cbi-29	177	2	and	and	CCONJ
cbi-29	177	3	khurshudyan	khurshudyan	PROPN
cbi-29	177	4	(	(	PUNCT
cbi-29	177	5	2018	2018	NUM
cbi-29	177	6	)	)	PUNCT
cbi-29	177	7	gives	give	VERB
cbi-29	177	8	several	several	ADJ
cbi-29	177	9	examples	example	NOUN
cbi-29	177	10	of	of	ADP
cbi-29	177	11	textbooks	textbook	NOUN
cbi-29	177	12	taking	take	VERB
cbi-29	177	13	this	this	DET
cbi-29	177	14	approach	approach	NOUN
cbi-29	177	15	.	.	PUNCT
cbi-29	178	1	however	however	ADV
cbi-29	178	2	,	,	PUNCT
cbi-29	178	3	the	the	DET
cbi-29	178	4	last	last	ADJ
cbi-29	178	5	term	term	NOUN
cbi-29	178	6	,	,	PUNCT
cbi-29	178	7	dx	dx	PROPN
cbi-29	178	8	,	,	PUNCT
cbi-29	178	9	stands	stand	VERB
cbi-29	178	10	in	in	ADP
cbi-29	178	11	the	the	DET
cbi-29	178	12	same	same	ADJ
cbi-29	178	13	relationship	relationship	NOUN
cbi-29	178	14	to	to	ADP
cbi-29	178	15	2x	2x	NUM
cbi-29	178	16	as	as	ADP
cbi-29	178	17	d(x2	d(x2	NOUN
cbi-29	178	18	)	)	PUNCT
cbi-29	178	19	does	do	VERB
cbi-29	178	20	to	to	PART
cbi-29	178	21	cos(x2	cos(x2	VERB
cbi-29	178	22	)	)	PUNCT
cbi-29	178	23	.	.	PUNCT
cbi-29	179	1	it	it	PRON
cbi-29	179	2	is	be	AUX
cbi-29	179	3	the	the	DET
cbi-29	179	4	differential	differential	NOUN
cbi-29	179	5	of	of	ADP
cbi-29	179	6	the	the	DET
cbi-29	179	7	interior	interior	ADJ
cbi-29	179	8	function	function	NOUN
cbi-29	179	9	.	.	PUNCT
cbi-29	180	1	therefore	therefore	ADV
cbi-29	180	2	,	,	PUNCT
cbi-29	180	3	dx	dx	PROPN
cbi-29	180	4	actually	actually	ADV
cbi-29	180	5	is	be	AUX
cbi-29	180	6	just	just	ADV
cbi-29	180	7	a	a	DET
cbi-29	180	8	shorthand	shorthand	NOUN
cbi-29	180	9	for	for	ADP
cbi-29	180	10	d(x	d(x	NOUN
cbi-29	180	11	)	)	PUNCT
cbi-29	180	12	.	.	PUNCT
cbi-29	181	1	since	since	SCONJ
cbi-29	181	2	it	it	PRON
cbi-29	181	3	is	be	AUX
cbi-29	181	4	irreducible	irreducible	ADJ
cbi-29	181	5	,	,	PUNCT
cbi-29	181	6	it	it	PRON
cbi-29	181	7	is	be	AUX
cbi-29	181	8	shortened	shorten	VERB
cbi-29	181	9	to	to	ADP
cbi-29	181	10	just	just	ADV
cbi-29	181	11	dx	dx	PROPN
cbi-29	181	12	.	.	PUNCT
cbi-29	182	1	this	this	DET
cbi-29	182	2	shortening	shortening	NOUN
cbi-29	182	3	happens	happen	VERB
cbi-29	182	4	both	both	PRON
cbi-29	182	5	to	to	PART
cbi-29	182	6	reduce	reduce	VERB
cbi-29	182	7	reading	reading	NOUN
cbi-29	182	8	and	and	CCONJ
cbi-29	182	9	writing	writing	NOUN
cbi-29	182	10	effort	effort	NOUN
cbi-29	182	11	,	,	PUNCT
cbi-29	182	12	and	and	CCONJ
cbi-29	182	13	also	also	ADV
cbi-29	182	14	to	to	PART
cbi-29	182	15	mark	mark	VERB
cbi-29	182	16	the	the	DET
cbi-29	182	17	fact	fact	NOUN
cbi-29	182	18	that	that	SCONJ
cbi-29	182	19	this	this	DET
cbi-29	182	20	differential	differential	NOUN
cbi-29	182	21	can	can	AUX
cbi-29	182	22	not	not	PART
cbi-29	182	23	be	be	AUX
cbi-29	182	24	further	far	ADV
cbi-29	182	25	reduced	reduce	VERB
cbi-29	182	26	.	.	PUNCT
cbi-29	183	1	nonetheless	nonetheless	ADV
cbi-29	183	2	,	,	PUNCT
cbi-29	183	3	dx	dx	PROPN
cbi-29	183	4	is	be	AUX
cbi-29	183	5	actually	actually	ADV
cbi-29	183	6	a	a	DET
cbi-29	183	7	composite	composite	NOUN
cbi-29	183	8	—	—	PUNCT
cbi-29	183	9	an	an	DET
cbi-29	183	10	operator	operator	NOUN
cbi-29	183	11	and	and	CCONJ
cbi-29	183	12	an	an	DET
cbi-29	183	13	operand.3	operand.3	NOUN
cbi-29	183	14	but	but	CCONJ
cbi-29	183	15	what	what	PRON
cbi-29	183	16	do	do	AUX
cbi-29	183	17	d2y	d2y	VERB
cbi-29	183	18	and	and	CCONJ
cbi-29	183	19	dx2	dx2	PROPN
cbi-29	183	20	mean	mean	VERB
cbi-29	183	21	?	?	PUNCT
cbi-29	184	1	the	the	DET
cbi-29	184	2	latter	latter	ADJ
cbi-29	184	3	is	be	AUX
cbi-29	184	4	straightforward	straightforward	ADJ
cbi-29	184	5	enough	enough	ADV
cbi-29	184	6	.	.	PUNCT
cbi-29	185	1	dx2	dx2	PROPN
cbi-29	185	2	is	be	AUX
cbi-29	185	3	simply	simply	ADV
cbi-29	185	4	a	a	DET
cbi-29	185	5	shorthand	shorthand	NOUN
cbi-29	185	6	for	for	ADP
cbi-29	185	7	(	(	PUNCT
cbi-29	185	8	d(x))2	d(x))2	PROPN
cbi-29	185	9	.	.	PUNCT
cbi-29	186	1	however	however	ADV
cbi-29	186	2	,	,	PUNCT
cbi-29	186	3	d2y	d2y	PROPN
cbi-29	186	4	(	(	PUNCT
cbi-29	186	5	with	with	ADP
cbi-29	186	6	the	the	DET
cbi-29	186	7	superscript	superscript	PROPN
cbi-29	186	8	after	after	ADP
cbi-29	186	9	the	the	DET
cbi-29	186	10	differential	differential	NOUN
cbi-29	186	11	operator	operator	NOUN
cbi-29	186	12	)	)	PUNCT
cbi-29	186	13	actually	actually	ADV
cbi-29	186	14	means	mean	VERB
cbi-29	186	15	applying	apply	VERB
cbi-29	186	16	the	the	DET
cbi-29	186	17	differential	differential	ADJ
cbi-29	186	18	operator	operator	NOUN
cbi-29	186	19	twice	twice	ADV
cbi-29	186	20	.	.	PUNCT
cbi-29	187	1	in	in	ADP
cbi-29	187	2	other	other	ADJ
cbi-29	187	3	words	word	NOUN
cbi-29	187	4	,	,	PUNCT
cbi-29	187	5	while	while	SCONJ
cbi-29	187	6	dy	dy	NOUN
cbi-29	187	7	is	be	AUX
cbi-29	187	8	short	short	ADJ
cbi-29	187	9	for	for	ADP
cbi-29	187	10	d(y	d(y	NOUN
cbi-29	187	11	)	)	PUNCT
cbi-29	187	12	,	,	PUNCT
cbi-29	187	13	d2y	d2y	PROPN
cbi-29	187	14	is	be	AUX
cbi-29	187	15	a	a	DET
cbi-29	187	16	shorthand	shorthand	NOUN
cbi-29	187	17	for	for	ADP
cbi-29	187	18	d(d(y	d(d(y	NOUN
cbi-29	187	19	)	)	PUNCT
cbi-29	187	20	)	)	PUNCT
cbi-29	187	21	.	.	PUNCT
cbi-29	188	1	to	to	PART
cbi-29	188	2	see	see	VERB
cbi-29	188	3	how	how	SCONJ
cbi-29	188	4	this	this	PRON
cbi-29	188	5	plays	play	VERB
cbi-29	188	6	out	out	ADP
cbi-29	188	7	,	,	PUNCT
cbi-29	188	8	imagine	imagine	VERB
cbi-29	188	9	the	the	DET
cbi-29	188	10	equation	equation	NOUN
cbi-29	188	11	y	y	PROPN
cbi-29	188	12	=	=	SYM
cbi-29	188	13	x3	x3	PROPN
cbi-29	188	14	.	.	PUNCT
cbi-29	189	1	(	(	PUNCT
cbi-29	189	2	1	1	X
cbi-29	189	3	)	)	PUNCT
cbi-29	189	4	let	let	VERB
cbi-29	189	5	’s	’s	PRON
cbi-29	189	6	start	start	VERB
cbi-29	189	7	by	by	ADP
cbi-29	189	8	taking	take	VERB
cbi-29	189	9	the	the	DET
cbi-29	189	10	differential	differential	NOUN
cbi-29	189	11	of	of	ADP
cbi-29	189	12	this	this	DET
cbi-29	189	13	equation	equation	NOUN
cbi-29	189	14	twice	twice	ADV
cbi-29	189	15	.	.	PUNCT
cbi-29	190	1	y	y	NOUN
cbi-29	190	2	=	=	PUNCT
cbi-29	190	3	x3	x3	PROPN
cbi-29	190	4	d(y	d(y	NOUN
cbi-29	190	5	)	)	PUNCT
cbi-29	191	1	=	=	PUNCT
cbi-29	191	2	d(x3	d(x3	NOUN
cbi-29	191	3	)	)	PUNCT
cbi-29	191	4	dy	dy	NOUN
cbi-29	191	5	=	=	SYM
cbi-29	191	6	3x2	3x2	NUM
cbi-29	191	7	dx	dx	PROPN
cbi-29	191	8	first	first	PROPN
cbi-29	191	9	differential	differential	PROPN
cbi-29	191	10	d(dy	d(dy	PROPN
cbi-29	191	11	)	)	PUNCT
cbi-29	192	1	=	=	PUNCT
cbi-29	192	2	d(3x2	d(3x2	NUM
cbi-29	192	3	dx	dx	PROPN
cbi-29	192	4	)	)	PUNCT
cbi-29	192	5	d2y	d2y	PROPN
cbi-29	193	1	=	=	SYM
cbi-29	193	2	3x2	3x2	NUM
cbi-29	194	1	d2x	d2x	NOUN
cbi-29	194	2	+	+	CCONJ
cbi-29	194	3	6x	6x	PROPN
cbi-29	194	4	dx2	dx2	PROPN
cbi-29	194	5	second	second	ADJ
cbi-29	194	6	differential	differential	NOUN
cbi-29	194	7	(	(	PUNCT
cbi-29	194	8	2	2	X
cbi-29	194	9	)	)	PUNCT
cbi-29	194	10	this	this	DET
cbi-29	194	11	result	result	NOUN
cbi-29	194	12	may	may	AUX
cbi-29	194	13	seem	seem	VERB
cbi-29	194	14	surprising	surprising	ADJ
cbi-29	194	15	,	,	PUNCT
cbi-29	194	16	but	but	CCONJ
cbi-29	194	17	allow	allow	VERB
cbi-29	194	18	for	for	ADP
cbi-29	194	19	an	an	DET
cbi-29	194	20	explanation	explanation	NOUN
cbi-29	194	21	.	.	PUNCT
cbi-29	195	1	the	the	DET
cbi-29	195	2	term	term	NOUN
cbi-29	195	3	3x2	3x2	NUM
cbi-29	195	4	d2x	d2x	PROPN
cbi-29	195	5	seems	seem	VERB
cbi-29	195	6	like	like	SCONJ
cbi-29	195	7	it	it	PRON
cbi-29	195	8	is	be	AUX
cbi-29	195	9	out	out	ADP
cbi-29	195	10	of	of	ADP
cbi-29	195	11	place	place	NOUN
cbi-29	195	12	,	,	PUNCT
cbi-29	195	13	but	but	CCONJ
cbi-29	195	14	it	it	PRON
cbi-29	195	15	is	be	AUX
cbi-29	195	16	not	not	PART
cbi-29	195	17	.	.	PUNCT
cbi-29	196	1	since	since	SCONJ
cbi-29	196	2	3x2	3x2	NUM
cbi-29	196	3	dx	dx	PROPN
cbi-29	196	4	is	be	AUX
cbi-29	196	5	the	the	DET
cbi-29	196	6	product	product	NOUN
cbi-29	196	7	of	of	ADP
cbi-29	196	8	3x2	3x2	NUM
cbi-29	196	9	and	and	CCONJ
cbi-29	196	10	dx	dx	PROPN
cbi-29	196	11	,	,	PUNCT
cbi-29	196	12	the	the	DET
cbi-29	196	13	product	product	NOUN
cbi-29	196	14	rule	rule	NOUN
cbi-29	196	15	has	have	VERB
cbi-29	196	16	to	to	PART
cbi-29	196	17	be	be	AUX
cbi-29	196	18	used	use	VERB
cbi-29	196	19	to	to	PART
cbi-29	196	20	resolve	resolve	VERB
cbi-29	196	21	the	the	DET
cbi-29	196	22	next	next	ADJ
cbi-29	196	23	differential	differential	NOUN
cbi-29	196	24	.	.	PUNCT
cbi-29	197	1	therefore	therefore	ADV
cbi-29	197	2	,	,	PUNCT
cbi-29	197	3	since	since	SCONJ
cbi-29	197	4	d(uv	d(uv	NOUN
cbi-29	197	5	)	)	PUNCT
cbi-29	198	1	=	=	SYM
cbi-29	198	2	u	u	PROPN
cbi-29	198	3	dv	dv	PROPN
cbi-29	198	4	+	+	PROPN
cbi-29	198	5	v	v	NUM
cbi-29	198	6	du	du	NOUN
cbi-29	198	7	,	,	PUNCT
cbi-29	198	8	while	while	SCONJ
cbi-29	198	9	one	one	NUM
cbi-29	198	10	of	of	ADP
cbi-29	198	11	the	the	DET
cbi-29	198	12	outputs	output	NOUN
cbi-29	198	13	is	be	AUX
cbi-29	198	14	the	the	DET
cbi-29	198	15	anticipated	anticipated	ADJ
cbi-29	198	16	6x	6x	NUM
cbi-29	198	17	dx2	dx2	NOUN
cbi-29	198	18	,	,	PUNCT
cbi-29	198	19	there	there	PRON
cbi-29	198	20	is	be	VERB
cbi-29	198	21	also	also	ADV
cbi-29	198	22	another	another	DET
cbi-29	198	23	one	one	NUM
cbi-29	198	24	,	,	PUNCT
cbi-29	198	25	3x2	3x2	NUM
cbi-29	198	26	d2x	d2x	PROPN
cbi-29	198	27	.	.	PUNCT
cbi-29	199	1	if	if	SCONJ
cbi-29	199	2	x	x	PRON
cbi-29	199	3	is	be	AUX
cbi-29	199	4	the	the	DET
cbi-29	199	5	independent	independent	ADJ
cbi-29	199	6	variable	variable	NOUN
cbi-29	199	7	,	,	PUNCT
cbi-29	199	8	this	this	DET
cbi-29	199	9	term	term	NOUN
cbi-29	199	10	goes	go	VERB
cbi-29	199	11	to	to	ADP
cbi-29	199	12	zero	zero	NUM
cbi-29	199	13	because	because	SCONJ
cbi-29	199	14	d2x	d2x	PROPN
cbi-29	199	15	goes	go	VERB
cbi-29	199	16	to	to	ADP
cbi-29	199	17	zero	zero	NUM
cbi-29	199	18	(	(	PUNCT
cbi-29	199	19	see	see	VERB
cbi-29	199	20	bartlett	bartlett	NOUN
cbi-29	199	21	and	and	CCONJ
cbi-29	199	22	khurshudyan	khurshudyan	PROPN
cbi-29	199	23	(	(	PUNCT
cbi-29	199	24	2018	2018	NUM
cbi-29	199	25	)	)	PUNCT
cbi-29	199	26	and	and	CCONJ
cbi-29	199	27	bos	bos	X
cbi-29	199	28	(	(	PUNCT
cbi-29	199	29	1974	1974	NUM
cbi-29	199	30	)	)	PUNCT
cbi-29	199	31	for	for	ADP
cbi-29	199	32	an	an	DET
cbi-29	199	33	explanation	explanation	NOUN
cbi-29	199	34	of	of	ADP
cbi-29	199	35	why	why	SCONJ
cbi-29	199	36	)	)	PUNCT
cbi-29	199	37	,	,	PUNCT
cbi-29	199	38	and	and	CCONJ
cbi-29	199	39	the	the	DET
cbi-29	199	40	result	result	NOUN
cbi-29	199	41	looks	look	VERB
cbi-29	199	42	like	like	SCONJ
cbi-29	199	43	it	it	PRON
cbi-29	199	44	is	be	AUX
cbi-29	199	45	expected	expect	VERB
cbi-29	199	46	to	to	PART
cbi-29	199	47	under	under	ADP
cbi-29	199	48	typical	typical	ADJ
cbi-29	199	49	understandings	understanding	NOUN
cbi-29	199	50	of	of	ADP
cbi-29	199	51	calculus	calculus	NOUN
cbi-29	199	52	.	.	PUNCT
cbi-29	200	1	however	however	ADV
cbi-29	200	2	,	,	PUNCT
cbi-29	200	3	if	if	SCONJ
cbi-29	200	4	x	x	PRON
cbi-29	200	5	is	be	AUX
cbi-29	200	6	not	not	PART
cbi-29	200	7	an	an	DET
cbi-29	200	8	independent	independent	ADJ
cbi-29	200	9	variable	variable	NOUN
cbi-29	200	10	,	,	PUNCT
cbi-29	200	11	the	the	DET
cbi-29	200	12	term	term	NOUN
cbi-29	200	13	is	be	AUX
cbi-29	200	14	vitally	vitally	ADV
cbi-29	200	15	important	important	ADJ
cbi-29	200	16	.	.	PUNCT
cbi-29	201	1	without	without	ADP
cbi-29	201	2	keeping	keep	VERB
cbi-29	201	3	the	the	DET
cbi-29	201	4	term	term	NOUN
cbi-29	201	5	,	,	PUNCT
cbi-29	201	6	the	the	DET
cbi-29	201	7	second	second	ADJ
cbi-29	201	8	differential	differential	NOUN
cbi-29	201	9	would	would	AUX
cbi-29	201	10	not	not	PART
cbi-29	201	11	be	be	AUX
cbi-29	201	12	algebraically	algebraically	ADV
cbi-29	201	13	manipulable	manipulable	ADJ
cbi-29	201	14	.	.	PUNCT
cbi-29	202	1	keeping	keep	VERB
cbi-29	202	2	the	the	DET
cbi-29	202	3	term	term	NOUN
cbi-29	202	4	then	then	ADV
cbi-29	202	5	allows	allow	VERB
cbi-29	202	6	higher	high	ADJ
cbi-29	202	7	order	order	NOUN
cbi-29	202	8	differentials	differential	NOUN
cbi-29	202	9	to	to	PART
cbi-29	202	10	remain	remain	VERB
cbi-29	202	11	as	as	ADP
cbi-29	202	12	algebraically	algebraically	ADV
cbi-29	202	13	manipulable	manipulable	ADJ
cbi-29	202	14	terms	term	NOUN
cbi-29	202	15	.	.	PUNCT
cbi-29	203	1	now	now	ADV
cbi-29	203	2	,	,	PUNCT
cbi-29	203	3	let	let	VERB
cbi-29	203	4	us	we	PRON
cbi-29	203	5	divide	divide	VERB
cbi-29	203	6	the	the	DET
cbi-29	203	7	whole	whole	ADJ
cbi-29	203	8	thing	thing	NOUN
cbi-29	203	9	by	by	ADP
cbi-29	203	10	dx2	dx2	PROPN
cbi-29	203	11	.	.	PUNCT
cbi-29	204	1	doing	do	VERB
cbi-29	204	2	so	so	ADV
cbi-29	204	3	yields	yield	NOUN
cbi-29	204	4	d2y	d2y	PROPN
cbi-29	204	5	dx2	dx2	PROPN
cbi-29	204	6	=	=	SYM
cbi-29	204	7	3x2	3x2	NUM
cbi-29	205	1	d2x	d2x	PROPN
cbi-29	205	2	dx2	dx2	PROPN
cbi-29	205	3	+	+	CCONJ
cbi-29	205	4	6x	6x	NUM
cbi-29	205	5	(	(	PUNCT
cbi-29	205	6	3	3	NUM
cbi-29	205	7	)	)	PUNCT
cbi-29	205	8	3to	3to	NOUN
cbi-29	205	9	emphasize	emphasize	VERB
cbi-29	205	10	this	this	PRON
cbi-29	205	11	,	,	PUNCT
cbi-29	205	12	i	i	PRON
cbi-29	205	13	usually	usually	ADV
cbi-29	205	14	typeset	typeset	VERB
cbi-29	205	15	dx	dx	PROPN
cbi-29	205	16	such	such	ADJ
cbi-29	205	17	that	that	SCONJ
cbi-29	205	18	the	the	DET
cbi-29	205	19	d	d	NOUN
cbi-29	205	20	is	be	AUX
cbi-29	205	21	in	in	ADP
cbi-29	205	22	roman	roman	ADJ
cbi-29	205	23	type	type	NOUN
cbi-29	205	24	and	and	CCONJ
cbi-29	205	25	the	the	PRON
cbi-29	205	26	x	x	NOUN
cbi-29	205	27	is	be	AUX
cbi-29	205	28	in	in	ADP
cbi-29	205	29	italic	italic	ADJ
cbi-29	205	30	.	.	PUNCT
cbi-29	206	1	this	this	PRON
cbi-29	206	2	is	be	AUX
cbi-29	206	3	similar	similar	ADJ
cbi-29	206	4	to	to	ADP
cbi-29	206	5	the	the	DET
cbi-29	206	6	way	way	NOUN
cbi-29	206	7	that	that	PRON
cbi-29	206	8	other	other	ADJ
cbi-29	206	9	functions	function	NOUN
cbi-29	206	10	such	such	ADJ
cbi-29	206	11	as	as	ADP
cbi-29	206	12	sin	sin	NOUN
cbi-29	206	13	x	x	VERB
cbi-29	206	14	are	be	AUX
cbi-29	206	15	typeset	typeset	VERB
cbi-29	206	16	.	.	PUNCT
cbi-29	207	1	22	22	NUM
cbi-29	207	2	simplifying	simplify	VERB
cbi-29	207	3	and	and	CCONJ
cbi-29	207	4	refactoring	refactore	VERB
cbi-29	207	5	introductory	introductory	PROPN
cbi-29	207	6	calculus	calculus	PROPN
cbi-29	207	7	however	however	ADV
cbi-29	207	8	,	,	PUNCT
cbi-29	207	9	this	this	PRON
cbi-29	207	10	has	have	VERB
cbi-29	207	11	more	more	ADJ
cbi-29	207	12	terms	term	NOUN
cbi-29	207	13	than	than	ADP
cbi-29	207	14	what	what	PRON
cbi-29	207	15	we	we	PRON
cbi-29	207	16	normally	normally	ADV
cbi-29	207	17	expect	expect	VERB
cbi-29	207	18	from	from	ADP
cbi-29	207	19	a	a	DET
cbi-29	207	20	second	second	ADJ
cbi-29	207	21	derivative	derivative	NOUN
cbi-29	207	22	.	.	PUNCT
cbi-29	208	1	this	this	PRON
cbi-29	208	2	is	be	AUX
cbi-29	208	3	because	because	SCONJ
cbi-29	208	4	the	the	DET
cbi-29	208	5	second	second	ADJ
cbi-29	208	6	derivative	derivative	NOUN
cbi-29	208	7	comes	come	VERB
cbi-29	208	8	from	from	ADP
cbi-29	208	9	the	the	DET
cbi-29	208	10	following	follow	VERB
cbi-29	208	11	sequence	sequence	NOUN
cbi-29	208	12	of	of	ADP
cbi-29	208	13	steps	step	NOUN
cbi-29	208	14	:	:	PUNCT
cbi-29	208	15	1	1	X
cbi-29	208	16	.	.	X
cbi-29	208	17	take	take	VERB
cbi-29	208	18	a	a	DET
cbi-29	208	19	differential	differential	NOUN
cbi-29	208	20	2	2	NUM
cbi-29	208	21	.	.	X
cbi-29	208	22	divide	divide	NOUN
cbi-29	208	23	by	by	ADP
cbi-29	208	24	dx	dx	PROPN
cbi-29	208	25	3	3	NUM
cbi-29	208	26	.	.	PUNCT
cbi-29	208	27	take	take	VERB
cbi-29	208	28	another	another	DET
cbi-29	208	29	differential	differential	NOUN
cbi-29	208	30	4	4	NUM
cbi-29	208	31	.	.	NOUN
cbi-29	208	32	divide	divide	NOUN
cbi-29	208	33	by	by	ADP
cbi-29	208	34	dx	dx	PROPN
cbi-29	208	35	because	because	SCONJ
cbi-29	208	36	the	the	DET
cbi-29	208	37	derivative	derivative	NOUN
cbi-29	208	38	is	be	AUX
cbi-29	208	39	the	the	DET
cbi-29	208	40	combination	combination	NOUN
cbi-29	208	41	of	of	ADP
cbi-29	208	42	steps	step	NOUN
cbi-29	208	43	1	1	NUM
cbi-29	208	44	&	&	CCONJ
cbi-29	208	45	2	2	NUM
cbi-29	208	46	,	,	PUNCT
cbi-29	208	47	the	the	DET
cbi-29	208	48	second	second	ADJ
cbi-29	208	49	derivative	derivative	NOUN
cbi-29	208	50	simply	simply	ADV
cbi-29	208	51	repeats	repeat	VERB
cbi-29	208	52	those	those	DET
cbi-29	208	53	steps	step	NOUN
cbi-29	208	54	.	.	PUNCT
cbi-29	209	1	however	however	ADV
cbi-29	209	2	,	,	PUNCT
cbi-29	209	3	if	if	SCONJ
cbi-29	209	4	you	you	PRON
cbi-29	209	5	take	take	VERB
cbi-29	209	6	the	the	DET
cbi-29	209	7	differential	differential	NOUN
cbi-29	209	8	twice	twice	ADV
cbi-29	209	9	in	in	ADP
cbi-29	209	10	a	a	DET
cbi-29	209	11	row	row	NOUN
cbi-29	209	12	before	before	ADP
cbi-29	209	13	dividing	divide	VERB
cbi-29	209	14	by	by	ADP
cbi-29	209	15	dx2	dx2	PROPN
cbi-29	209	16	,	,	PUNCT
cbi-29	209	17	then	then	ADV
cbi-29	209	18	you	you	PRON
cbi-29	209	19	wind	wind	VERB
cbi-29	209	20	up	up	ADP
cbi-29	209	21	with	with	ADP
cbi-29	209	22	a	a	DET
cbi-29	209	23	strange	strange	ADJ
cbi-29	209	24	-	-	PUNCT
cbi-29	209	25	looking	look	VERB
cbi-29	209	26	answer	answer	NOUN
cbi-29	209	27	,	,	PUNCT
cbi-29	209	28	as	as	SCONJ
cbi-29	209	29	we	we	PRON
cbi-29	209	30	did	do	VERB
cbi-29	209	31	in	in	ADP
cbi-29	209	32	equation	equation	NOUN
cbi-29	209	33	3	3	NUM
cbi-29	209	34	.	.	PUNCT
cbi-29	210	1	a	a	DET
cbi-29	210	2	few	few	ADJ
cbi-29	210	3	things	thing	NOUN
cbi-29	210	4	to	to	PART
cbi-29	210	5	note	note	VERB
cbi-29	210	6	about	about	ADP
cbi-29	210	7	equation	equation	NOUN
cbi-29	210	8	3	3	NUM
cbi-29	210	9	:	:	SYM
cbi-29	210	10	1	1	NUM
cbi-29	210	11	.	.	X
cbi-29	211	1	the	the	DET
cbi-29	211	2	left	left	ADJ
cbi-29	211	3	-	-	PUNCT
cbi-29	211	4	hand	hand	NOUN
cbi-29	211	5	side	side	NOUN
cbi-29	211	6	has	have	VERB
cbi-29	211	7	the	the	DET
cbi-29	211	8	form	form	NOUN
cbi-29	211	9	that	that	PRON
cbi-29	211	10	we	we	PRON
cbi-29	211	11	normally	normally	ADV
cbi-29	211	12	associate	associate	VERB
cbi-29	211	13	with	with	ADP
cbi-29	211	14	the	the	DET
cbi-29	211	15	second	second	ADJ
cbi-29	211	16	derivative	derivative	NOUN
cbi-29	211	17	.	.	PUNCT
cbi-29	212	1	2	2	X
cbi-29	212	2	.	.	X
cbi-29	212	3	the	the	DET
cbi-29	212	4	right	right	ADJ
cbi-29	212	5	-	-	PUNCT
cbi-29	212	6	hand	hand	NOUN
cbi-29	212	7	side	side	NOUN
cbi-29	212	8	does	do	AUX
cbi-29	212	9	not	not	PART
cbi-29	212	10	have	have	VERB
cbi-29	212	11	the	the	DET
cbi-29	212	12	form	form	NOUN
cbi-29	212	13	that	that	PRON
cbi-29	212	14	we	we	PRON
cbi-29	212	15	normally	normally	ADV
cbi-29	212	16	associate	associate	VERB
cbi-29	212	17	with	with	ADP
cbi-29	212	18	the	the	DET
cbi-29	212	19	second	second	ADJ
cbi-29	212	20	derivative	derivative	NOUN
cbi-29	212	21	.	.	PUNCT
cbi-29	213	1	it	it	PRON
cbi-29	213	2	has	have	VERB
cbi-29	213	3	an	an	DET
cbi-29	213	4	extra	extra	ADJ
cbi-29	213	5	term	term	NOUN
cbi-29	213	6	in	in	ADP
cbi-29	213	7	it	it	PRON
cbi-29	213	8	.	.	PUNCT
cbi-29	214	1	3	3	X
cbi-29	214	2	.	.	X
cbi-29	214	3	the	the	DET
cbi-29	214	4	reason	reason	NOUN
cbi-29	214	5	for	for	ADP
cbi-29	214	6	this	this	PRON
cbi-29	214	7	is	be	AUX
cbi-29	214	8	that	that	SCONJ
cbi-29	214	9	,	,	PUNCT
cbi-29	214	10	even	even	ADV
cbi-29	214	11	though	though	SCONJ
cbi-29	214	12	it	it	PRON
cbi-29	214	13	is	be	AUX
cbi-29	214	14	normally	normally	ADV
cbi-29	214	15	associated	associate	VERB
cbi-29	214	16	with	with	ADP
cbi-29	214	17	the	the	DET
cbi-29	214	18	second	second	ADJ
cbi-29	214	19	derivative	derivative	NOUN
cbi-29	214	20	,	,	PUNCT
cbi-29	214	21	the	the	DET
cbi-29	214	22	left	left	ADJ
cbi-29	214	23	-	-	PUNCT
cbi-29	214	24	hand	hand	NOUN
cbi-29	214	25	side	side	NOUN
cbi-29	214	26	is	be	AUX
cbi-29	214	27	not	not	PART
cbi-29	214	28	the	the	DET
cbi-29	214	29	correct	correct	ADJ
cbi-29	214	30	notation	notation	NOUN
cbi-29	214	31	for	for	ADP
cbi-29	214	32	the	the	DET
cbi-29	214	33	derivative	derivative	NOUN
cbi-29	214	34	of	of	ADP
cbi-29	214	35	the	the	DET
cbi-29	214	36	derivative	derivative	NOUN
cbi-29	214	37	of	of	ADP
cbi-29	214	38	y.	y.	PROPN
cbi-29	214	39	4	4	NUM
cbi-29	214	40	.	.	PUNCT
cbi-29	215	1	in	in	ADP
cbi-29	215	2	other	other	ADJ
cbi-29	215	3	words	word	NOUN
cbi-29	215	4	,	,	PUNCT
cbi-29	215	5	the	the	DET
cbi-29	215	6	equation	equation	NOUN
cbi-29	215	7	given	give	VERB
cbi-29	215	8	by	by	ADP
cbi-29	215	9	equation	equation	NOUN
cbi-29	215	10	3	3	NUM
cbi-29	215	11	is	be	AUX
cbi-29	215	12	correct	correct	ADJ
cbi-29	215	13	as	as	ADV
cbi-29	215	14	far	far	ADV
cbi-29	215	15	as	as	SCONJ
cbi-29	215	16	it	it	PRON
cbi-29	215	17	goes	go	VERB
cbi-29	215	18	(	(	PUNCT
cbi-29	215	19	both	both	DET
cbi-29	215	20	sides	side	NOUN
cbi-29	215	21	are	be	AUX
cbi-29	215	22	in	in	ADP
cbi-29	215	23	fact	fact	NOUN
cbi-29	215	24	equal	equal	ADJ
cbi-29	215	25	)	)	PUNCT
cbi-29	215	26	,	,	PUNCT
cbi-29	215	27	but	but	CCONJ
cbi-29	215	28	it	it	PRON
cbi-29	215	29	is	be	AUX
cbi-29	215	30	not	not	PART
cbi-29	215	31	the	the	DET
cbi-29	215	32	second	second	ADJ
cbi-29	215	33	derivative	derivative	NOUN
cbi-29	215	34	,	,	PUNCT
cbi-29	215	35	because	because	SCONJ
cbi-29	215	36	the	the	DET
cbi-29	215	37	notation	notation	NOUN
cbi-29	215	38	we	we	PRON
cbi-29	215	39	have	have	AUX
cbi-29	215	40	come	come	VERB
cbi-29	215	41	to	to	PART
cbi-29	215	42	associate	associate	VERB
cbi-29	215	43	with	with	ADP
cbi-29	215	44	the	the	DET
cbi-29	215	45	second	second	ADJ
cbi-29	215	46	derivative	derivative	NOUN
cbi-29	215	47	actually	actually	ADV
cbi-29	215	48	refers	refer	VERB
cbi-29	215	49	to	to	ADP
cbi-29	215	50	a	a	DET
cbi-29	215	51	different	different	ADJ
cbi-29	215	52	quantity	quantity	NOUN
cbi-29	215	53	altogether	altogether	ADV
cbi-29	215	54	.	.	PUNCT
cbi-29	216	1	according	accord	VERB
cbi-29	216	2	to	to	ADP
cbi-29	216	3	bartlett	bartlett	PROPN
cbi-29	216	4	and	and	CCONJ
cbi-29	216	5	khurshudyan	khurshudyan	PROPN
cbi-29	216	6	(	(	PUNCT
cbi-29	216	7	2018	2018	NUM
cbi-29	216	8	)	)	PUNCT
cbi-29	216	9	,	,	PUNCT
cbi-29	216	10	the	the	DET
cbi-29	216	11	full	full	ADJ
cbi-29	216	12	notation	notation	NOUN
cbi-29	216	13	for	for	ADP
cbi-29	216	14	the	the	DET
cbi-29	216	15	second	second	ADJ
cbi-29	216	16	derivatives	derivative	NOUN
cbi-29	216	17	should	should	AUX
cbi-29	216	18	be	be	AUX
cbi-29	216	19	d2y	d2y	ADJ
cbi-29	216	20	dx2	dx2	NOUN
cbi-29	216	21	−	−	PROPN
cbi-29	217	1	dy	dy	NOUN
cbi-29	218	1	dx	dx	PROPN
cbi-29	218	2	d2x	d2x	PROPN
cbi-29	218	3	dx2	dx2	PROPN
cbi-29	218	4	.	.	PUNCT
cbi-29	219	1	(	(	PUNCT
cbi-29	219	2	4	4	X
cbi-29	219	3	)	)	PUNCT
cbi-29	219	4	this	this	PRON
cbi-29	219	5	can	can	AUX
cbi-29	219	6	be	be	AUX
cbi-29	219	7	deduced	deduce	VERB
cbi-29	219	8	simply	simply	ADV
cbi-29	219	9	from	from	ADP
cbi-29	219	10	taking	take	VERB
cbi-29	219	11	two	two	NUM
cbi-29	219	12	derivatives	derivative	NOUN
cbi-29	219	13	of	of	ADP
cbi-29	219	14	y.	y.	NOUN
cbi-29	219	15	the	the	DET
cbi-29	219	16	first	first	ADJ
cbi-29	219	17	derivative	derivative	NOUN
cbi-29	219	18	is	be	AUX
cbi-29	219	19	obviously	obviously	ADV
cbi-29	219	20	dy	dy	VERB
cbi-29	219	21	dx	dx	PROPN
cbi-29	219	22	.	.	PUNCT
cbi-29	220	1	the	the	DET
cbi-29	220	2	second	second	ADJ
cbi-29	220	3	derivative	derivative	NOUN
cbi-29	220	4	is	be	AUX
cbi-29	220	5	found	find	VERB
cbi-29	220	6	by	by	ADP
cbi-29	220	7	taking	take	VERB
cbi-29	220	8	the	the	DET
cbi-29	220	9	differential	differential	NOUN
cbi-29	220	10	of	of	ADP
cbi-29	220	11	dy	dy	NOUN
cbi-29	220	12	dx	dx	PROPN
cbi-29	220	13	and	and	CCONJ
cbi-29	220	14	then	then	ADV
cbi-29	220	15	dividing	divide	VERB
cbi-29	220	16	by	by	ADP
cbi-29	220	17	dx	dx	PROPN
cbi-29	220	18	.	.	PUNCT
cbi-29	221	1	d	d	PROPN
cbi-29	221	2	#	#	NOUN
cbi-29	221	3	dy	dy	NOUN
cbi-29	221	4	dx	dx	PROPN
cbi-29	221	5	$	$	SYM
cbi-29	221	6	dx	dx	PROPN
cbi-29	221	7	=	=	PUNCT
cbi-29	221	8	dx	dx	PROPN
cbi-29	221	9	d(dy)−dy	d(dy)−dy	VERB
cbi-29	221	10	d(dx	d(dx	NOUN
cbi-29	221	11	)	)	PUNCT
cbi-29	221	12	dx2	dx2	PROPN
cbi-29	221	13	dx	dx	PROPN
cbi-29	221	14	=	=	PROPN
cbi-29	221	15	dx	dx	PROPN
cbi-29	221	16	d(dy	d(dy	PROPN
cbi-29	221	17	)	)	PUNCT
cbi-29	221	18	−	−	PROPN
cbi-29	221	19	dy	dy	NOUN
cbi-29	221	20	d(dx	d(dx	PROPN
cbi-29	221	21	)	)	PUNCT
cbi-29	221	22	dx3	dx3	PROPN
cbi-29	222	1	=	=	PUNCT
cbi-29	222	2	dx	dx	PROPN
cbi-29	222	3	d(dy	d(dy	PROPN
cbi-29	222	4	)	)	PUNCT
cbi-29	222	5	dx3	dx3	PROPN
cbi-29	222	6	−	−	PROPN
cbi-29	222	7	dy	dy	PROPN
cbi-29	222	8	d(dx	d(dx	PROPN
cbi-29	222	9	)	)	PUNCT
cbi-29	222	10	dx3	dx3	PROPN
cbi-29	222	11	=	=	SYM
cbi-29	222	12	d(dy	d(dy	PROPN
cbi-29	222	13	)	)	PUNCT
cbi-29	222	14	dx2	dx2	NOUN
cbi-29	222	15	−	−	PROPN
cbi-29	222	16	dy	dy	PROPN
cbi-29	222	17	dx	dx	PROPN
cbi-29	222	18	d(dx	d(dx	PROPN
cbi-29	222	19	)	)	PUNCT
cbi-29	222	20	dx2	dx2	PROPN
cbi-29	222	21	(	(	PUNCT
cbi-29	222	22	5	5	NUM
cbi-29	222	23	)	)	PUNCT
cbi-29	222	24	by	by	ADP
cbi-29	222	25	noting	note	VERB
cbi-29	222	26	that	that	SCONJ
cbi-29	222	27	d(dy	d(dy	PROPN
cbi-29	222	28	)	)	PUNCT
cbi-29	222	29	=	=	SYM
cbi-29	222	30	d(d(y	d(d(y	NOUN
cbi-29	222	31	)	)	PUNCT
cbi-29	222	32	)	)	PUNCT
cbi-29	223	1	=	=	SYM
cbi-29	223	2	d2y	d2y	PROPN
cbi-29	223	3	and	and	CCONJ
cbi-29	223	4	d(dx	d(dx	NOUN
cbi-29	223	5	)	)	PUNCT
cbi-29	223	6	=	=	SYM
cbi-29	223	7	d(d(x	d(d(x	NOUN
cbi-29	223	8	)	)	PUNCT
cbi-29	223	9	)	)	PUNCT
cbi-29	224	1	=	=	VERB
cbi-29	224	2	d2x	d2x	ADJ
cbi-29	224	3	we	we	PRON
cbi-29	224	4	can	can	AUX
cbi-29	224	5	see	see	VERB
cbi-29	224	6	that	that	SCONJ
cbi-29	224	7	this	this	PRON
cbi-29	224	8	is	be	AUX
cbi-29	224	9	equivalent	equivalent	ADJ
cbi-29	224	10	with	with	ADP
cbi-29	224	11	equation	equation	NOUN
cbi-29	224	12	4	4	NUM
cbi-29	224	13	.	.	PUNCT
cbi-29	225	1	so	so	ADV
cbi-29	225	2	how	how	SCONJ
cbi-29	225	3	does	do	AUX
cbi-29	225	4	this	this	PRON
cbi-29	225	5	square	square	NOUN
cbi-29	225	6	with	with	ADP
cbi-29	225	7	equation	equation	NOUN
cbi-29	225	8	3	3	NUM
cbi-29	225	9	?	?	PUNCT
cbi-29	226	1	if	if	SCONJ
cbi-29	226	2	we	we	PRON
cbi-29	226	3	subtract	subtract	VERB
cbi-29	226	4	3x2	3x2	NUM
cbi-29	226	5	d2x	d2x	ADJ
cbi-29	226	6	dx2	dx2	PROPN
cbi-29	226	7	from	from	ADP
cbi-29	226	8	both	both	DET
cbi-29	226	9	sides	side	NOUN
cbi-29	226	10	of	of	ADP
cbi-29	226	11	equation	equation	NOUN
cbi-29	226	12	3	3	NUM
cbi-29	226	13	,	,	PUNCT
cbi-29	226	14	it	it	PRON
cbi-29	226	15	will	will	AUX
cbi-29	226	16	result	result	VERB
cbi-29	226	17	in	in	ADP
cbi-29	226	18	d2y	d2y	PROPN
cbi-29	226	19	dx2	dx2	NOUN
cbi-29	226	20	−	−	PROPN
cbi-29	226	21	3x2	3x2	NUM
cbi-29	226	22	d2x	d2x	ADJ
cbi-29	226	23	dx2	dx2	PROPN
cbi-29	226	24	=	=	NOUN
cbi-29	226	25	6x	6x	NOUN
cbi-29	226	26	.	.	PUNCT
cbi-29	227	1	if	if	SCONJ
cbi-29	227	2	you	you	PRON
cbi-29	227	3	recognize	recognize	VERB
cbi-29	227	4	3x2	3x2	NUM
cbi-29	227	5	as	as	ADP
cbi-29	227	6	being	be	AUX
cbi-29	227	7	the	the	DET
cbi-29	227	8	first	first	ADJ
cbi-29	227	9	derivative	derivative	NOUN
cbi-29	227	10	(	(	PUNCT
cbi-29	227	11	i.e.	i.e.	X
cbi-29	227	12	,	,	PUNCT
cbi-29	227	13	dy	dy	X
cbi-29	227	14	dx	dx	PROPN
cbi-29	227	15	)	)	PUNCT
cbi-29	228	1	it	it	PRON
cbi-29	228	2	is	be	AUX
cbi-29	228	3	apparent	apparent	ADJ
cbi-29	228	4	that	that	SCONJ
cbi-29	228	5	the	the	DET
cbi-29	228	6	left	left	ADJ
cbi-29	228	7	-	-	PUNCT
cbi-29	228	8	hand	hand	NOUN
cbi-29	228	9	side	side	NOUN
cbi-29	228	10	of	of	ADP
cbi-29	228	11	this	this	DET
cbi-29	228	12	equation	equation	NOUN
cbi-29	228	13	is	be	AUX
cbi-29	228	14	the	the	DET
cbi-29	228	15	same	same	ADJ
cbi-29	228	16	as	as	ADP
cbi-29	228	17	the	the	DET
cbi-29	228	18	improved	improved	ADJ
cbi-29	228	19	form	form	NOUN
cbi-29	228	20	of	of	ADP
cbi-29	228	21	the	the	DET
cbi-29	228	22	second	second	ADJ
cbi-29	228	23	derivative	derivative	NOUN
cbi-29	228	24	listed	list	VERB
cbi-29	228	25	in	in	ADP
cbi-29	228	26	equation	equation	NOUN
cbi-29	228	27	4	4	NUM
cbi-29	228	28	.	.	PUNCT
cbi-29	228	29	because	because	SCONJ
cbi-29	228	30	we	we	PRON
cbi-29	228	31	are	be	AUX
cbi-29	228	32	using	use	VERB
cbi-29	228	33	this	this	DET
cbi-29	228	34	form	form	NOUN
cbi-29	228	35	of	of	ADP
cbi-29	228	36	the	the	DET
cbi-29	228	37	second	second	ADJ
cbi-29	228	38	derivative	derivative	NOUN
cbi-29	228	39	,	,	PUNCT
cbi-29	228	40	this	this	DET
cbi-29	228	41	formula	formula	NOUN
cbi-29	228	42	can	can	AUX
cbi-29	228	43	be	be	AUX
cbi-29	228	44	algebraically	algebraically	ADV
cbi-29	228	45	rearranged	rearrange	VERB
cbi-29	228	46	to	to	PART
cbi-29	228	47	yield	yield	VERB
cbi-29	228	48	a	a	DET
cbi-29	228	49	wide	wide	ADJ
cbi-29	228	50	variety	variety	NOUN
cbi-29	228	51	of	of	ADP
cbi-29	228	52	results	result	NOUN
cbi-29	228	53	.	.	PUNCT
cbi-29	229	1	we	we	PRON
cbi-29	229	2	can	can	AUX
cbi-29	229	3	rearrange	rearrange	VERB
cbi-29	229	4	the	the	DET
cbi-29	229	5	terms	term	NOUN
cbi-29	229	6	to	to	PART
cbi-29	229	7	find	find	VERB
cbi-29	229	8	the	the	DET
cbi-29	229	9	second	second	ADJ
cbi-29	229	10	derivative	derivative	NOUN
cbi-29	229	11	of	of	ADP
cbi-29	229	12	x	x	PUNCT
cbi-29	229	13	with	with	ADP
cbi-29	229	14	respect	respect	NOUN
cbi-29	229	15	to	to	ADP
cbi-29	229	16	y	y	PROPN
cbi-29	229	17	(	(	PUNCT
cbi-29	229	18	instead	instead	ADV
cbi-29	229	19	of	of	ADP
cbi-29	229	20	the	the	DET
cbi-29	229	21	second	second	ADJ
cbi-29	229	22	derivative	derivative	NOUN
cbi-29	229	23	of	of	ADP
cbi-29	229	24	y	y	PROPN
cbi-29	229	25	with	with	ADP
cbi-29	229	26	respect	respect	NOUN
cbi-29	229	27	to	to	ADP
cbi-29	229	28	x	x	NOUN
cbi-29	229	29	)	)	PUNCT
cbi-29	229	30	.	.	PUNCT
cbi-29	230	1	or	or	CCONJ
cbi-29	230	2	,	,	PUNCT
cbi-29	230	3	it	it	PRON
cbi-29	230	4	can	can	AUX
cbi-29	230	5	be	be	AUX
cbi-29	230	6	combined	combine	VERB
cbi-29	230	7	with	with	ADP
cbi-29	230	8	other	other	ADJ
cbi-29	230	9	formulas	formula	NOUN
cbi-29	230	10	and	and	CCONJ
cbi-29	230	11	differential	differential	ADJ
cbi-29	230	12	formulas	formula	NOUN
cbi-29	230	13	(	(	PUNCT
cbi-29	230	14	say	say	INTJ
cbi-29	230	15	,	,	PUNCT
cbi-29	230	16	the	the	DET
cbi-29	230	17	relationship	relationship	NOUN
cbi-29	230	18	of	of	ADP
cbi-29	230	19	x	x	INTJ
cbi-29	230	20	to	to	ADP
cbi-29	230	21	some	some	DET
cbi-29	230	22	variable	variable	ADJ
cbi-29	230	23	t	t	PROPN
cbi-29	230	24	)	)	PUNCT
cbi-29	230	25	to	to	PART
cbi-29	230	26	algebraically	algebraically	ADV
cbi-29	230	27	accomplish	accomplish	VERB
cbi-29	230	28	a	a	DET
cbi-29	230	29	change	change	NOUN
cbi-29	230	30	of	of	ADP
cbi-29	230	31	variables	variable	NOUN
cbi-29	230	32	.	.	PUNCT
cbi-29	231	1	previously	previously	ADV
cbi-29	231	2	,	,	PUNCT
cbi-29	231	3	this	this	PRON
cbi-29	231	4	was	be	AUX
cbi-29	231	5	only	only	ADV
cbi-29	231	6	available	available	ADJ
cbi-29	231	7	using	use	VERB
cbi-29	231	8	specialty	specialty	NOUN
cbi-29	231	9	formulas	formula	NOUN
cbi-29	231	10	such	such	ADJ
cbi-29	231	11	as	as	ADP
cbi-29	231	12	faà	faà	PROPN
cbi-29	231	13	di	di	PROPN
cbi-29	231	14	bruno	bruno	PROPN
cbi-29	231	15	’s	’s	PART
cbi-29	231	16	formula	formula	NOUN
cbi-29	231	17	.	.	PUNCT
cbi-29	232	1	thus	thus	ADV
cbi-29	232	2	,	,	PUNCT
cbi-29	232	3	teaching	teach	VERB
cbi-29	232	4	using	use	VERB
cbi-29	232	5	leibnizian	leibnizian	ADJ
cbi-29	232	6	differentials	differential	NOUN
cbi-29	232	7	confers	confer	VERB
cbi-29	232	8	numerous	numerous	ADJ
cbi-29	232	9	advantages	advantage	NOUN
cbi-29	232	10	for	for	ADP
cbi-29	232	11	higher	high	ADJ
cbi-29	232	12	order	order	NOUN
cbi-29	232	13	differentials	differential	NOUN
cbi-29	232	14	:	:	PUNCT
cbi-29	233	1	1	1	X
cbi-29	233	2	.	.	PUNCT
cbi-29	233	3	the	the	DET
cbi-29	233	4	notation	notation	NOUN
cbi-29	233	5	is	be	AUX
cbi-29	233	6	clearer	clear	ADJ
cbi-29	233	7	,	,	PUNCT
cbi-29	233	8	because	because	SCONJ
cbi-29	233	9	there	there	PRON
cbi-29	233	10	is	be	VERB
cbi-29	233	11	a	a	DET
cbi-29	233	12	definitive	definitive	ADJ
cbi-29	233	13	reason	reason	NOUN
cbi-29	233	14	for	for	ADP
cbi-29	233	15	the	the	DET
cbi-29	233	16	way	way	NOUN
cbi-29	233	17	that	that	PRON
cbi-29	233	18	the	the	DET
cbi-29	233	19	notation	notation	NOUN
cbi-29	233	20	looks	look	VERB
cbi-29	233	21	.	.	PUNCT
cbi-29	234	1	2	2	X
cbi-29	234	2	.	.	X
cbi-29	234	3	the	the	DET
cbi-29	234	4	notation	notation	NOUN
cbi-29	234	5	allows	allow	VERB
cbi-29	234	6	differentials	differential	NOUN
cbi-29	234	7	to	to	PART
cbi-29	234	8	be	be	AUX
cbi-29	234	9	modified	modify	VERB
cbi-29	234	10	algebraically	algebraically	ADV
cbi-29	234	11	,	,	PUNCT
cbi-29	234	12	which	which	PRON
cbi-29	234	13	was	be	AUX
cbi-29	234	14	not	not	PART
cbi-29	234	15	previously	previously	ADV
cbi-29	234	16	possible	possible	ADJ
cbi-29	234	17	for	for	ADP
cbi-29	234	18	higher	high	ADJ
cbi-29	234	19	order	order	NOUN
cbi-29	234	20	derivatives	derivative	NOUN
cbi-29	234	21	.	.	PUNCT
cbi-29	235	1	3	3	X
cbi-29	235	2	.	.	X
cbi-29	235	3	because	because	SCONJ
cbi-29	235	4	the	the	DET
cbi-29	235	5	notation	notation	NOUN
cbi-29	235	6	is	be	AUX
cbi-29	235	7	algebraically	algebraically	ADV
cbi-29	235	8	manipulable	manipulable	ADJ
cbi-29	235	9	,	,	PUNCT
cbi-29	235	10	the	the	DET
cbi-29	235	11	notation	notation	NOUN
cbi-29	235	12	allows	allow	VERB
cbi-29	235	13	for	for	SCONJ
cbi-29	235	14	students	student	NOUN
cbi-29	235	15	to	to	PART
cbi-29	235	16	easily	easily	ADV
cbi-29	235	17	find	find	VERB
cbi-29	235	18	relationships	relationship	NOUN
cbi-29	235	19	that	that	PRON
cbi-29	235	20	previously	previously	ADV
cbi-29	235	21	required	require	VERB
cbi-29	235	22	memorized	memorized	ADJ
cbi-29	235	23	formulas	formula	NOUN
cbi-29	235	24	.	.	PUNCT
cbi-29	236	1	9	9	NUM
cbi-29	236	2	getting	getting	AUX
cbi-29	236	3	rid	rid	VERB
cbi-29	236	4	of	of	ADP
cbi-29	236	5	logarithmic	logarithmic	ADJ
cbi-29	236	6	differentiation	differentiation	NOUN
cbi-29	236	7	logarithmic	logarithmic	ADJ
cbi-29	236	8	differentiation	differentiation	NOUN
cbi-29	236	9	is	be	AUX
cbi-29	236	10	the	the	DET
cbi-29	236	11	process	process	NOUN
cbi-29	236	12	taught	teach	VERB
cbi-29	236	13	by	by	ADP
cbi-29	236	14	most	most	ADJ
cbi-29	236	15	calculus	calculus	NOUN
cbi-29	236	16	textbooks	textbook	NOUN
cbi-29	236	17	for	for	ADP
cbi-29	236	18	taking	take	VERB
cbi-29	236	19	the	the	DET
cbi-29	236	20	derivative	derivative	NOUN
cbi-29	236	21	of	of	ADP
cbi-29	236	22	functions	function	NOUN
cbi-29	236	23	of	of	ADP
cbi-29	236	24	the	the	DET
cbi-29	236	25	form	form	NOUN
cbi-29	236	26	uv	uv	INTJ
cbi-29	236	27	.	.	PUNCT
cbi-29	237	1	essentially	essentially	ADV
cbi-29	237	2	,	,	PUNCT
cbi-29	237	3	what	what	PRON
cbi-29	237	4	is	be	AUX
cbi-29	237	5	taught	teach	VERB
cbi-29	237	6	is	be	AUX
cbi-29	237	7	to	to	PART
cbi-29	237	8	use	use	VERB
cbi-29	237	9	logarithms	logarithm	NOUN
cbi-29	237	10	to	to	PART
cbi-29	237	11	remove	remove	VERB
cbi-29	237	12	the	the	DET
cbi-29	237	13	exponent	exponent	NOUN
cbi-29	237	14	,	,	PUNCT
cbi-29	237	15	and	and	CCONJ
cbi-29	237	16	then	then	ADV
cbi-29	237	17	take	take	VERB
cbi-29	237	18	the	the	DET
cbi-29	237	19	derivative	derivative	NOUN
cbi-29	237	20	now	now	ADV
cbi-29	237	21	that	that	SCONJ
cbi-29	237	22	the	the	DET
cbi-29	237	23	exponent	exponent	NOUN
cbi-29	237	24	is	be	AUX
cbi-29	237	25	removed	remove	VERB
cbi-29	237	26	.	.	PUNCT
cbi-29	238	1	the	the	DET
cbi-29	238	2	problem	problem	NOUN
cbi-29	238	3	with	with	ADP
cbi-29	238	4	this	this	PRON
cbi-29	238	5	is	be	AUX
cbi-29	238	6	that	that	SCONJ
cbi-29	238	7	it	it	PRON
cbi-29	238	8	is	be	AUX
cbi-29	238	9	needlessly	needlessly	ADV
cbi-29	238	10	complicated	complicated	ADJ
cbi-29	238	11	,	,	PUNCT
cbi-29	238	12	and	and	CCONJ
cbi-29	238	13	forces	force	VERB
cbi-29	238	14	the	the	DET
cbi-29	238	15	student	student	NOUN
cbi-29	238	16	volume	volume	NOUN
cbi-29	238	17	1	1	NUM
cbi-29	238	18	,	,	PUNCT
cbi-29	238	19	issue	issue	VERB
cbi-29	238	20	1	1	NUM
cbi-29	238	21	10	10	NUM
cbi-29	238	22	.	.	PUNCT
cbi-29	239	1	hyperreals	hyperreal	NOUN
cbi-29	239	2	for	for	ADP
cbi-29	239	3	limit	limit	NOUN
cbi-29	239	4	analysis	analysis	NOUN
cbi-29	239	5	23	23	NUM
cbi-29	239	6	to	to	PART
cbi-29	239	7	use	use	VERB
cbi-29	239	8	different	different	ADJ
cbi-29	239	9	processes	process	NOUN
cbi-29	239	10	depending	depend	VERB
cbi-29	239	11	on	on	ADP
cbi-29	239	12	the	the	DET
cbi-29	239	13	derivative	derivative	NOUN
cbi-29	239	14	in	in	ADP
cbi-29	239	15	question.4	question.4	NOUN
cbi-29	239	16	before	before	ADP
cbi-29	239	17	learning	learn	VERB
cbi-29	239	18	logarithmic	logarithmic	ADJ
cbi-29	239	19	differentiation	differentiation	NOUN
cbi-29	239	20	,	,	PUNCT
cbi-29	239	21	the	the	DET
cbi-29	239	22	student	student	NOUN
cbi-29	239	23	had	have	VERB
cbi-29	239	24	a	a	DET
cbi-29	239	25	more	more	ADV
cbi-29	239	26	-	-	PUNCT
cbi-29	239	27	or	or	CCONJ
cbi-29	239	28	-	-	PUNCT
cbi-29	239	29	less	less	ADV
cbi-29	239	30	unified	unified	ADJ
cbi-29	239	31	process	process	NOUN
cbi-29	239	32	for	for	ADP
cbi-29	239	33	taking	take	VERB
cbi-29	239	34	derivatives	derivative	NOUN
cbi-29	239	35	:	:	PUNCT
cbi-29	239	36	1	1	X
cbi-29	239	37	.	.	X
cbi-29	239	38	look	look	VERB
cbi-29	239	39	at	at	ADP
cbi-29	239	40	the	the	DET
cbi-29	239	41	form	form	NOUN
cbi-29	239	42	of	of	ADP
cbi-29	239	43	the	the	DET
cbi-29	239	44	function	function	NOUN
cbi-29	239	45	.	.	PUNCT
cbi-29	240	1	2	2	X
cbi-29	240	2	.	.	X
cbi-29	240	3	find	find	VERB
cbi-29	240	4	the	the	DET
cbi-29	240	5	corresponding	correspond	VERB
cbi-29	240	6	rule	rule	NOUN
cbi-29	240	7	(	(	PUNCT
cbi-29	240	8	memorized	memorized	ADJ
cbi-29	240	9	or	or	CCONJ
cbi-29	240	10	from	from	ADP
cbi-29	240	11	the	the	DET
cbi-29	240	12	book	book	NOUN
cbi-29	240	13	)	)	PUNCT
cbi-29	240	14	.	.	PUNCT
cbi-29	241	1	3	3	X
cbi-29	241	2	.	.	X
cbi-29	241	3	apply	apply	VERB
cbi-29	241	4	the	the	DET
cbi-29	241	5	rule	rule	NOUN
cbi-29	241	6	.	.	PUNCT
cbi-29	242	1	however	however	ADV
cbi-29	242	2	,	,	PUNCT
cbi-29	242	3	logarithmic	logarithmic	ADJ
cbi-29	242	4	differentiation	differentiation	NOUN
cbi-29	242	5	breaks	break	NOUN
cbi-29	242	6	that	that	DET
cbi-29	242	7	process	process	NOUN
cbi-29	242	8	,	,	PUNCT
cbi-29	242	9	adding	add	VERB
cbi-29	242	10	extra	extra	ADJ
cbi-29	242	11	steps	step	NOUN
cbi-29	242	12	in	in	ADP
cbi-29	242	13	some	some	DET
cbi-29	242	14	circumstances	circumstance	NOUN
cbi-29	242	15	.	.	PUNCT
cbi-29	243	1	if	if	SCONJ
cbi-29	243	2	the	the	DET
cbi-29	243	3	mathematics	mathematic	NOUN
cbi-29	243	4	required	require	VERB
cbi-29	243	5	this	this	PRON
cbi-29	243	6	,	,	PUNCT
cbi-29	243	7	that	that	PRON
cbi-29	243	8	would	would	AUX
cbi-29	243	9	be	be	AUX
cbi-29	243	10	one	one	NUM
cbi-29	243	11	thing	thing	NOUN
cbi-29	243	12	.	.	PUNCT
cbi-29	244	1	however	however	ADV
cbi-29	244	2	,	,	PUNCT
cbi-29	244	3	there	there	PRON
cbi-29	244	4	is	be	VERB
cbi-29	244	5	actually	actually	ADV
cbi-29	244	6	a	a	DET
cbi-29	244	7	rule	rule	NOUN
cbi-29	244	8	available	available	ADJ
cbi-29	244	9	for	for	ADP
cbi-29	244	10	forms	form	NOUN
cbi-29	244	11	of	of	ADP
cbi-29	244	12	the	the	DET
cbi-29	244	13	type	type	NOUN
cbi-29	244	14	uv	uv	NOUN
cbi-29	244	15	which	which	PRON
cbi-29	244	16	is	be	AUX
cbi-29	244	17	rarely	rarely	ADV
cbi-29	244	18	mentioned	mention	VERB
cbi-29	244	19	even	even	ADV
cbi-29	244	20	in	in	ADP
cbi-29	244	21	the	the	DET
cbi-29	244	22	appendices	appendix	NOUN
cbi-29	244	23	of	of	ADP
cbi-29	244	24	most	most	ADJ
cbi-29	244	25	calculus	calculus	NOUN
cbi-29	244	26	books	book	NOUN
cbi-29	244	27	.	.	PUNCT
cbi-29	245	1	the	the	DET
cbi-29	245	2	rule	rule	NOUN
cbi-29	245	3	is	be	AUX
cbi-29	245	4	d(uv	d(uv	NOUN
cbi-29	245	5	)	)	PUNCT
cbi-29	246	1	=	=	PUNCT
cbi-29	246	2	vuv−1du	vuv−1du	NOUN
cbi-29	246	3	+	+	NUM
cbi-29	246	4	ln(u)uvdv	ln(u)uvdv	X
cbi-29	246	5	(	(	PUNCT
cbi-29	246	6	6	6	NUM
cbi-29	246	7	)	)	PUNCT
cbi-29	246	8	this	this	DET
cbi-29	246	9	formula	formula	NOUN
cbi-29	246	10	can	can	AUX
cbi-29	246	11	be	be	AUX
cbi-29	246	12	derived	derive	VERB
cbi-29	246	13	in	in	ADP
cbi-29	246	14	many	many	ADJ
cbi-29	246	15	ways	way	NOUN
cbi-29	246	16	.	.	PUNCT
cbi-29	247	1	the	the	DET
cbi-29	247	2	most	most	ADV
cbi-29	247	3	straightforward	straightforward	ADJ
cbi-29	247	4	is	be	AUX
cbi-29	247	5	to	to	PART
cbi-29	247	6	first	first	ADV
cbi-29	247	7	set	set	VERB
cbi-29	247	8	z	z	NOUN
cbi-29	247	9	=	=	PUNCT
cbi-29	247	10	uv	uv	NOUN
cbi-29	247	11	and	and	CCONJ
cbi-29	247	12	then	then	ADV
cbi-29	247	13	differentiate	differentiate	VERB
cbi-29	247	14	both	both	DET
cbi-29	247	15	sides	side	NOUN
cbi-29	247	16	using	use	VERB
cbi-29	247	17	logarithmic	logarithmic	ADJ
cbi-29	247	18	differentiation	differentiation	NOUN
cbi-29	247	19	(	(	PUNCT
cbi-29	247	20	logarithmic	logarithmic	ADJ
cbi-29	247	21	differentiation	differentiation	NOUN
cbi-29	247	22	is	be	AUX
cbi-29	247	23	useful	useful	ADJ
cbi-29	247	24	to	to	PART
cbi-29	247	25	prove	prove	VERB
cbi-29	247	26	the	the	DET
cbi-29	247	27	formula	formula	NOUN
cbi-29	247	28	for	for	ADP
cbi-29	247	29	uv	uv	NOUN
cbi-29	247	30	but	but	CCONJ
cbi-29	247	31	after	after	ADP
cbi-29	247	32	that	that	PRON
cbi-29	247	33	it	it	PRON
cbi-29	247	34	is	be	AUX
cbi-29	247	35	fairly	fairly	ADV
cbi-29	247	36	useless	useless	ADJ
cbi-29	247	37	because	because	SCONJ
cbi-29	247	38	you	you	PRON
cbi-29	247	39	can	can	AUX
cbi-29	247	40	just	just	ADV
cbi-29	247	41	apply	apply	VERB
cbi-29	247	42	the	the	DET
cbi-29	247	43	formula	formula	NOUN
cbi-29	247	44	)	)	PUNCT
cbi-29	247	45	.	.	PUNCT
cbi-29	248	1	doing	do	VERB
cbi-29	248	2	this	this	DET
cbi-29	248	3	yields	yield	NOUN
cbi-29	248	4	z	z	NOUN
cbi-29	248	5	=	=	SYM
cbi-29	248	6	uv	uv	NOUN
cbi-29	248	7	ln(z	ln(z	AUX
cbi-29	248	8	)	)	PUNCT
cbi-29	248	9	=	=	SYM
cbi-29	248	10	ln(uv	ln(uv	PROPN
cbi-29	248	11	)	)	PUNCT
cbi-29	248	12	ln(z	ln(z	VERB
cbi-29	248	13	)	)	PUNCT
cbi-29	249	1	=	=	SYM
cbi-29	249	2	v	v	NUM
cbi-29	249	3	ln(u	ln(u	NOUN
cbi-29	249	4	)	)	PUNCT
cbi-29	249	5	d(ln(z	d(ln(z	NOUN
cbi-29	249	6	)	)	PUNCT
cbi-29	249	7	)	)	PUNCT
cbi-29	250	1	=	=	PUNCT
cbi-29	250	2	d(v	d(v	ADJ
cbi-29	250	3	ln(u	ln(u	NOUN
cbi-29	250	4	)	)	PUNCT
cbi-29	250	5	)	)	PUNCT
cbi-29	250	6	1	1	NUM
cbi-29	250	7	z	z	NOUN
cbi-29	250	8	dz	dz	NOUN
cbi-29	250	9	=	=	PUNCT
cbi-29	250	10	v	v	PROPN
cbi-29	250	11	u	u	PROPN
cbi-29	250	12	du	du	X
cbi-29	250	13	+	+	CCONJ
cbi-29	250	14	ln(u)dv	ln(u)dv	ADJ
cbi-29	250	15	dz	dz	PROPN
cbi-29	250	16	=	=	SYM
cbi-29	250	17	zv	zv	PROPN
cbi-29	250	18	u	u	NOUN
cbi-29	250	19	du	du	PROPN
cbi-29	250	20	+	+	PROPN
cbi-29	250	21	z	z	PROPN
cbi-29	250	22	ln(u)dv	ln(u)dv	NOUN
cbi-29	250	23	dz	dz	PROPN
cbi-29	250	24	=	=	PUNCT
cbi-29	250	25	v	v	PROPN
cbi-29	250	26	uv	uv	NOUN
cbi-29	250	27	u	u	NOUN
cbi-29	250	28	du	du	X
cbi-29	250	29	+	+	X
cbi-29	250	30	ln(u	ln(u	X
cbi-29	250	31	)	)	PUNCT
cbi-29	250	32	uvdv	uvdv	ADJ
cbi-29	250	33	dz	dz	X
cbi-29	250	34	=	=	SYM
cbi-29	250	35	v	v	ADP
cbi-29	250	36	uv−1du	uv−1du	NUM
cbi-29	250	37	+	+	NUM
cbi-29	250	38	ln(u	ln(u	X
cbi-29	250	39	)	)	PUNCT
cbi-29	250	40	uvdv	uvdv	NOUN
cbi-29	250	41	this	this	PRON
cbi-29	250	42	is	be	AUX
cbi-29	250	43	a	a	DET
cbi-29	250	44	decent	decent	ADJ
cbi-29	250	45	proof	proof	NOUN
cbi-29	250	46	for	for	ADP
cbi-29	250	47	first	first	ADJ
cbi-29	250	48	-	-	PUNCT
cbi-29	250	49	year	year	NOUN
cbi-29	250	50	calculus	calculus	NOUN
cbi-29	250	51	.	.	PUNCT
cbi-29	251	1	however	however	ADV
cbi-29	251	2	,	,	PUNCT
cbi-29	251	3	a	a	DET
cbi-29	251	4	more	more	ADV
cbi-29	251	5	interesting	interesting	ADJ
cbi-29	251	6	proof	proof	NOUN
cbi-29	251	7	can	can	AUX
cbi-29	251	8	be	be	AUX
cbi-29	251	9	found	find	VERB
cbi-29	251	10	by	by	ADP
cbi-29	251	11	simply	simply	ADV
cbi-29	251	12	recognizing	recognize	VERB
cbi-29	251	13	that	that	SCONJ
cbi-29	251	14	a	a	DET
cbi-29	251	15	total	total	ADJ
cbi-29	251	16	differential	differential	NOUN
cbi-29	251	17	is	be	AUX
cbi-29	251	18	the	the	DET
cbi-29	251	19	sum	sum	NOUN
cbi-29	251	20	of	of	ADP
cbi-29	251	21	its	its	PRON
cbi-29	251	22	partials	partial	NOUN
cbi-29	251	23	.	.	PUNCT
cbi-29	252	1	so	so	ADV
cbi-29	252	2	,	,	PUNCT
cbi-29	252	3	the	the	DET
cbi-29	252	4	partial	partial	ADJ
cbi-29	252	5	differential	differential	NOUN
cbi-29	252	6	of	of	ADP
cbi-29	252	7	uv	uv	NOUN
cbi-29	252	8	with	with	ADP
cbi-29	252	9	v	v	NUM
cbi-29	252	10	kept	keep	VERB
cbi-29	252	11	constant	constant	ADJ
cbi-29	252	12	is	be	AUX
cbi-29	252	13	v	v	ADP
cbi-29	252	14	uv−1du	uv−1du	NUM
cbi-29	252	15	and	and	CCONJ
cbi-29	252	16	the	the	DET
cbi-29	252	17	partial	partial	ADJ
cbi-29	252	18	differential	differential	NOUN
cbi-29	252	19	of	of	ADP
cbi-29	252	20	uv	uv	NOUN
cbi-29	252	21	with	with	ADP
cbi-29	252	22	u	u	NOUN
cbi-29	252	23	kept	keep	VERB
cbi-29	252	24	constant	constant	ADJ
cbi-29	252	25	is	be	AUX
cbi-29	252	26	ln(u)uvdv	ln(u)uvdv	ADJ
cbi-29	252	27	.	.	PUNCT
cbi-29	253	1	therefore	therefore	ADV
cbi-29	253	2	,	,	PUNCT
cbi-29	253	3	the	the	DET
cbi-29	253	4	total	total	ADJ
cbi-29	253	5	differential	differential	NOUN
cbi-29	253	6	is	be	AUX
cbi-29	253	7	merely	merely	ADV
cbi-29	253	8	the	the	DET
cbi-29	253	9	sum	sum	NOUN
cbi-29	253	10	of	of	ADP
cbi-29	253	11	these	these	PRON
cbi-29	253	12	,	,	PUNCT
cbi-29	253	13	as	as	SCONJ
cbi-29	253	14	you	you	PRON
cbi-29	253	15	can	can	AUX
cbi-29	253	16	see	see	VERB
cbi-29	253	17	in	in	ADP
cbi-29	253	18	equation	equation	NOUN
cbi-29	253	19	6	6	NUM
cbi-29	253	20	.	.	PUNCT
cbi-29	254	1	probably	probably	ADV
cbi-29	254	2	due	due	ADP
cbi-29	254	3	to	to	ADP
cbi-29	254	4	its	its	PRON
cbi-29	254	5	rarity	rarity	NOUN
cbi-29	254	6	of	of	ADP
cbi-29	254	7	actually	actually	ADV
cbi-29	254	8	appearing	appear	VERB
cbi-29	254	9	in	in	ADP
cbi-29	254	10	textbooks	textbook	NOUN
cbi-29	254	11	,	,	PUNCT
cbi-29	254	12	this	this	DET
cbi-29	254	13	rule	rule	NOUN
cbi-29	254	14	has	have	AUX
cbi-29	254	15	been	be	AUX
cbi-29	254	16	given	give	VERB
cbi-29	254	17	a	a	DET
cbi-29	254	18	variety	variety	NOUN
cbi-29	254	19	of	of	ADP
cbi-29	254	20	names	name	NOUN
cbi-29	254	21	,	,	PUNCT
cbi-29	254	22	the	the	DET
cbi-29	254	23	4the	4the	NUM
cbi-29	254	24	process	process	NOUN
cbi-29	254	25	of	of	ADP
cbi-29	254	26	logarithmic	logarithmic	ADJ
cbi-29	254	27	differentiation	differentiation	NOUN
cbi-29	254	28	is	be	AUX
cbi-29	254	29	necessary	necessary	ADJ
cbi-29	254	30	in	in	ADP
cbi-29	254	31	the	the	DET
cbi-29	254	32	proof	proof	NOUN
cbi-29	254	33	of	of	ADP
cbi-29	254	34	some	some	DET
cbi-29	254	35	important	important	ADJ
cbi-29	254	36	rules	rule	NOUN
cbi-29	254	37	,	,	PUNCT
cbi-29	254	38	but	but	CCONJ
cbi-29	254	39	not	not	PART
cbi-29	254	40	in	in	ADP
cbi-29	254	41	their	their	PRON
cbi-29	254	42	usage	usage	NOUN
cbi-29	254	43	.	.	PUNCT
cbi-29	255	1	two	two	NUM
cbi-29	255	2	most	most	ADV
cbi-29	255	3	common	common	ADJ
cbi-29	255	4	being	be	AUX
cbi-29	255	5	the	the	DET
cbi-29	255	6	generalized	generalized	ADJ
cbi-29	255	7	power	power	NOUN
cbi-29	255	8	rule	rule	NOUN
cbi-29	255	9	and	and	CCONJ
cbi-29	255	10	the	the	DET
cbi-29	255	11	functional	functional	ADJ
cbi-29	255	12	power	power	NOUN
cbi-29	255	13	rule	rule	NOUN
cbi-29	255	14	.	.	PUNCT
cbi-29	256	1	logarithmic	logarithmic	ADJ
cbi-29	256	2	differentiation	differentiation	NOUN
cbi-29	256	3	does	do	AUX
cbi-29	256	4	have	have	VERB
cbi-29	256	5	some	some	DET
cbi-29	256	6	unique	unique	ADJ
cbi-29	256	7	uses	use	NOUN
cbi-29	256	8	,	,	PUNCT
cbi-29	256	9	but	but	CCONJ
cbi-29	256	10	these	these	PRON
cbi-29	256	11	are	be	AUX
cbi-29	256	12	mostly	mostly	ADV
cbi-29	256	13	upper	upper	ADJ
cbi-29	256	14	-	-	PUNCT
cbi-29	256	15	level	level	NOUN
cbi-29	256	16	ideas	idea	NOUN
cbi-29	256	17	.	.	PUNCT
cbi-29	257	1	for	for	ADP
cbi-29	257	2	instance	instance	NOUN
cbi-29	257	3	,	,	PUNCT
cbi-29	257	4	logarithmic	logarithmic	ADJ
cbi-29	257	5	differentiation	differentiation	NOUN
cbi-29	257	6	can	can	AUX
cbi-29	257	7	be	be	AUX
cbi-29	257	8	used	use	VERB
cbi-29	257	9	to	to	PART
cbi-29	257	10	convert	convert	VERB
cbi-29	257	11	products	product	NOUN
cbi-29	257	12	of	of	ADP
cbi-29	257	13	sequences	sequence	NOUN
cbi-29	257	14	(	(	PUNCT
cbi-29	257	15	which	which	PRON
cbi-29	257	16	are	be	AUX
cbi-29	257	17	difficult	difficult	ADJ
cbi-29	257	18	to	to	PART
cbi-29	257	19	integrate	integrate	VERB
cbi-29	257	20	)	)	PUNCT
cbi-29	257	21	into	into	ADP
cbi-29	257	22	a	a	DET
cbi-29	257	23	sum	sum	NOUN
cbi-29	257	24	of	of	ADP
cbi-29	257	25	sequences	sequence	NOUN
cbi-29	257	26	(	(	PUNCT
cbi-29	257	27	which	which	PRON
cbi-29	257	28	tend	tend	VERB
cbi-29	257	29	to	to	PART
cbi-29	257	30	be	be	AUX
cbi-29	257	31	easier	easy	ADJ
cbi-29	257	32	)	)	PUNCT
cbi-29	257	33	.	.	PUNCT
cbi-29	258	1	for	for	ADP
cbi-29	258	2	instance	instance	NOUN
cbi-29	258	3	,	,	PUNCT
cbi-29	258	4	logarithmic	logarithmic	ADJ
cbi-29	258	5	differentiation	differentiation	NOUN
cbi-29	258	6	allows	allow	VERB
cbi-29	258	7	us	we	PRON
cbi-29	258	8	to	to	PART
cbi-29	258	9	say	say	VERB
cbi-29	258	10	that	that	SCONJ
cbi-29	258	11	if	if	SCONJ
cbi-29	258	12	y	y	PROPN
cbi-29	258	13	=	=	SYM
cbi-29	258	14	n%	n%	PROPN
cbi-29	259	1	j=1	j=1	PROPN
cbi-29	259	2	f	f	PROPN
cbi-29	259	3	(	(	PUNCT
cbi-29	259	4	x	x	PROPN
cbi-29	259	5	,	,	PUNCT
cbi-29	259	6	j	j	PROPN
cbi-29	259	7	)	)	PUNCT
cbi-29	259	8	then	then	ADV
cbi-29	259	9	y′	y′	ADV
cbi-29	259	10	=	=	SYM
cbi-29	259	11	y	y	PROPN
cbi-29	259	12	n	n	CCONJ
cbi-29	259	13	&	&	CCONJ
cbi-29	259	14	j=1	j=1	PROPN
cbi-29	259	15	d(ln	d(ln	PROPN
cbi-29	259	16	(	(	PUNCT
cbi-29	259	17	f	f	PROPN
cbi-29	259	18	(	(	PUNCT
cbi-29	259	19	x	x	PROPN
cbi-29	259	20	,	,	PUNCT
cbi-29	259	21	j	j	NOUN
cbi-29	259	22	)	)	PUNCT
cbi-29	259	23	)	)	PUNCT
cbi-29	259	24	)	)	PUNCT
cbi-29	260	1	(	(	PUNCT
cbi-29	260	2	7	7	X
cbi-29	260	3	)	)	PUNCT
cbi-29	260	4	logarithmic	logarithmic	ADJ
cbi-29	260	5	differentiation	differentiation	NOUN
cbi-29	260	6	is	be	AUX
cbi-29	260	7	also	also	ADV
cbi-29	260	8	sometimes	sometimes	ADV
cbi-29	260	9	used	use	VERB
cbi-29	260	10	to	to	PART
cbi-29	260	11	simplify	simplify	VERB
cbi-29	260	12	complicated	complicated	ADJ
cbi-29	260	13	fractions	fraction	NOUN
cbi-29	260	14	,	,	PUNCT
cbi-29	260	15	exponents	exponent	NOUN
cbi-29	260	16	,	,	PUNCT
cbi-29	260	17	and	and	CCONJ
cbi-29	260	18	even	even	ADV
cbi-29	260	19	products	product	NOUN
cbi-29	260	20	,	,	PUNCT
cbi-29	260	21	but	but	CCONJ
cbi-29	260	22	,	,	PUNCT
cbi-29	260	23	since	since	SCONJ
cbi-29	260	24	there	there	PRON
cbi-29	260	25	are	be	VERB
cbi-29	260	26	already	already	ADV
cbi-29	260	27	rules	rule	NOUN
cbi-29	260	28	for	for	ADP
cbi-29	260	29	all	all	PRON
cbi-29	260	30	of	of	ADP
cbi-29	260	31	these	these	PRON
cbi-29	260	32	,	,	PUNCT
cbi-29	260	33	the	the	DET
cbi-29	260	34	“	"	PUNCT
cbi-29	260	35	simplification	simplification	NOUN
cbi-29	260	36	”	"	PUNCT
cbi-29	260	37	usually	usually	ADV
cbi-29	260	38	just	just	ADV
cbi-29	260	39	makes	make	VERB
cbi-29	260	40	learning	learn	VERB
cbi-29	260	41	the	the	DET
cbi-29	260	42	process	process	NOUN
cbi-29	260	43	more	more	ADV
cbi-29	260	44	difficult	difficult	ADJ
cbi-29	260	45	for	for	ADP
cbi-29	260	46	students	student	NOUN
cbi-29	260	47	.	.	PUNCT
cbi-29	261	1	students	student	NOUN
cbi-29	261	2	need	need	VERB
cbi-29	261	3	unified	unified	ADJ
cbi-29	261	4	processes	process	NOUN
cbi-29	261	5	more	more	ADJ
cbi-29	261	6	than	than	SCONJ
cbi-29	261	7	they	they	PRON
cbi-29	261	8	need	need	VERB
cbi-29	261	9	tricks	trick	NOUN
cbi-29	261	10	to	to	PART
cbi-29	261	11	make	make	VERB
cbi-29	261	12	things	thing	NOUN
cbi-29	261	13	easier	easy	ADJ
cbi-29	261	14	.	.	PUNCT
cbi-29	262	1	conceptual	conceptual	ADJ
cbi-29	262	2	simplicity	simplicity	NOUN
cbi-29	262	3	is	be	AUX
cbi-29	262	4	usually	usually	ADV
cbi-29	262	5	preferable	preferable	ADJ
cbi-29	262	6	to	to	ADP
cbi-29	262	7	speed	speed	NOUN
cbi-29	262	8	of	of	ADP
cbi-29	262	9	computation	computation	NOUN
cbi-29	262	10	.	.	PUNCT
cbi-29	263	1	10	10	NUM
cbi-29	263	2	hyperreals	hyperreal	NOUN
cbi-29	263	3	for	for	ADP
cbi-29	263	4	limit	limit	NOUN
cbi-29	263	5	analysis	analysis	NOUN
cbi-29	263	6	ϵ-δ	ϵ-δ	ADJ
cbi-29	263	7	proofs	proof	NOUN
cbi-29	263	8	have	have	AUX
cbi-29	263	9	long	long	ADV
cbi-29	263	10	been	be	AUX
cbi-29	263	11	the	the	DET
cbi-29	263	12	bane	bane	NOUN
cbi-29	263	13	of	of	ADP
cbi-29	263	14	calculus	calculus	NOUN
cbi-29	263	15	students	student	NOUN
cbi-29	263	16	.	.	PUNCT
cbi-29	264	1	while	while	SCONJ
cbi-29	264	2	they	they	PRON
cbi-29	264	3	do	do	AUX
cbi-29	264	4	present	present	VERB
cbi-29	264	5	an	an	DET
cbi-29	264	6	interesting	interesting	ADJ
cbi-29	264	7	mathematical	mathematical	ADJ
cbi-29	264	8	technique	technique	NOUN
cbi-29	264	9	,	,	PUNCT
cbi-29	264	10	the	the	DET
cbi-29	264	11	retention	retention	NOUN
cbi-29	264	12	rate	rate	NOUN
cbi-29	264	13	for	for	ADP
cbi-29	264	14	understanding	understand	VERB
cbi-29	264	15	ϵ-δ	ϵ-δ	PROPN
cbi-29	264	16	proofs	proof	NOUN
cbi-29	264	17	is	be	AUX
cbi-29	264	18	so	so	ADV
cbi-29	264	19	low	low	ADJ
cbi-29	264	20	as	as	SCONJ
cbi-29	264	21	to	to	PART
cbi-29	264	22	hardly	hardly	ADV
cbi-29	264	23	be	be	AUX
cbi-29	264	24	worth	worth	ADJ
cbi-29	264	25	doing	do	VERB
cbi-29	264	26	(	(	PUNCT
cbi-29	264	27	katz	katz	PROPN
cbi-29	264	28	and	and	CCONJ
cbi-29	264	29	polev	polev	NOUN
cbi-29	264	30	,	,	PUNCT
cbi-29	264	31	2017	2017	NUM
cbi-29	264	32	)	)	PUNCT
cbi-29	264	33	.	.	PUNCT
cbi-29	265	1	instead	instead	ADV
cbi-29	265	2	,	,	PUNCT
cbi-29	265	3	the	the	DET
cbi-29	265	4	method	method	NOUN
cbi-29	265	5	which	which	PRON
cbi-29	265	6	helps	help	VERB
cbi-29	265	7	students	student	NOUN
cbi-29	265	8	understand	understand	VERB
cbi-29	265	9	the	the	DET
cbi-29	265	10	process	process	NOUN
cbi-29	265	11	of	of	ADP
cbi-29	265	12	limits	limit	NOUN
cbi-29	265	13	the	the	DET
cbi-29	265	14	most	most	ADJ
cbi-29	265	15	is	be	AUX
cbi-29	265	16	to	to	PART
cbi-29	265	17	use	use	VERB
cbi-29	265	18	the	the	DET
cbi-29	265	19	hyperreal	hyperreal	ADJ
cbi-29	265	20	number	number	NOUN
cbi-29	265	21	line	line	NOUN
cbi-29	265	22	.	.	PUNCT
cbi-29	266	1	on	on	ADP
cbi-29	266	2	the	the	DET
cbi-29	266	3	hyperreal	hyperreal	ADJ
cbi-29	266	4	number	number	NOUN
cbi-29	266	5	line	line	NOUN
cbi-29	266	6	,	,	PUNCT
cbi-29	266	7	ϵ	ϵ	PROPN
cbi-29	266	8	is	be	AUX
cbi-29	266	9	the	the	DET
cbi-29	266	10	unit	unit	NOUN
cbi-29	266	11	of	of	ADP
cbi-29	266	12	the	the	DET
cbi-29	266	13	infinitesimal	infinitesimal	ADJ
cbi-29	266	14	(	(	PUNCT
cbi-29	266	15	not	not	PART
cbi-29	266	16	the	the	DET
cbi-29	266	17	same	same	ADJ
cbi-29	266	18	as	as	ADP
cbi-29	266	19	the	the	DET
cbi-29	266	20	ϵ	ϵ	NOUN
cbi-29	266	21	in	in	ADP
cbi-29	266	22	ϵ-δ	ϵ-δ	PROPN
cbi-29	266	23	proofs	proof	NOUN
cbi-29	266	24	)	)	PUNCT
cbi-29	266	25	.	.	PUNCT
cbi-29	267	1	to	to	PART
cbi-29	267	2	take	take	VERB
cbi-29	267	3	a	a	DET
cbi-29	267	4	righthanded	righthande	VERB
cbi-29	267	5	limit	limit	NOUN
cbi-29	267	6	,	,	PUNCT
cbi-29	267	7	the	the	DET
cbi-29	267	8	student	student	NOUN
cbi-29	267	9	merely	merely	ADV
cbi-29	267	10	replaces	replace	VERB
cbi-29	267	11	x	x	PUNCT
cbi-29	267	12	with	with	ADP
cbi-29	267	13	x	x	PROPN
cbi-29	268	1	+	+	CCONJ
cbi-29	268	2	ϵ	ϵ	X
cbi-29	268	3	everywhere	everywhere	ADV
cbi-29	268	4	it	it	PRON
cbi-29	268	5	occurs	occur	VERB
cbi-29	268	6	in	in	ADP
cbi-29	268	7	the	the	DET
cbi-29	268	8	expression	expression	NOUN
cbi-29	268	9	.	.	PUNCT
cbi-29	269	1	this	this	PRON
cbi-29	269	2	“	"	PUNCT
cbi-29	269	3	looks	look	VERB
cbi-29	269	4	at	at	ADP
cbi-29	269	5	”	"	PUNCT
cbi-29	269	6	the	the	DET
cbi-29	269	7	function	function	NOUN
cbi-29	269	8	immediately	immediately	ADV
cbi-29	269	9	to	to	ADP
cbi-29	269	10	the	the	DET
cbi-29	269	11	right	right	NOUN
cbi-29	269	12	of	of	ADP
cbi-29	269	13	the	the	DET
cbi-29	269	14	point	point	NOUN
cbi-29	269	15	in	in	ADP
cbi-29	269	16	question	question	NOUN
cbi-29	269	17	—	—	PUNCT
cbi-29	269	18	an	an	DET
cbi-29	269	19	infinitely	infinitely	ADV
cbi-29	269	20	small	small	ADJ
cbi-29	269	21	step	step	NOUN
cbi-29	269	22	to	to	ADP
cbi-29	269	23	the	the	DET
cbi-29	269	24	right	right	NOUN
cbi-29	269	25	.	.	PUNCT
cbi-29	270	1	the	the	DET
cbi-29	270	2	left	left	ADV
cbi-29	270	3	-	-	PUNCT
cbi-29	270	4	handed	hand	VERB
cbi-29	270	5	limit	limit	NOUN
cbi-29	270	6	is	be	AUX
cbi-29	270	7	found	find	VERB
cbi-29	270	8	by	by	ADP
cbi-29	270	9	subtracting	subtract	VERB
cbi-29	270	10	ϵ	ϵ	X
cbi-29	270	11	.	.	PUNCT
cbi-29	271	1	as	as	ADP
cbi-29	271	2	an	an	DET
cbi-29	271	3	example	example	NOUN
cbi-29	271	4	,	,	PUNCT
cbi-29	271	5	the	the	DET
cbi-29	271	6	expression	expression	NOUN
cbi-29	271	7	x2−25	x2−25	PROPN
cbi-29	272	1	x−5	x−5	PROPN
cbi-29	272	2	can	can	AUX
cbi-29	272	3	not	not	PART
cbi-29	272	4	be	be	AUX
cbi-29	272	5	evaluated	evaluate	VERB
cbi-29	272	6	at	at	ADP
cbi-29	272	7	x	x	X
cbi-29	272	8	=	=	SYM
cbi-29	272	9	5	5	NUM
cbi-29	272	10	because	because	SCONJ
cbi-29	272	11	it	it	PRON
cbi-29	272	12	results	result	VERB
cbi-29	272	13	in	in	ADP
cbi-29	272	14	a	a	DET
cbi-29	272	15	zero	zero	NUM
cbi-29	272	16	in	in	ADP
cbi-29	272	17	the	the	DET
cbi-29	272	18	denominator	denominator	NOUN
cbi-29	272	19	.	.	PUNCT
cbi-29	273	1	however	however	ADV
cbi-29	273	2	,	,	PUNCT
cbi-29	273	3	any	any	DET
cbi-29	273	4	value	value	NOUN
cbi-29	273	5	except	except	SCONJ
cbi-29	273	6	5	5	NUM
cbi-29	273	7	will	will	AUX
cbi-29	273	8	work	work	VERB
cbi-29	273	9	.	.	PUNCT
cbi-29	274	1	therefore	therefore	ADV
cbi-29	274	2	,	,	PUNCT
cbi-29	274	3	if	if	SCONJ
cbi-29	274	4	we	we	PRON
cbi-29	274	5	bump	bump	VERB
cbi-29	274	6	x	x	PUNCT
cbi-29	274	7	an	an	DET
cbi-29	274	8	infinitely	infinitely	ADV
cbi-29	274	9	small	small	ADJ
cbi-29	274	10	amount	amount	NOUN
cbi-29	274	11	to	to	ADP
cbi-29	274	12	the	the	DET
cbi-29	274	13	right	right	NOUN
cbi-29	274	14	,	,	PUNCT
cbi-29	274	15	the	the	DET
cbi-29	274	16	divideby	divideby	NOUN
cbi-29	274	17	-	-	PUNCT
cbi-29	274	18	zero	zero	NUM
cbi-29	274	19	problem	problem	NOUN
cbi-29	274	20	will	will	AUX
cbi-29	274	21	no	no	ADV
cbi-29	274	22	longer	long	ADV
cbi-29	274	23	exist	exist	VERB
cbi-29	274	24	.	.	PUNCT
cbi-29	275	1	therefore	therefore	ADV
cbi-29	275	2	,	,	PUNCT
cbi-29	275	3	to	to	PART
cbi-29	275	4	find	find	VERB
cbi-29	275	5	24	24	NUM
cbi-29	275	6	simplifying	simplifying	NOUN
cbi-29	275	7	and	and	CCONJ
cbi-29	275	8	refactoring	refactoring	NOUN
cbi-29	275	9	introductory	introductory	PROPN
cbi-29	275	10	calculus	calculus	PROPN
cbi-29	275	11	lim	lim	PROPN
cbi-29	275	12	x→5	x→5	PROPN
cbi-29	275	13	+	+	CCONJ
cbi-29	275	14	x2−25	x2−25	PROPN
cbi-29	275	15	x−5	x−5	PROPN
cbi-29	275	16	,	,	PUNCT
cbi-29	275	17	we	we	PRON
cbi-29	275	18	merely	merely	ADV
cbi-29	275	19	replace	replace	VERB
cbi-29	275	20	x	x	PUNCT
cbi-29	275	21	with	with	ADP
cbi-29	275	22	x	x	PROPN
cbi-29	276	1	+	+	ADP
cbi-29	276	2	ϵ	ϵ	X
cbi-29	276	3	.	.	PUNCT
cbi-29	277	1	this	this	DET
cbi-29	277	2	yields	yield	VERB
cbi-29	277	3	lim	lim	PROPN
cbi-29	277	4	x→5	x→5	PROPN
cbi-29	278	1	+	+	PROPN
cbi-29	279	1	x2	x2	PROPN
cbi-29	280	1	−	−	PROPN
cbi-29	281	1	25	25	NUM
cbi-29	281	2	x	x	SYM
cbi-29	281	3	−	−	PROPN
cbi-29	281	4	5	5	NUM
cbi-29	281	5	=	=	SYM
cbi-29	281	6	(	(	PUNCT
cbi-29	281	7	x	x	PROPN
cbi-29	281	8	+	+	NUM
cbi-29	281	9	ϵ	ϵ	X
cbi-29	281	10	)	)	PUNCT
cbi-29	281	11	2	2	NUM
cbi-29	281	12	−	−	PROPN
cbi-29	281	13	25	25	NUM
cbi-29	281	14	x	x	SYM
cbi-29	281	15	+	+	ADP
cbi-29	282	1	ϵ	ϵ	X
cbi-29	282	2	−	−	PROPN
cbi-29	282	3	5	5	NUM
cbi-29	282	4	=	=	SYM
cbi-29	282	5	x2	x2	PROPN
cbi-29	283	1	+	+	NUM
cbi-29	283	2	2xϵ	2xϵ	NOUN
cbi-29	283	3	+	+	CCONJ
cbi-29	283	4	ϵ2	ϵ2	ADJ
cbi-29	283	5	−	−	NUM
cbi-29	283	6	25	25	NUM
cbi-29	283	7	x	x	SYM
cbi-29	284	1	+	+	ADP
cbi-29	285	1	ϵ	ϵ	X
cbi-29	285	2	−	−	PROPN
cbi-29	285	3	5	5	NUM
cbi-29	285	4	=	=	SYM
cbi-29	285	5	(	(	PUNCT
cbi-29	285	6	5)2	5)2	NUM
cbi-29	285	7	+	+	SYM
cbi-29	285	8	2(5)ϵ	2(5)ϵ	NUM
cbi-29	285	9	+	+	CCONJ
cbi-29	285	10	ϵ2	ϵ2	ADJ
cbi-29	285	11	−	−	PROPN
cbi-29	285	12	25	25	NUM
cbi-29	285	13	(	(	PUNCT
cbi-29	285	14	5	5	NUM
cbi-29	285	15	)	)	PUNCT
cbi-29	285	16	+	+	CCONJ
cbi-29	286	1	ϵ	ϵ	DET
cbi-29	286	2	−	−	NOUN
cbi-29	286	3	5	5	NUM
cbi-29	286	4	=	=	SYM
cbi-29	286	5	25	25	NUM
cbi-29	286	6	+	+	NUM
cbi-29	286	7	10ϵ	10ϵ	NOUN
cbi-29	286	8	+	+	CCONJ
cbi-29	286	9	ϵ2	ϵ2	ADJ
cbi-29	286	10	−	−	PROPN
cbi-29	286	11	25	25	NUM
cbi-29	286	12	ϵ	ϵ	NOUN
cbi-29	286	13	=	=	SYM
cbi-29	286	14	10	10	NUM
cbi-29	287	1	+	+	CCONJ
cbi-29	287	2	ϵ	ϵ	ADP
cbi-29	287	3	this	this	PRON
cbi-29	287	4	is	be	AUX
cbi-29	287	5	infinitely	infinitely	ADV
cbi-29	287	6	close	close	ADJ
cbi-29	287	7	to	to	ADP
cbi-29	287	8	10	10	NUM
cbi-29	287	9	.	.	PUNCT
cbi-29	288	1	therefore	therefore	ADV
cbi-29	288	2	,	,	PUNCT
cbi-29	288	3	the	the	DET
cbi-29	288	4	limit	limit	NOUN
cbi-29	288	5	is	be	AUX
cbi-29	288	6	10	10	NUM
cbi-29	288	7	.	.	PUNCT
cbi-29	289	1	additionally	additionally	ADV
cbi-29	289	2	,	,	PUNCT
cbi-29	289	3	i	i	PRON
cbi-29	289	4	have	have	AUX
cbi-29	289	5	found	find	VERB
cbi-29	289	6	from	from	ADP
cbi-29	289	7	experience	experience	NOUN
cbi-29	289	8	that	that	SCONJ
cbi-29	289	9	limits	limit	NOUN
cbi-29	289	10	are	be	AUX
cbi-29	289	11	best	well	ADV
cbi-29	289	12	taught	teach	VERB
cbi-29	289	13	at	at	ADP
cbi-29	289	14	the	the	DET
cbi-29	289	15	end	end	NOUN
cbi-29	289	16	of	of	ADP
cbi-29	289	17	a	a	DET
cbi-29	289	18	year	year	NOUN
cbi-29	289	19	of	of	ADP
cbi-29	289	20	calculus	calculus	NOUN
cbi-29	289	21	rather	rather	ADV
cbi-29	289	22	than	than	ADP
cbi-29	289	23	at	at	ADP
cbi-29	289	24	the	the	DET
cbi-29	289	25	beginning	beginning	NOUN
cbi-29	289	26	.	.	PUNCT
cbi-29	290	1	teaching	teach	VERB
cbi-29	290	2	about	about	ADP
cbi-29	290	3	hyperreal	hyperreal	ADJ
cbi-29	290	4	numbers	number	NOUN
cbi-29	290	5	and	and	CCONJ
cbi-29	290	6	then	then	ADV
cbi-29	290	7	using	use	VERB
cbi-29	290	8	them	they	PRON
cbi-29	290	9	in	in	ADP
cbi-29	290	10	limits	limit	NOUN
cbi-29	290	11	provides	provide	VERB
cbi-29	290	12	a	a	DET
cbi-29	290	13	good	good	ADJ
cbi-29	290	14	way	way	NOUN
cbi-29	290	15	to	to	PART
cbi-29	290	16	make	make	VERB
cbi-29	290	17	many	many	ADJ
cbi-29	290	18	of	of	ADP
cbi-29	290	19	the	the	DET
cbi-29	290	20	intuitions	intuition	NOUN
cbi-29	290	21	developed	develop	VERB
cbi-29	290	22	over	over	ADP
cbi-29	290	23	the	the	DET
cbi-29	290	24	first	first	ADJ
cbi-29	290	25	year	year	NOUN
cbi-29	290	26	of	of	ADP
cbi-29	290	27	calculus	calculus	NOUN
cbi-29	290	28	more	more	ADV
cbi-29	290	29	rigorous	rigorous	ADJ
cbi-29	290	30	.	.	PUNCT
cbi-29	291	1	11	11	NUM
cbi-29	292	1	the	the	DET
cbi-29	292	2	integral	integral	ADJ
cbi-29	292	3	as	as	ADP
cbi-29	292	4	an	an	DET
cbi-29	292	5	infinite	infinite	ADJ
cbi-29	292	6	sum	sum	NOUN
cbi-29	292	7	one	one	NUM
cbi-29	292	8	more	more	ADJ
cbi-29	292	9	change	change	NOUN
cbi-29	292	10	that	that	PRON
cbi-29	292	11	improves	improve	VERB
cbi-29	292	12	calculus	calculus	NOUN
cbi-29	292	13	for	for	ADP
cbi-29	292	14	first	first	ADJ
cbi-29	292	15	-	-	PUNCT
cbi-29	292	16	year	year	NOUN
cbi-29	292	17	students	student	NOUN
cbi-29	292	18	is	be	AUX
cbi-29	292	19	redefining	redefine	VERB
cbi-29	292	20	the	the	DET
cbi-29	292	21	integral	integral	ADJ
cbi-29	292	22	from	from	ADP
cbi-29	292	23	an	an	DET
cbi-29	292	24	area	area	NOUN
cbi-29	292	25	to	to	ADP
cbi-29	292	26	an	an	DET
cbi-29	292	27	infinite	infinite	ADJ
cbi-29	292	28	sum	sum	NOUN
cbi-29	292	29	.	.	PUNCT
cbi-29	293	1	this	this	PRON
cbi-29	293	2	is	be	AUX
cbi-29	293	3	a	a	DET
cbi-29	293	4	very	very	ADV
cbi-29	293	5	subtle	subtle	ADJ
cbi-29	293	6	difference	difference	NOUN
cbi-29	293	7	,	,	PUNCT
cbi-29	293	8	but	but	CCONJ
cbi-29	293	9	one	one	NUM
cbi-29	293	10	that	that	PRON
cbi-29	293	11	i	i	PRON
cbi-29	293	12	have	have	AUX
cbi-29	293	13	found	find	VERB
cbi-29	293	14	to	to	PART
cbi-29	293	15	be	be	AUX
cbi-29	293	16	important	important	ADJ
cbi-29	293	17	.	.	PUNCT
cbi-29	294	1	finding	find	VERB
cbi-29	294	2	the	the	DET
cbi-29	294	3	area	area	NOUN
cbi-29	294	4	under	under	ADP
cbi-29	294	5	a	a	DET
cbi-29	294	6	curve	curve	NOUN
cbi-29	294	7	is	be	AUX
cbi-29	294	8	one	one	NUM
cbi-29	294	9	particular	particular	ADJ
cbi-29	294	10	usage	usage	NOUN
cbi-29	294	11	of	of	ADP
cbi-29	294	12	the	the	DET
cbi-29	294	13	integral	integral	NOUN
cbi-29	294	14	.	.	PUNCT
cbi-29	295	1	however	however	ADV
cbi-29	295	2	,	,	PUNCT
cbi-29	295	3	more	more	ADV
cbi-29	295	4	generally	generally	ADV
cbi-29	295	5	,	,	PUNCT
cbi-29	295	6	the	the	DET
cbi-29	295	7	integral	integral	NOUN
cbi-29	295	8	is	be	AUX
cbi-29	295	9	used	use	VERB
cbi-29	295	10	as	as	ADP
cbi-29	295	11	a	a	DET
cbi-29	295	12	tool	tool	NOUN
cbi-29	295	13	of	of	ADP
cbi-29	295	14	summation	summation	NOUN
cbi-29	295	15	.	.	PUNCT
cbi-29	296	1	using	use	VERB
cbi-29	296	2	the	the	DET
cbi-29	296	3	idea	idea	NOUN
cbi-29	296	4	of	of	ADP
cbi-29	296	5	the	the	DET
cbi-29	296	6	integral	integral	ADJ
cbi-29	296	7	as	as	ADP
cbi-29	296	8	a	a	DET
cbi-29	296	9	tool	tool	NOUN
cbi-29	296	10	of	of	ADP
cbi-29	296	11	summation	summation	NOUN
cbi-29	296	12	helps	help	VERB
cbi-29	296	13	explain	explain	VERB
cbi-29	296	14	the	the	DET
cbi-29	296	15	usage	usage	NOUN
cbi-29	296	16	of	of	ADP
cbi-29	296	17	the	the	DET
cbi-29	296	18	integral	integral	ADJ
cbi-29	296	19	as	as	ADP
cbi-29	296	20	the	the	DET
cbi-29	296	21	area	area	NOUN
cbi-29	296	22	under	under	ADP
cbi-29	296	23	the	the	DET
cbi-29	296	24	curve	curve	NOUN
cbi-29	296	25	,	,	PUNCT
cbi-29	296	26	but	but	CCONJ
cbi-29	296	27	the	the	DET
cbi-29	296	28	converse	converse	NOUN
cbi-29	296	29	is	be	AUX
cbi-29	296	30	not	not	PART
cbi-29	296	31	true	true	ADJ
cbi-29	296	32	—	—	PUNCT
cbi-29	296	33	explaining	explain	VERB
cbi-29	296	34	the	the	DET
cbi-29	296	35	integral	integral	ADJ
cbi-29	296	36	as	as	ADP
cbi-29	296	37	the	the	DET
cbi-29	296	38	area	area	NOUN
cbi-29	296	39	under	under	ADP
cbi-29	296	40	the	the	DET
cbi-29	296	41	curve	curve	NOUN
cbi-29	296	42	does	do	AUX
cbi-29	296	43	not	not	PART
cbi-29	296	44	help	help	VERB
cbi-29	296	45	students	student	NOUN
cbi-29	296	46	imagine	imagine	VERB
cbi-29	296	47	other	other	ADJ
cbi-29	296	48	uses	use	NOUN
cbi-29	296	49	of	of	ADP
cbi-29	296	50	the	the	DET
cbi-29	296	51	integral	integral	ADJ
cbi-29	296	52	such	such	ADJ
cbi-29	296	53	as	as	ADP
cbi-29	296	54	arc	arc	NOUN
cbi-29	296	55	lengths	length	NOUN
cbi-29	296	56	and	and	CCONJ
cbi-29	296	57	volumes	volume	NOUN
cbi-29	296	58	of	of	ADP
cbi-29	296	59	revolution	revolution	NOUN
cbi-29	296	60	.	.	PUNCT
cbi-29	297	1	when	when	SCONJ
cbi-29	297	2	the	the	DET
cbi-29	297	3	integral	integral	ADJ
cbi-29	297	4	is	be	AUX
cbi-29	297	5	defined	define	VERB
cbi-29	297	6	as	as	ADP
cbi-29	297	7	an	an	DET
cbi-29	297	8	infinite	infinite	ADJ
cbi-29	297	9	sum	sum	NOUN
cbi-29	297	10	of	of	ADP
cbi-29	297	11	infinitely	infinitely	ADV
cbi-29	297	12	small	small	ADJ
cbi-29	297	13	pieces	piece	NOUN
cbi-29	297	14	,	,	PUNCT
cbi-29	297	15	then	then	ADV
cbi-29	297	16	it	it	PRON
cbi-29	297	17	is	be	AUX
cbi-29	297	18	straightforward	straightforward	ADJ
cbi-29	297	19	to	to	PART
cbi-29	297	20	then	then	ADV
cbi-29	297	21	say	say	VERB
cbi-29	297	22	that	that	SCONJ
cbi-29	297	23	what	what	PRON
cbi-29	297	24	is	be	AUX
cbi-29	297	25	to	to	ADP
cbi-29	297	26	the	the	DET
cbi-29	297	27	right	right	NOUN
cbi-29	297	28	of	of	ADP
cbi-29	297	29	the	the	DET
cbi-29	297	30	integral	integral	ADJ
cbi-29	297	31	defines	define	NOUN
cbi-29	297	32	what	what	PRON
cbi-29	297	33	each	each	DET
cbi-29	297	34	individual	individual	ADJ
cbi-29	297	35	small	small	ADJ
cbi-29	297	36	piece	piece	NOUN
cbi-29	297	37	that	that	SCONJ
cbi-29	297	38	we	we	PRON
cbi-29	297	39	are	be	AUX
cbi-29	297	40	adding	add	VERB
cbi-29	297	41	together	together	ADV
cbi-29	297	42	looks	look	VERB
cbi-29	297	43	like	like	ADP
cbi-29	297	44	.	.	PUNCT
cbi-29	298	1	figure	figure	NOUN
cbi-29	298	2	1	1	NUM
cbi-29	298	3	lists	list	NOUN
cbi-29	298	4	several	several	ADJ
cbi-29	298	5	different	different	ADJ
cbi-29	298	6	sorts	sort	NOUN
cbi-29	298	7	of	of	ADP
cbi-29	298	8	things	thing	NOUN
cbi-29	298	9	we	we	PRON
cbi-29	298	10	can	can	AUX
cbi-29	298	11	add	add	VERB
cbi-29	298	12	together	together	ADV
cbi-29	298	13	using	use	VERB
cbi-29	298	14	integrals	integral	NOUN
cbi-29	298	15	.	.	PUNCT
cbi-29	299	1	in	in	ADP
cbi-29	299	2	each	each	PRON
cbi-29	299	3	of	of	ADP
cbi-29	299	4	these	these	PRON
cbi-29	299	5	,	,	PUNCT
cbi-29	299	6	the	the	DET
cbi-29	299	7	integral	integral	NOUN
cbi-29	299	8	represents	represent	VERB
cbi-29	299	9	the	the	DET
cbi-29	299	10	infinite	infinite	ADJ
cbi-29	299	11	sum	sum	NOUN
cbi-29	299	12	of	of	ADP
cbi-29	299	13	well	well	ADV
cbi-29	299	14	-	-	PUNCT
cbi-29	299	15	defined	define	VERB
cbi-29	299	16	infinitely	infinitely	ADV
cbi-29	299	17	small	small	ADJ
cbi-29	299	18	objects	object	NOUN
cbi-29	299	19	.	.	PUNCT
cbi-29	300	1	if	if	SCONJ
cbi-29	300	2	the	the	DET
cbi-29	300	3	integral	integral	ADJ
cbi-29	300	4	is	be	AUX
cbi-29	300	5	defined	define	VERB
cbi-29	300	6	as	as	ADP
cbi-29	300	7	an	an	DET
cbi-29	300	8	infinite	infinite	ADJ
cbi-29	300	9	sum	sum	NOUN
cbi-29	300	10	,	,	PUNCT
cbi-29	300	11	this	this	PRON
cbi-29	300	12	makes	make	VERB
cbi-29	300	13	an	an	DET
cbi-29	300	14	intuitive	intuitive	ADJ
cbi-29	300	15	connection	connection	NOUN
cbi-29	300	16	for	for	ADP
cbi-29	300	17	the	the	DET
cbi-29	300	18	student	student	NOUN
cbi-29	300	19	.	.	PUNCT
cbi-29	301	1	however	however	ADV
cbi-29	301	2	,	,	PUNCT
cbi-29	301	3	if	if	SCONJ
cbi-29	301	4	the	the	DET
cbi-29	301	5	integral	integral	ADJ
cbi-29	301	6	is	be	AUX
cbi-29	301	7	defined	define	VERB
cbi-29	301	8	as	as	ADP
cbi-29	301	9	the	the	DET
cbi-29	301	10	area	area	NOUN
cbi-29	301	11	under	under	ADP
cbi-29	301	12	the	the	DET
cbi-29	301	13	curve	curve	NOUN
cbi-29	301	14	,	,	PUNCT
cbi-29	301	15	jumping	jump	VERB
cbi-29	301	16	out	out	ADP
cbi-29	301	17	of	of	ADP
cbi-29	301	18	this	this	PRON
cbi-29	301	19	to	to	PART
cbi-29	301	20	understand	understand	VERB
cbi-29	301	21	how	how	SCONJ
cbi-29	301	22	the	the	DET
cbi-29	301	23	area	area	NOUN
cbi-29	301	24	under	under	ADP
cbi-29	301	25	the	the	DET
cbi-29	301	26	curve	curve	NOUN
cbi-29	301	27	can	can	AUX
cbi-29	301	28	be	be	AUX
cbi-29	301	29	reconfigured	reconfigure	VERB
cbi-29	301	30	as	as	ADP
cbi-29	301	31	one	one	NUM
cbi-29	301	32	of	of	ADP
cbi-29	301	33	the	the	DET
cbi-29	301	34	other	other	ADJ
cbi-29	301	35	operations	operation	NOUN
cbi-29	301	36	is	be	AUX
cbi-29	301	37	quite	quite	ADV
cbi-29	301	38	confusing	confusing	ADJ
cbi-29	301	39	.	.	PUNCT
cbi-29	302	1	additionally	additionally	ADV
cbi-29	302	2	,	,	PUNCT
cbi-29	302	3	defining	define	VERB
cbi-29	302	4	the	the	DET
cbi-29	302	5	integral	integral	ADJ
cbi-29	302	6	as	as	ADP
cbi-29	302	7	an	an	DET
cbi-29	302	8	infinite	infinite	ADJ
cbi-29	302	9	sum	sum	NOUN
cbi-29	302	10	allows	allow	VERB
cbi-29	302	11	for	for	SCONJ
cbi-29	302	12	the	the	DET
cbi-29	302	13	integral	integral	ADJ
cbi-29	302	14	to	to	PART
cbi-29	302	15	be	be	AUX
cbi-29	302	16	more	more	ADV
cbi-29	302	17	easily	easily	ADV
cbi-29	302	18	defined	define	VERB
cbi-29	302	19	in	in	ADP
cbi-29	302	20	multivariable	multivariable	ADJ
cbi-29	302	21	situations	situation	NOUN
cbi-29	302	22	.	.	PUNCT
cbi-29	303	1	the	the	DET
cbi-29	303	2	reason	reason	NOUN
cbi-29	303	3	for	for	ADP
cbi-29	303	4	this	this	PRON
cbi-29	303	5	is	be	AUX
cbi-29	303	6	that	that	SCONJ
cbi-29	303	7	,	,	PUNCT
cbi-29	303	8	as	as	ADP
cbi-29	303	9	an	an	DET
cbi-29	303	10	infinite	infinite	ADJ
cbi-29	303	11	sum	sum	NOUN
cbi-29	303	12	,	,	PUNCT
cbi-29	303	13	the	the	DET
cbi-29	303	14	integral	integral	NOUN
cbi-29	303	15	is	be	AUX
cbi-29	303	16	adding	add	VERB
cbi-29	303	17	up	up	ADP
cbi-29	303	18	all	all	PRON
cbi-29	303	19	of	of	ADP
cbi-29	303	20	the	the	DET
cbi-29	303	21	differences	difference	NOUN
cbi-29	303	22	that	that	PRON
cbi-29	303	23	occur	occur	VERB
cbi-29	303	24	into	into	ADP
cbi-29	303	25	a	a	DET
cbi-29	303	26	total	total	ADJ
cbi-29	303	27	difference	difference	NOUN
cbi-29	303	28	.	.	PUNCT
cbi-29	304	1	this	this	PRON
cbi-29	304	2	works	work	VERB
cbi-29	304	3	just	just	ADV
cbi-29	304	4	a	a	DET
cbi-29	304	5	straightforwardly	straightforwardly	ADV
cbi-29	304	6	for	for	ADP
cbi-29	304	7	multivariable	multivariable	ADJ
cbi-29	304	8	differentials	differential	NOUN
cbi-29	304	9	as	as	SCONJ
cbi-29	304	10	it	it	PRON
cbi-29	304	11	does	do	VERB
cbi-29	304	12	for	for	ADP
cbi-29	304	13	single	single	ADJ
cbi-29	304	14	variable	variable	ADJ
cbi-29	304	15	differentials	differential	NOUN
cbi-29	304	16	.	.	PUNCT
cbi-29	305	1	for	for	ADP
cbi-29	305	2	instance	instance	NOUN
cbi-29	305	3	,	,	PUNCT
cbi-29	305	4	let	let	VERB
cbi-29	305	5	’s	’s	PRON
cbi-29	305	6	say	say	VERB
cbi-29	305	7	we	we	PRON
cbi-29	305	8	have	have	VERB
cbi-29	305	9	the	the	DET
cbi-29	305	10	equation	equation	NOUN
cbi-29	305	11	dz	dz	NOUN
cbi-29	305	12	=	=	PUNCT
cbi-29	305	13	dy	dy	PROPN
cbi-29	305	14	+	+	X
cbi-29	305	15	dx	dx	PROPN
cbi-29	305	16	.	.	PUNCT
cbi-29	306	1	the	the	DET
cbi-29	306	2	integral	integral	ADJ
cbi-29	306	3	of	of	ADP
cbi-29	306	4	this	this	PRON
cbi-29	306	5	is	be	AUX
cbi-29	306	6	just	just	ADV
cbi-29	306	7	z	z	NOUN
cbi-29	306	8	=	=	SYM
cbi-29	306	9	y	y	PROPN
cbi-29	306	10	+	+	NUM
cbi-29	306	11	x	x	PROPN
cbi-29	306	12	+	+	CCONJ
cbi-29	306	13	c.	c.	NOUN
cbi-29	306	14	as	as	ADP
cbi-29	306	15	an	an	DET
cbi-29	306	16	“	"	PUNCT
cbi-29	306	17	area	area	NOUN
cbi-29	306	18	under	under	ADP
cbi-29	306	19	the	the	DET
cbi-29	306	20	curve	curve	NOUN
cbi-29	306	21	”	"	PUNCT
cbi-29	306	22	this	this	PRON
cbi-29	306	23	makes	make	VERB
cbi-29	306	24	no	no	DET
cbi-29	306	25	sense	sense	NOUN
cbi-29	306	26	.	.	PUNCT
cbi-29	307	1	however	however	ADV
cbi-29	307	2	,	,	PUNCT
cbi-29	307	3	as	as	ADP
cbi-29	307	4	an	an	DET
cbi-29	307	5	“	"	PUNCT
cbi-29	307	6	infinite	infinite	ADJ
cbi-29	307	7	sum	sum	NOUN
cbi-29	307	8	”	"	PUNCT
cbi-29	307	9	this	this	PRON
cbi-29	307	10	makes	make	VERB
cbi-29	307	11	perfect	perfect	ADJ
cbi-29	307	12	sense	sense	NOUN
cbi-29	307	13	.	.	PUNCT
cbi-29	308	1	if	if	SCONJ
cbi-29	308	2	dz	dz	PROPN
cbi-29	308	3	represents	represent	VERB
cbi-29	308	4	the	the	DET
cbi-29	308	5	sum	sum	NOUN
cbi-29	308	6	of	of	ADP
cbi-29	308	7	dy	dy	NOUN
cbi-29	308	8	+	+	X
cbi-29	308	9	dx	dx	PROPN
cbi-29	308	10	,	,	PUNCT
cbi-29	308	11	then	then	ADV
cbi-29	308	12	the	the	DET
cbi-29	308	13	total	total	ADJ
cbi-29	308	14	sum	sum	NOUN
cbi-29	308	15	will	will	AUX
cbi-29	308	16	be	be	AUX
cbi-29	308	17	the	the	DET
cbi-29	308	18	difference	difference	NOUN
cbi-29	308	19	of	of	ADP
cbi-29	308	20	y+	y+	NUM
cbi-29	308	21	x+c	x+c	PROPN
cbi-29	308	22	evaluated	evaluate	VERB
cbi-29	308	23	at	at	ADP
cbi-29	308	24	two	two	NUM
cbi-29	308	25	points	point	NOUN
cbi-29	308	26	.	.	PUNCT
cbi-29	309	1	so	so	ADV
cbi-29	309	2	,	,	PUNCT
cbi-29	309	3	traveling	travel	VERB
cbi-29	309	4	from	from	ADP
cbi-29	309	5	x	x	PROPN
cbi-29	309	6	=	=	SYM
cbi-29	309	7	2	2	NUM
cbi-29	309	8	,	,	PUNCT
cbi-29	309	9	y	y	PROPN
cbi-29	309	10	=	=	NOUN
cbi-29	309	11	3	3	NUM
cbi-29	309	12	to	to	ADP
cbi-29	309	13	x	x	SYM
cbi-29	309	14	=	=	SYM
cbi-29	309	15	7	7	NUM
cbi-29	309	16	,	,	PUNCT
cbi-29	309	17	y	y	PROPN
cbi-29	309	18	=	=	NOUN
cbi-29	309	19	4	4	NUM
cbi-29	309	20	will	will	AUX
cbi-29	309	21	give	give	VERB
cbi-29	309	22	a	a	DET
cbi-29	309	23	sum	sum	NOUN
cbi-29	309	24	total	total	NOUN
cbi-29	309	25	of	of	ADP
cbi-29	309	26	(	(	PUNCT
cbi-29	309	27	7	7	NUM
cbi-29	309	28	+	+	SYM
cbi-29	309	29	4	4	NUM
cbi-29	309	30	+	+	CCONJ
cbi-29	309	31	c	c	NOUN
cbi-29	309	32	)	)	PUNCT
cbi-29	309	33	−	−	PROPN
cbi-29	309	34	(	(	PUNCT
cbi-29	309	35	2	2	NUM
cbi-29	309	36	+	+	NUM
cbi-29	309	37	3	3	NUM
cbi-29	309	38	+	+	CCONJ
cbi-29	309	39	c	c	X
cbi-29	309	40	)	)	PUNCT
cbi-29	309	41	=	=	SYM
cbi-29	310	1	11	11	NUM
cbi-29	311	1	+	+	CCONJ
cbi-29	311	2	c	c	NOUN
cbi-29	311	3	−	−	NOUN
cbi-29	311	4	5	5	NUM
cbi-29	311	5	−	−	NOUN
cbi-29	311	6	c	c	NOUN
cbi-29	311	7	=	=	SYM
cbi-29	311	8	6	6	NUM
cbi-29	311	9	.	.	PUNCT
cbi-29	311	10	therefore	therefore	ADV
cbi-29	311	11	,	,	PUNCT
cbi-29	311	12	treating	treat	VERB
cbi-29	311	13	the	the	DET
cbi-29	311	14	integral	integral	ADJ
cbi-29	311	15	as	as	ADP
cbi-29	311	16	an	an	DET
cbi-29	311	17	infinite	infinite	ADJ
cbi-29	311	18	sum	sum	NOUN
cbi-29	311	19	not	not	PART
cbi-29	311	20	only	only	ADV
cbi-29	311	21	helps	help	VERB
cbi-29	311	22	students	student	NOUN
cbi-29	311	23	generalize	generalize	VERB
cbi-29	311	24	the	the	DET
cbi-29	311	25	integral	integral	ADJ
cbi-29	311	26	to	to	ADP
cbi-29	311	27	various	various	ADJ
cbi-29	311	28	integrationrelated	integrationrelate	VERB
cbi-29	311	29	formulas	formula	NOUN
cbi-29	311	30	,	,	PUNCT
cbi-29	311	31	but	but	CCONJ
cbi-29	311	32	it	it	PRON
cbi-29	311	33	also	also	ADV
cbi-29	311	34	helps	help	VERB
cbi-29	311	35	students	student	NOUN
cbi-29	311	36	generalize	generalize	VERB
cbi-29	311	37	the	the	DET
cbi-29	311	38	integral	integral	ADJ
cbi-29	311	39	into	into	ADP
cbi-29	311	40	a	a	DET
cbi-29	311	41	multivariable	multivariable	ADJ
cbi-29	311	42	version	version	NOUN
cbi-29	311	43	,	,	PUNCT
cbi-29	311	44	and	and	CCONJ
cbi-29	311	45	similarly	similarly	ADV
cbi-29	311	46	to	to	ADP
cbi-29	311	47	complex	complex	ADJ
cbi-29	311	48	number	number	NOUN
cbi-29	311	49	situations	situation	NOUN
cbi-29	311	50	.	.	PUNCT
cbi-29	312	1	the	the	DET
cbi-29	312	2	area	area	NOUN
cbi-29	312	3	under	under	ADP
cbi-29	312	4	the	the	DET
cbi-29	312	5	curve	curve	NOUN
cbi-29	312	6	can	can	AUX
cbi-29	312	7	be	be	AUX
cbi-29	312	8	seen	see	VERB
cbi-29	312	9	as	as	ADP
cbi-29	312	10	a	a	DET
cbi-29	312	11	particular	particular	ADJ
cbi-29	312	12	,	,	PUNCT
cbi-29	312	13	easyto	easyto	PROPN
cbi-29	312	14	-	-	PUNCT
cbi-29	312	15	understand	understand	VERB
cbi-29	312	16	instance	instance	NOUN
cbi-29	312	17	of	of	ADP
cbi-29	312	18	infinite	infinite	ADJ
cbi-29	312	19	summation	summation	NOUN
cbi-29	312	20	.	.	PUNCT
cbi-29	313	1	one	one	NUM
cbi-29	313	2	other	other	ADJ
cbi-29	313	3	benefit	benefit	NOUN
cbi-29	313	4	of	of	ADP
cbi-29	313	5	treating	treat	VERB
cbi-29	313	6	the	the	DET
cbi-29	313	7	integral	integral	ADJ
cbi-29	313	8	as	as	ADP
cbi-29	313	9	an	an	DET
cbi-29	313	10	infinite	infinite	ADJ
cbi-29	313	11	sum	sum	NOUN
cbi-29	313	12	is	be	AUX
cbi-29	313	13	that	that	SCONJ
cbi-29	313	14	it	it	PRON
cbi-29	313	15	makes	make	VERB
cbi-29	313	16	the	the	DET
cbi-29	313	17	notation	notation	NOUN
cbi-29	313	18	more	more	ADV
cbi-29	313	19	clear	clear	ADJ
cbi-29	313	20	.	.	PUNCT
cbi-29	314	1	some	some	DET
cbi-29	314	2	introductory	introductory	ADJ
cbi-29	314	3	texts	text	NOUN
cbi-29	314	4	,	,	PUNCT
cbi-29	314	5	when	when	SCONJ
cbi-29	314	6	defining	define	VERB
cbi-29	314	7	the	the	DET
cbi-29	314	8	integral	integral	ADJ
cbi-29	314	9	as	as	ADP
cbi-29	314	10	the	the	DET
cbi-29	314	11	area	area	NOUN
cbi-29	314	12	under	under	ADP
cbi-29	314	13	the	the	DET
cbi-29	314	14	curve	curve	NOUN
cbi-29	314	15	,	,	PUNCT
cbi-29	314	16	simply	simply	ADV
cbi-29	314	17	use	use	VERB
cbi-29	314	18	the	the	DET
cbi-29	314	19	integral	integral	ADJ
cbi-29	314	20	form	form	NOUN
cbi-29	314	21	as	as	ADP
cbi-29	314	22	a	a	DET
cbi-29	314	23	pro	pro	ADJ
cbi-29	314	24	forma	forma	NOUN
cbi-29	314	25	way	way	NOUN
cbi-29	314	26	of	of	ADP
cbi-29	314	27	specifying	specify	VERB
cbi-29	314	28	the	the	DET
cbi-29	314	29	variable	variable	NOUN
cbi-29	314	30	of	of	ADP
cbi-29	314	31	integration	integration	NOUN
cbi-29	314	32	.	.	PUNCT
cbi-29	315	1	for	for	ADP
cbi-29	315	2	instance	instance	NOUN
cbi-29	315	3	,	,	PUNCT
cbi-29	315	4	it	it	PRON
cbi-29	315	5	will	will	AUX
cbi-29	315	6	often	often	ADV
cbi-29	315	7	be	be	AUX
cbi-29	315	8	explained	explain	VERB
cbi-29	315	9	like	like	ADP
cbi-29	315	10	this	this	DET
cbi-29	315	11	:	:	PUNCT
cbi-29	315	12	'	'	PUNCT
cbi-29	315	13	formula	formula	NOUN
cbi-29	315	14	to	to	PART
cbi-29	315	15	be	be	AUX
cbi-29	315	16	integrated(!!!!!!!!!!!!!!!!!)*!!!!!!!!!!!!!!!!!+	integrated(!!!!!!!!!!!!!!!!!)*!!!!!!!!!!!!!!!!!+	NOUN
cbi-29	315	17	x3	x3	ADJ
cbi-29	315	18	+	+	CCONJ
cbi-29	316	1	2x2	2x2	NUM
cbi-29	316	2	−	−	NOUN
cbi-29	316	3	3x	3x	NUM
cbi-29	316	4	+	+	CCONJ
cbi-29	316	5	5	5	NUM
cbi-29	316	6	dx*+	dx*+	NOUN
cbi-29	316	7	(	(	PUNCT
cbi-29	316	8	)	)	PUNCT
cbi-29	316	9	variable	variable	NOUN
cbi-29	316	10	of	of	ADP
cbi-29	316	11	integration	integration	NOUN
cbi-29	316	12	however	however	ADV
cbi-29	316	13	,	,	PUNCT
cbi-29	316	14	doing	do	VERB
cbi-29	316	15	it	it	PRON
cbi-29	316	16	this	this	DET
cbi-29	316	17	way	way	NOUN
cbi-29	316	18	needlessly	needlessly	ADV
cbi-29	316	19	restricts	restrict	VERB
cbi-29	316	20	the	the	DET
cbi-29	316	21	usage	usage	NOUN
cbi-29	316	22	of	of	ADP
cbi-29	316	23	integration	integration	NOUN
cbi-29	316	24	to	to	ADP
cbi-29	316	25	only	only	ADV
cbi-29	316	26	area	area	VERB
cbi-29	316	27	under	under	ADP
cbi-29	316	28	the	the	DET
cbi-29	316	29	curve	curve	NOUN
cbi-29	316	30	,	,	PUNCT
cbi-29	316	31	and	and	CCONJ
cbi-29	316	32	makes	make	VERB
cbi-29	316	33	the	the	DET
cbi-29	316	34	other	other	ADJ
cbi-29	316	35	uses	use	NOUN
cbi-29	316	36	of	of	ADP
cbi-29	316	37	it	it	PRON
cbi-29	316	38	harder	hard	ADV
cbi-29	316	39	to	to	PART
cbi-29	316	40	understand	understand	VERB
cbi-29	316	41	.	.	PUNCT
cbi-29	317	1	12	12	NUM
cbi-29	317	2	resistance	resistance	NOUN
cbi-29	317	3	to	to	ADP
cbi-29	317	4	hyperreals	hyperreal	NOUN
cbi-29	317	5	the	the	DET
cbi-29	317	6	primary	primary	ADJ
cbi-29	317	7	reason	reason	NOUN
cbi-29	317	8	that	that	SCONJ
cbi-29	317	9	these	these	DET
cbi-29	317	10	methods	method	NOUN
cbi-29	317	11	are	be	AUX
cbi-29	317	12	not	not	PART
cbi-29	317	13	more	more	ADV
cbi-29	317	14	widespread	widespread	ADJ
cbi-29	317	15	is	be	AUX
cbi-29	317	16	the	the	DET
cbi-29	317	17	lack	lack	NOUN
cbi-29	317	18	of	of	ADP
cbi-29	317	19	enthusiasm	enthusiasm	NOUN
cbi-29	317	20	for	for	ADP
cbi-29	317	21	the	the	DET
cbi-29	317	22	hyperreal	hyperreal	ADJ
cbi-29	317	23	number	number	NOUN
cbi-29	317	24	system	system	NOUN
cbi-29	317	25	.	.	PUNCT
cbi-29	318	1	this	this	PRON
cbi-29	318	2	comes	come	VERB
cbi-29	318	3	from	from	ADP
cbi-29	318	4	two	two	NUM
cbi-29	318	5	sources	source	NOUN
cbi-29	318	6	.	.	PUNCT
cbi-29	319	1	the	the	DET
cbi-29	319	2	first	first	ADJ
cbi-29	319	3	is	be	AUX
cbi-29	319	4	a	a	DET
cbi-29	319	5	historical	historical	ADJ
cbi-29	319	6	bias	bias	NOUN
cbi-29	319	7	against	against	ADP
cbi-29	319	8	infinities	infinity	NOUN
cbi-29	319	9	and	and	CCONJ
cbi-29	319	10	infinitesimals	infinitesimal	NOUN
cbi-29	319	11	,	,	PUNCT
cbi-29	319	12	with	with	ADP
cbi-29	319	13	volume	volume	NOUN
cbi-29	319	14	1	1	NUM
cbi-29	319	15	,	,	PUNCT
cbi-29	319	16	issue	issue	NOUN
cbi-29	319	17	1	1	NUM
cbi-29	319	18	12	12	NUM
cbi-29	319	19	.	.	PUNCT
cbi-29	320	1	resistance	resistance	NOUN
cbi-29	320	2	to	to	ADP
cbi-29	320	3	hyperreals	hyperreal	NOUN
cbi-29	320	4	25	25	NUM
cbi-29	320	5	figure	figure	NOUN
cbi-29	320	6	1	1	NUM
cbi-29	320	7	:	:	PUNCT
cbi-29	320	8	summations	summation	NOUN
cbi-29	320	9	using	use	VERB
cbi-29	320	10	integration	integration	NOUN
cbi-29	320	11	general	general	ADJ
cbi-29	320	12	geometry	geometry	NOUN
cbi-29	320	13	infinitesimal	infinitesimal	ADJ
cbi-29	320	14	geometry	geometry	NOUN
cbi-29	320	15	formula	formula	NOUN
cbi-29	320	16	integral	integral	ADJ
cbi-29	320	17	area	area	NOUN
cbi-29	320	18	under	under	ADP
cbi-29	320	19	the	the	DET
cbi-29	320	20	curve	curve	NOUN
cbi-29	320	21	ultrathin	ultrathin	NOUN
cbi-29	320	22	rectangles	rectangle	NOUN
cbi-29	320	23	height	height	NOUN
cbi-29	320	24	·	·	PUNCT
cbi-29	320	25	width	width	NOUN
cbi-29	320	26	,	,	PUNCT
cbi-29	320	27	y	y	PROPN
cbi-29	320	28	dx	dx	PROPN
cbi-29	320	29	arc	arc	PROPN
cbi-29	320	30	length	length	PROPN
cbi-29	320	31	line	line	NOUN
cbi-29	320	32	length	length	NOUN
cbi-29	320	33	(	(	PUNCT
cbi-29	321	1	x1	x1	NOUN
cbi-29	321	2	−	−	PROPN
cbi-29	321	3	x0)2	x0)2	X
cbi-29	322	1	+	+	CCONJ
cbi-29	322	2	(	(	PUNCT
cbi-29	322	3	y1	y1	INTJ
cbi-29	322	4	−	−	PROPN
cbi-29	322	5	y0)2	y0)2	INTJ
cbi-29	322	6	,	,	PUNCT
cbi-29	322	7	dx2	dx2	PROPN
cbi-29	322	8	+	+	PROPN
cbi-29	322	9	dy2	dy2	PROPN
cbi-29	322	10	revolution	revolution	NOUN
cbi-29	322	11	about	about	ADP
cbi-29	322	12	x	x	PUNCT
cbi-29	322	13	ultrashort	ultrashort	NOUN
cbi-29	322	14	cylinders	cylinder	NOUN
cbi-29	322	15	π	π	PROPN
cbi-29	322	16	r2h	r2h	PROPN
cbi-29	322	17	,	,	PUNCT
cbi-29	322	18	π	π	PROPN
cbi-29	322	19	y2	y2	PROPN
cbi-29	322	20	dx	dx	PROPN
cbi-29	322	21	revolution	revolution	PROPN
cbi-29	322	22	about	about	ADP
cbi-29	322	23	y	y	PROPN
cbi-29	322	24	ultrathin	ultrathin	ADJ
cbi-29	322	25	shells	shell	NOUN
cbi-29	322	26	(	(	PUNCT
cbi-29	322	27	curved	curved	ADJ
cbi-29	322	28	boxes	box	NOUN
cbi-29	322	29	)	)	PUNCT
cbi-29	322	30	height	height	NOUN
cbi-29	322	31	·	·	PUNCT
cbi-29	322	32	length	length	NOUN
cbi-29	322	33	·	·	PUNCT
cbi-29	322	34	thickness	thickness	NOUN
cbi-29	322	35	,	,	PUNCT
cbi-29	322	36	y	y	PROPN
cbi-29	322	37	2πx	2πx	NOUN
cbi-29	322	38	dx	dx	PROPN
cbi-29	322	39	infinitesimals	infinitesimal	NOUN
cbi-29	322	40	actually	actually	ADV
cbi-29	322	41	having	have	VERB
cbi-29	322	42	the	the	DET
cbi-29	322	43	stronger	strong	ADJ
cbi-29	322	44	of	of	ADP
cbi-29	322	45	the	the	DET
cbi-29	322	46	negative	negative	ADJ
cbi-29	322	47	biases	bias	NOUN
cbi-29	322	48	.	.	PUNCT
cbi-29	323	1	the	the	DET
cbi-29	323	2	primary	primary	ADJ
cbi-29	323	3	bias	bias	NOUN
cbi-29	323	4	against	against	ADP
cbi-29	323	5	infinitesimals	infinitesimal	NOUN
cbi-29	323	6	comes	come	VERB
cbi-29	323	7	from	from	ADP
cbi-29	323	8	the	the	DET
cbi-29	323	9	fact	fact	NOUN
cbi-29	323	10	that	that	SCONJ
cbi-29	323	11	they	they	PRON
cbi-29	323	12	were	be	AUX
cbi-29	323	13	used	use	VERB
cbi-29	323	14	long	long	ADV
cbi-29	323	15	before	before	SCONJ
cbi-29	323	16	they	they	PRON
cbi-29	323	17	were	be	AUX
cbi-29	323	18	proved	prove	VERB
cbi-29	323	19	.	.	PUNCT
cbi-29	324	1	before	before	SCONJ
cbi-29	324	2	rigorous	rigorous	ADJ
cbi-29	324	3	means	mean	NOUN
cbi-29	324	4	of	of	ADP
cbi-29	324	5	working	work	VERB
cbi-29	324	6	with	with	ADP
cbi-29	324	7	infinitesimals	infinitesimal	NOUN
cbi-29	324	8	were	be	AUX
cbi-29	324	9	established	establish	VERB
cbi-29	324	10	,	,	PUNCT
cbi-29	324	11	many	many	ADJ
cbi-29	324	12	critics	critic	NOUN
cbi-29	324	13	pointed	point	VERB
cbi-29	324	14	to	to	ADP
cbi-29	324	15	the	the	DET
cbi-29	324	16	inconsistent	inconsistent	ADJ
cbi-29	324	17	ways	way	NOUN
cbi-29	324	18	in	in	ADP
cbi-29	324	19	which	which	PRON
cbi-29	324	20	infinitesimals	infinitesimal	NOUN
cbi-29	324	21	were	be	AUX
cbi-29	324	22	handled	handle	VERB
cbi-29	324	23	as	as	ADP
cbi-29	324	24	proof	proof	NOUN
cbi-29	324	25	that	that	SCONJ
cbi-29	324	26	they	they	PRON
cbi-29	324	27	were	be	AUX
cbi-29	324	28	non	non	NOUN
cbi-29	324	29	-	-	NOUN
cbi-29	324	30	entities	entity	NOUN
cbi-29	324	31	.	.	PUNCT
cbi-29	325	1	in	in	ADP
cbi-29	325	2	some	some	DET
cbi-29	325	3	circumstances	circumstance	NOUN
cbi-29	325	4	,	,	PUNCT
cbi-29	325	5	infinitesimals	infinitesimal	NOUN
cbi-29	325	6	were	be	AUX
cbi-29	325	7	treated	treat	VERB
cbi-29	325	8	as	as	ADP
cbi-29	325	9	zero	zero	NUM
cbi-29	325	10	and	and	CCONJ
cbi-29	325	11	thrown	throw	VERB
cbi-29	325	12	away	away	ADV
cbi-29	325	13	,	,	PUNCT
cbi-29	325	14	and	and	CCONJ
cbi-29	325	15	,	,	PUNCT
cbi-29	325	16	in	in	ADP
cbi-29	325	17	other	other	ADJ
cbi-29	325	18	circumstances	circumstance	NOUN
cbi-29	325	19	,	,	PUNCT
cbi-29	325	20	they	they	PRON
cbi-29	325	21	were	be	AUX
cbi-29	325	22	used	use	VERB
cbi-29	325	23	in	in	ADP
cbi-29	325	24	denominators	denominator	NOUN
cbi-29	325	25	and	and	CCONJ
cbi-29	325	26	were	be	AUX
cbi-29	325	27	therefore	therefore	ADV
cbi-29	325	28	treated	treat	VERB
cbi-29	325	29	as	as	ADP
cbi-29	325	30	non	non	ADJ
cbi-29	325	31	-	-	ADJ
cbi-29	325	32	zero	zero	ADJ
cbi-29	325	33	entities	entity	NOUN
cbi-29	325	34	which	which	PRON
cbi-29	325	35	could	could	AUX
cbi-29	325	36	also	also	ADV
cbi-29	325	37	be	be	AUX
cbi-29	325	38	used	use	VERB
cbi-29	325	39	for	for	ADP
cbi-29	325	40	algebraic	algebraic	ADJ
cbi-29	325	41	cancelling	cancelling	NOUN
cbi-29	325	42	.	.	PUNCT
cbi-29	326	1	in	in	ADP
cbi-29	326	2	the	the	DET
cbi-29	326	3	latter	latter	ADJ
cbi-29	326	4	half	half	NOUN
cbi-29	326	5	of	of	ADP
cbi-29	326	6	the	the	DET
cbi-29	326	7	twentieth	twentieth	ADJ
cbi-29	326	8	century	century	NOUN
cbi-29	326	9	,	,	PUNCT
cbi-29	326	10	robinson	robinson	PROPN
cbi-29	326	11	’s	’s	PART
cbi-29	326	12	hyperreal	hyperreal	ADJ
cbi-29	326	13	number	number	NOUN
cbi-29	326	14	system	system	NOUN
cbi-29	326	15	made	make	VERB
cbi-29	326	16	these	these	DET
cbi-29	326	17	operations	operation	NOUN
cbi-29	326	18	rigorous	rigorous	ADJ
cbi-29	326	19	with	with	ADP
cbi-29	326	20	the	the	DET
cbi-29	326	21	hyperreal	hyperreal	ADJ
cbi-29	326	22	number	number	NOUN
cbi-29	326	23	system	system	NOUN
cbi-29	326	24	(	(	PUNCT
cbi-29	326	25	robinson	robinson	PROPN
cbi-29	326	26	,	,	PUNCT
cbi-29	326	27	1974	1974	NUM
cbi-29	326	28	)	)	PUNCT
cbi-29	326	29	.	.	PUNCT
cbi-29	327	1	however	however	ADV
cbi-29	327	2	,	,	PUNCT
cbi-29	327	3	by	by	ADP
cbi-29	327	4	that	that	DET
cbi-29	327	5	time	time	NOUN
cbi-29	327	6	,	,	PUNCT
cbi-29	327	7	the	the	DET
cbi-29	327	8	damage	damage	NOUN
cbi-29	327	9	from	from	ADP
cbi-29	327	10	hundreds	hundred	NOUN
cbi-29	327	11	of	of	ADP
cbi-29	327	12	years	year	NOUN
cbi-29	327	13	of	of	ADP
cbi-29	327	14	skepticism	skepticism	NOUN
cbi-29	327	15	had	have	AUX
cbi-29	327	16	already	already	ADV
cbi-29	327	17	taken	take	VERB
cbi-29	327	18	its	its	PRON
cbi-29	327	19	toll	toll	NOUN
cbi-29	327	20	.	.	PUNCT
cbi-29	328	1	the	the	DET
cbi-29	328	2	most	most	ADV
cbi-29	328	3	classic	classic	ADJ
cbi-29	328	4	recrimination	recrimination	NOUN
cbi-29	328	5	against	against	ADP
cbi-29	328	6	infinitesimals	infinitesimal	NOUN
cbi-29	328	7	was	be	AUX
cbi-29	328	8	done	do	VERB
cbi-29	328	9	by	by	ADP
cbi-29	328	10	george	george	PROPN
cbi-29	328	11	berkeley	berkeley	PROPN
cbi-29	328	12	,	,	PUNCT
cbi-29	328	13	in	in	ADP
cbi-29	328	14	his	his	PRON
cbi-29	328	15	famouse	famouse	NOUN
cbi-29	328	16	quote	quote	INTJ
cbi-29	328	17	:	:	PUNCT
cbi-29	328	18	and	and	CCONJ
cbi-29	328	19	what	what	PRON
cbi-29	328	20	are	be	AUX
cbi-29	328	21	these	these	DET
cbi-29	328	22	fluxions	fluxion	NOUN
cbi-29	328	23	?	?	PUNCT
cbi-29	329	1	the	the	DET
cbi-29	329	2	velocities	velocity	NOUN
cbi-29	329	3	of	of	ADP
cbi-29	329	4	evanescent	evanescent	NOUN
cbi-29	329	5	increments	increment	NOUN
cbi-29	329	6	?	?	PUNCT
cbi-29	330	1	and	and	CCONJ
cbi-29	330	2	what	what	PRON
cbi-29	330	3	are	be	AUX
cbi-29	330	4	these	these	DET
cbi-29	330	5	same	same	ADJ
cbi-29	330	6	evanescent	evanescent	NOUN
cbi-29	330	7	increments	increment	NOUN
cbi-29	330	8	?	?	PUNCT
cbi-29	331	1	they	they	PRON
cbi-29	331	2	are	be	AUX
cbi-29	331	3	neither	neither	CCONJ
cbi-29	331	4	finite	finite	ADJ
cbi-29	331	5	quantities	quantity	NOUN
cbi-29	331	6	nor	nor	CCONJ
cbi-29	331	7	quantities	quantity	NOUN
cbi-29	331	8	infinitely	infinitely	ADV
cbi-29	331	9	small	small	ADJ
cbi-29	331	10	,	,	PUNCT
cbi-29	331	11	nor	nor	CCONJ
cbi-29	331	12	yet	yet	ADV
cbi-29	331	13	nothing	nothing	PRON
cbi-29	331	14	.	.	PUNCT
cbi-29	332	1	may	may	AUX
cbi-29	332	2	we	we	PRON
cbi-29	332	3	not	not	PART
cbi-29	332	4	call	call	VERB
cbi-29	332	5	them	they	PRON
cbi-29	332	6	the	the	DET
cbi-29	332	7	ghosts	ghost	NOUN
cbi-29	332	8	of	of	ADP
cbi-29	332	9	departed	depart	VERB
cbi-29	332	10	quantities	quantity	NOUN
cbi-29	332	11	?	?	PUNCT
cbi-29	333	1	(	(	PUNCT
cbi-29	333	2	berkeley	berkeley	PROPN
cbi-29	333	3	,	,	PUNCT
cbi-29	333	4	1734)5	1734)5	NUM
cbi-29	333	5	additionally	additionally	ADV
cbi-29	333	6	,	,	PUNCT
cbi-29	333	7	even	even	ADV
cbi-29	333	8	though	though	SCONJ
cbi-29	333	9	the	the	DET
cbi-29	333	10	hyperreal	hyperreal	NOUN
cbi-29	333	11	number	number	NOUN
cbi-29	333	12	system	system	NOUN
cbi-29	333	13	has	have	AUX
cbi-29	333	14	been	be	AUX
cbi-29	333	15	shown	show	VERB
cbi-29	333	16	to	to	PART
cbi-29	333	17	be	be	AUX
cbi-29	333	18	usable	usable	ADJ
cbi-29	333	19	as	as	ADP
cbi-29	333	20	a	a	DET
cbi-29	333	21	consistent	consistent	ADJ
cbi-29	333	22	system	system	NOUN
cbi-29	333	23	for	for	ADP
cbi-29	333	24	the	the	DET
cbi-29	333	25	inclusion	inclusion	NOUN
cbi-29	333	26	of	of	ADP
cbi-29	333	27	infinities	infinity	NOUN
cbi-29	333	28	and	and	CCONJ
cbi-29	333	29	infinitesimals	infinitesimal	NOUN
cbi-29	333	30	,	,	PUNCT
cbi-29	333	31	it	it	PRON
cbi-29	333	32	is	be	AUX
cbi-29	333	33	not	not	PART
cbi-29	333	34	the	the	DET
cbi-29	333	35	only	only	ADJ
cbi-29	333	36	viable	viable	ADJ
cbi-29	333	37	candidate	candidate	NOUN
cbi-29	333	38	.	.	PUNCT
cbi-29	334	1	cantor	cantor	PROPN
cbi-29	334	2	’s	’s	PART
cbi-29	334	3	transfinite	transfinite	ADJ
cbi-29	334	4	number	number	NOUN
cbi-29	334	5	system	system	NOUN
cbi-29	334	6	(	(	PUNCT
cbi-29	334	7	cantor	cantor	NOUN
cbi-29	334	8	,	,	PUNCT
cbi-29	334	9	1915	1915	NUM
cbi-29	334	10	)	)	PUNCT
cbi-29	334	11	,	,	PUNCT
cbi-29	334	12	surreal	surreal	ADJ
cbi-29	334	13	numbers	number	NOUN
cbi-29	334	14	(	(	PUNCT
cbi-29	334	15	knuth	knuth	NOUN
cbi-29	334	16	,	,	PUNCT
cbi-29	334	17	1974	1974	NUM
cbi-29	334	18	)	)	PUNCT
cbi-29	334	19	,	,	PUNCT
cbi-29	334	20	dual	dual	ADJ
cbi-29	334	21	numbers	number	NOUN
cbi-29	334	22	(	(	PUNCT
cbi-29	334	23	wolfe	wolfe	PROPN
cbi-29	334	24	,	,	PUNCT
cbi-29	334	25	2014	2014	NUM
cbi-29	334	26	)	)	PUNCT
cbi-29	334	27	,	,	PUNCT
cbi-29	334	28	and	and	CCONJ
cbi-29	334	29	other	other	ADJ
cbi-29	334	30	systems	system	NOUN
cbi-29	334	31	have	have	AUX
cbi-29	334	32	all	all	PRON
cbi-29	334	33	been	be	AUX
cbi-29	334	34	proposed	propose	VERB
cbi-29	334	35	for	for	ADP
cbi-29	334	36	extending	extend	VERB
cbi-29	334	37	the	the	DET
cbi-29	334	38	real	real	ADJ
cbi-29	334	39	number	number	NOUN
cbi-29	334	40	line	line	NOUN
cbi-29	334	41	into	into	ADP
cbi-29	334	42	infinities	infinity	NOUN
cbi-29	334	43	and	and	CCONJ
cbi-29	334	44	infinitesimals	infinitesimal	NOUN
cbi-29	334	45	.	.	PUNCT
cbi-29	335	1	while	while	SCONJ
cbi-29	335	2	the	the	DET
cbi-29	335	3	hyperreals	hyperreal	NOUN
cbi-29	335	4	are	be	AUX
cbi-29	335	5	the	the	DET
cbi-29	335	6	most	most	ADV
cbi-29	335	7	widespread	widespread	ADJ
cbi-29	335	8	,	,	PUNCT
cbi-29	335	9	it	it	PRON
cbi-29	335	10	is	be	AUX
cbi-29	335	11	not	not	PART
cbi-29	335	12	the	the	DET
cbi-29	335	13	only	only	ADJ
cbi-29	335	14	system	system	NOUN
cbi-29	335	15	available	available	ADJ
cbi-29	335	16	.	.	PUNCT
cbi-29	336	1	this	this	DET
cbi-29	336	2	lack	lack	NOUN
cbi-29	336	3	of	of	ADP
cbi-29	336	4	standard	standard	ADJ
cbi-29	336	5	convention	convention	NOUN
cbi-29	336	6	has	have	AUX
cbi-29	336	7	prevented	prevent	VERB
cbi-29	336	8	a	a	DET
cbi-29	336	9	lot	lot	NOUN
cbi-29	336	10	of	of	ADP
cbi-29	336	11	building	building	NOUN
cbi-29	336	12	on	on	ADP
cbi-29	336	13	any	any	DET
cbi-29	336	14	one	one	NUM
cbi-29	336	15	foundation	foundation	NOUN
cbi-29	336	16	.	.	PUNCT
cbi-29	337	1	5	5	NUM
cbi-29	337	2	in	in	ADP
cbi-29	337	3	modern	modern	ADJ
cbi-29	337	4	terminology	terminology	NOUN
cbi-29	337	5	,	,	PUNCT
cbi-29	337	6	fluxions	fluxion	NOUN
cbi-29	337	7	refer	refer	VERB
cbi-29	337	8	to	to	ADP
cbi-29	337	9	derivatives	derivative	NOUN
cbi-29	337	10	,	,	PUNCT
cbi-29	337	11	and	and	CCONJ
cbi-29	337	12	evanescent	evanescent	NOUN
cbi-29	337	13	increments	increment	NOUN
cbi-29	337	14	refer	refer	VERB
cbi-29	337	15	to	to	ADP
cbi-29	337	16	infinitesimals	infinitesimal	NOUN
cbi-29	337	17	.	.	PUNCT
cbi-29	338	1	finally	finally	ADV
cbi-29	338	2	,	,	PUNCT
cbi-29	338	3	there	there	PRON
cbi-29	338	4	is	be	VERB
cbi-29	338	5	also	also	ADV
cbi-29	338	6	a	a	DET
cbi-29	338	7	philosophical	philosophical	ADJ
cbi-29	338	8	distrust	distrust	NOUN
cbi-29	338	9	of	of	ADP
cbi-29	338	10	hyperreal	hyperreal	ADJ
cbi-29	338	11	numbers	number	NOUN
cbi-29	338	12	based	base	VERB
cbi-29	338	13	on	on	ADP
cbi-29	338	14	general	general	ADJ
cbi-29	338	15	concerns	concern	NOUN
cbi-29	338	16	over	over	ADP
cbi-29	338	17	infinities	infinity	NOUN
cbi-29	338	18	and	and	CCONJ
cbi-29	338	19	infinitesimals	infinitesimal	NOUN
cbi-29	338	20	.	.	PUNCT
cbi-29	339	1	both	both	DET
cbi-29	339	2	infinities	infinity	NOUN
cbi-29	339	3	and	and	CCONJ
cbi-29	339	4	infinitesimals	infinitesimal	NOUN
cbi-29	339	5	have	have	AUX
cbi-29	339	6	troubled	trouble	VERB
cbi-29	339	7	certain	certain	ADJ
cbi-29	339	8	schools	school	NOUN
cbi-29	339	9	of	of	ADP
cbi-29	339	10	mathematicians	mathematician	NOUN
cbi-29	339	11	.	.	PUNCT
cbi-29	340	1	these	these	DET
cbi-29	340	2	concerns	concern	NOUN
cbi-29	340	3	can	can	AUX
cbi-29	340	4	be	be	AUX
cbi-29	340	5	divided	divide	VERB
cbi-29	340	6	into	into	ADP
cbi-29	340	7	ontological	ontological	ADJ
cbi-29	340	8	concerns	concern	NOUN
cbi-29	340	9	and	and	CCONJ
cbi-29	340	10	epistemological	epistemological	ADJ
cbi-29	340	11	concerns	concern	NOUN
cbi-29	340	12	.	.	PUNCT
cbi-29	341	1	the	the	DET
cbi-29	341	2	ontological	ontological	ADJ
cbi-29	341	3	concern	concern	NOUN
cbi-29	341	4	is	be	AUX
cbi-29	341	5	about	about	ADP
cbi-29	341	6	whether	whether	SCONJ
cbi-29	341	7	infinities	infinity	NOUN
cbi-29	341	8	exist	exist	VERB
cbi-29	341	9	and/or	and/or	CCONJ
cbi-29	341	10	are	be	AUX
cbi-29	341	11	needed	need	VERB
cbi-29	341	12	in	in	ADP
cbi-29	341	13	mathematics	mathematic	NOUN
cbi-29	341	14	.	.	PUNCT
cbi-29	342	1	this	this	DET
cbi-29	342	2	concern	concern	NOUN
cbi-29	342	3	stems	stem	VERB
cbi-29	342	4	from	from	ADP
cbi-29	342	5	the	the	DET
cbi-29	342	6	line	line	NOUN
cbi-29	342	7	of	of	ADP
cbi-29	342	8	mathematicians	mathematician	NOUN
cbi-29	342	9	following	follow	VERB
cbi-29	342	10	in	in	ADP
cbi-29	342	11	the	the	DET
cbi-29	342	12	footsteps	footstep	NOUN
cbi-29	342	13	of	of	ADP
cbi-29	342	14	leopold	leopold	PROPN
cbi-29	342	15	kronecker	kronecker	PROPN
cbi-29	342	16	.	.	PUNCT
cbi-29	343	1	kronecker	kronecker	PROPN
cbi-29	343	2	opposed	opposed	PROPN
cbi-29	343	3	cantor	cantor	PROPN
cbi-29	343	4	’s	’s	PART
cbi-29	343	5	theory	theory	NOUN
cbi-29	343	6	of	of	ADP
cbi-29	343	7	infinities	infinity	NOUN
cbi-29	343	8	because	because	SCONJ
cbi-29	343	9	kronecker	kronecker	NOUN
cbi-29	343	10	only	only	ADV
cbi-29	343	11	admitted	admit	VERB
cbi-29	343	12	mathematical	mathematical	ADJ
cbi-29	343	13	concepts	concept	NOUN
cbi-29	343	14	which	which	PRON
cbi-29	343	15	could	could	AUX
cbi-29	343	16	be	be	AUX
cbi-29	343	17	constructed	construct	VERB
cbi-29	343	18	in	in	ADP
cbi-29	343	19	a	a	DET
cbi-29	343	20	finite	finite	ADJ
cbi-29	343	21	number	number	NOUN
cbi-29	343	22	of	of	ADP
cbi-29	343	23	steps	step	NOUN
cbi-29	343	24	from	from	ADP
cbi-29	343	25	the	the	DET
cbi-29	343	26	natural	natural	ADJ
cbi-29	343	27	numbers	number	NOUN
cbi-29	343	28	(	(	PUNCT
cbi-29	343	29	dauben	dauben	NOUN
cbi-29	343	30	,	,	PUNCT
cbi-29	343	31	1990	1990	NUM
cbi-29	343	32	)	)	PUNCT
cbi-29	343	33	.	.	PUNCT
cbi-29	344	1	david	david	PROPN
cbi-29	344	2	hilbert	hilbert	PROPN
cbi-29	344	3	’s	’s	PART
cbi-29	344	4	program	program	NOUN
cbi-29	344	5	was	be	AUX
cbi-29	344	6	similar	similar	ADJ
cbi-29	344	7	to	to	ADP
cbi-29	344	8	kronecker	kronecker	NOUN
cbi-29	344	9	’s	’s	NOUN
cbi-29	344	10	.	.	PUNCT
cbi-29	345	1	however	however	ADV
cbi-29	345	2	,	,	PUNCT
cbi-29	345	3	hilbert	hilbert	PROPN
cbi-29	345	4	was	be	AUX
cbi-29	345	5	not	not	PART
cbi-29	345	6	actively	actively	ADV
cbi-29	345	7	opposed	oppose	VERB
cbi-29	345	8	to	to	PART
cbi-29	345	9	infinity	infinity	NOUN
cbi-29	345	10	per	per	ADP
cbi-29	345	11	se	se	ADV
cbi-29	345	12	,	,	PUNCT
cbi-29	345	13	but	but	CCONJ
cbi-29	345	14	believed	believe	VERB
cbi-29	345	15	that	that	SCONJ
cbi-29	345	16	infinities	infinity	NOUN
cbi-29	345	17	were	be	AUX
cbi-29	345	18	ideals	ideal	NOUN
cbi-29	345	19	and	and	CCONJ
cbi-29	345	20	the	the	DET
cbi-29	345	21	natural	natural	ADJ
cbi-29	345	22	numbers	number	NOUN
cbi-29	345	23	were	be	AUX
cbi-29	345	24	reality	reality	NOUN
cbi-29	345	25	.	.	PUNCT
cbi-29	346	1	therefore	therefore	ADV
cbi-29	346	2	,	,	PUNCT
cbi-29	346	3	hilbert	hilbert	PROPN
cbi-29	346	4	believed	believe	VERB
cbi-29	346	5	that	that	SCONJ
cbi-29	346	6	any	any	DET
cbi-29	346	7	true	true	ADJ
cbi-29	346	8	statement	statement	NOUN
cbi-29	346	9	about	about	ADP
cbi-29	346	10	natural	natural	ADJ
cbi-29	346	11	numbers	number	NOUN
cbi-29	346	12	that	that	PRON
cbi-29	346	13	were	be	AUX
cbi-29	346	14	proved	prove	VERB
cbi-29	346	15	with	with	ADP
cbi-29	346	16	infinity	infinity	NOUN
cbi-29	346	17	could	could	AUX
cbi-29	346	18	also	also	ADV
cbi-29	346	19	be	be	AUX
cbi-29	346	20	proven	prove	VERB
cbi-29	346	21	without	without	ADP
cbi-29	346	22	them	they	PRON
cbi-29	346	23	.	.	PUNCT
cbi-29	347	1	infinities	infinity	NOUN
cbi-29	347	2	were	be	AUX
cbi-29	347	3	n’t	not	PART
cbi-29	347	4	invalid	invalid	ADJ
cbi-29	347	5	,	,	PUNCT
cbi-29	347	6	they	they	PRON
cbi-29	347	7	were	be	AUX
cbi-29	347	8	just	just	ADV
cbi-29	347	9	superfluous	superfluous	ADJ
cbi-29	347	10	.	.	PUNCT
cbi-29	348	1	thus	thus	ADV
cbi-29	348	2	,	,	PUNCT
cbi-29	348	3	hilbert	hilbert	PROPN
cbi-29	348	4	’s	’s	PART
cbi-29	348	5	program	program	NOUN
cbi-29	348	6	was	be	AUX
cbi-29	348	7	to	to	PART
cbi-29	348	8	define	define	VERB
cbi-29	348	9	a	a	DET
cbi-29	348	10	finite	finite	ADJ
cbi-29	348	11	set	set	NOUN
cbi-29	348	12	of	of	ADP
cbi-29	348	13	axioms	axiom	NOUN
cbi-29	348	14	which	which	PRON
cbi-29	348	15	were	be	AUX
cbi-29	348	16	consistent	consistent	ADJ
cbi-29	348	17	and	and	CCONJ
cbi-29	348	18	complete	complete	ADJ
cbi-29	348	19	,	,	PUNCT
cbi-29	348	20	and	and	CCONJ
cbi-29	348	21	could	could	AUX
cbi-29	348	22	prove	prove	VERB
cbi-29	348	23	any	any	DET
cbi-29	348	24	valid	valid	ADJ
cbi-29	348	25	theorem	theorem	NOUN
cbi-29	348	26	without	without	ADP
cbi-29	348	27	explicitly	explicitly	ADV
cbi-29	348	28	relying	rely	VERB
cbi-29	348	29	on	on	ADP
cbi-29	348	30	any	any	DET
cbi-29	348	31	concepts	concept	NOUN
cbi-29	348	32	of	of	ADP
cbi-29	348	33	infinity	infinity	NOUN
cbi-29	348	34	(	(	PUNCT
cbi-29	348	35	zach	zach	NOUN
cbi-29	348	36	,	,	PUNCT
cbi-29	348	37	2016	2016	NUM
cbi-29	348	38	)	)	PUNCT
cbi-29	348	39	.	.	PUNCT
cbi-29	349	1	gödel	gödel	PROPN
cbi-29	349	2	later	later	ADV
cbi-29	349	3	proved	prove	VERB
cbi-29	349	4	that	that	SCONJ
cbi-29	349	5	hilbert	hilbert	PROPN
cbi-29	349	6	’s	’s	PART
cbi-29	349	7	program	program	NOUN
cbi-29	349	8	was	be	AUX
cbi-29	349	9	unworkable	unworkable	ADJ
cbi-29	349	10	,	,	PUNCT
cbi-29	349	11	but	but	CCONJ
cbi-29	349	12	the	the	DET
cbi-29	349	13	motivations	motivation	NOUN
cbi-29	349	14	and	and	CCONJ
cbi-29	349	15	concerns	concern	NOUN
cbi-29	349	16	behind	behind	ADP
cbi-29	349	17	it	it	PRON
cbi-29	349	18	remain	remain	VERB
cbi-29	349	19	today	today	NOUN
cbi-29	349	20	.	.	PUNCT
cbi-29	350	1	even	even	ADV
cbi-29	350	2	for	for	ADP
cbi-29	350	3	mathematicians	mathematician	NOUN
cbi-29	350	4	who	who	PRON
cbi-29	350	5	accept	accept	VERB
cbi-29	350	6	cantor	cantor	NOUN
cbi-29	350	7	and	and	CCONJ
cbi-29	350	8	gödel	gödel	PROPN
cbi-29	350	9	’s	’s	PART
cbi-29	350	10	infinities	infinity	NOUN
cbi-29	350	11	,	,	PUNCT
cbi-29	350	12	a	a	DET
cbi-29	350	13	continued	continued	ADJ
cbi-29	350	14	concern	concern	NOUN
cbi-29	350	15	about	about	ADP
cbi-29	350	16	over	over	ADP
cbi-29	350	17	-	-	PUNCT
cbi-29	350	18	reliances	reliance	NOUN
cbi-29	350	19	on	on	ADP
cbi-29	350	20	infinities	infinity	NOUN
cbi-29	350	21	and	and	CCONJ
cbi-29	350	22	infinitesimals	infinitesimal	NOUN
cbi-29	350	23	remains	remain	VERB
cbi-29	350	24	.	.	PUNCT
cbi-29	351	1	for	for	ADP
cbi-29	351	2	the	the	DET
cbi-29	351	3	epistemological	epistemological	ADJ
cbi-29	351	4	concern	concern	NOUN
cbi-29	351	5	,	,	PUNCT
cbi-29	351	6	i	i	PRON
cbi-29	351	7	can	can	AUX
cbi-29	351	8	not	not	PART
cbi-29	351	9	point	point	VERB
cbi-29	351	10	to	to	ADP
cbi-29	351	11	any	any	DET
cbi-29	351	12	one	one	NUM
cbi-29	351	13	bright	bright	ADJ
cbi-29	351	14	source	source	NOUN
cbi-29	351	15	.	.	PUNCT
cbi-29	352	1	however	however	ADV
cbi-29	352	2	,	,	PUNCT
cbi-29	352	3	this	this	DET
cbi-29	352	4	concern	concern	NOUN
cbi-29	352	5	stands	stand	VERB
cbi-29	352	6	as	as	ADP
cbi-29	352	7	a	a	DET
cbi-29	352	8	subtext	subtext	NOUN
cbi-29	352	9	to	to	ADP
cbi-29	352	10	many	many	ADJ
cbi-29	352	11	conversations	conversation	NOUN
cbi-29	352	12	i	i	PRON
cbi-29	352	13	have	have	AUX
cbi-29	352	14	had	have	VERB
cbi-29	352	15	regarding	regard	VERB
cbi-29	352	16	hyperreal	hyperreal	ADJ
cbi-29	352	17	numbers	number	NOUN
cbi-29	352	18	,	,	PUNCT
cbi-29	352	19	infinities	infinity	NOUN
cbi-29	352	20	,	,	PUNCT
cbi-29	352	21	and	and	CCONJ
cbi-29	352	22	infinitesimals	infinitesimal	NOUN
cbi-29	352	23	.	.	PUNCT
cbi-29	353	1	essentially	essentially	ADV
cbi-29	353	2	,	,	PUNCT
cbi-29	353	3	the	the	DET
cbi-29	353	4	idea	idea	NOUN
cbi-29	353	5	is	be	AUX
cbi-29	353	6	that	that	SCONJ
cbi-29	353	7	since	since	SCONJ
cbi-29	353	8	we	we	PRON
cbi-29	353	9	can	can	AUX
cbi-29	353	10	not	not	PART
cbi-29	353	11	point	point	VERB
cbi-29	353	12	to	to	ADP
cbi-29	353	13	anything	anything	PRON
cbi-29	353	14	that	that	PRON
cbi-29	353	15	is	be	AUX
cbi-29	353	16	infinitely	infinitely	ADV
cbi-29	353	17	small	small	ADJ
cbi-29	353	18	or	or	CCONJ
cbi-29	353	19	infinitely	infinitely	ADV
cbi-29	353	20	big	big	ADJ
cbi-29	353	21	in	in	ADP
cbi-29	353	22	the	the	DET
cbi-29	353	23	world	world	NOUN
cbi-29	353	24	around	around	ADP
cbi-29	353	25	us	we	PRON
cbi-29	353	26	,	,	PUNCT
cbi-29	353	27	it	it	PRON
cbi-29	353	28	is	be	AUX
cbi-29	353	29	not	not	PART
cbi-29	353	30	safe	safe	ADJ
cbi-29	353	31	to	to	PART
cbi-29	353	32	make	make	VERB
cbi-29	353	33	solid	solid	ADJ
cbi-29	353	34	assertions	assertion	NOUN
cbi-29	353	35	about	about	ADP
cbi-29	353	36	such	such	ADJ
cbi-29	353	37	entities	entity	NOUN
cbi-29	353	38	,	,	PUNCT
cbi-29	353	39	as	as	SCONJ
cbi-29	353	40	those	those	DET
cbi-29	353	41	assertions	assertion	NOUN
cbi-29	353	42	can	can	AUX
cbi-29	353	43	not	not	PART
cbi-29	353	44	be	be	AUX
cbi-29	353	45	tested	test	VERB
cbi-29	353	46	.	.	PUNCT
cbi-29	354	1	our	our	PRON
cbi-29	354	2	minds	mind	NOUN
cbi-29	354	3	(	(	PUNCT
cbi-29	354	4	and	and	CCONJ
cbi-29	354	5	therefore	therefore	ADV
cbi-29	354	6	our	our	PRON
cbi-29	354	7	proofs	proof	NOUN
cbi-29	354	8	)	)	PUNCT
cbi-29	354	9	can	can	AUX
cbi-29	354	10	always	always	ADV
cbi-29	354	11	fail	fail	VERB
cbi-29	354	12	,	,	PUNCT
cbi-29	354	13	therefore	therefore	ADV
cbi-29	354	14	,	,	PUNCT
cbi-29	354	15	building	build	VERB
cbi-29	354	16	on	on	ADP
cbi-29	354	17	premises	premise	NOUN
cbi-29	354	18	which	which	PRON
cbi-29	354	19	can	can	AUX
cbi-29	354	20	only	only	ADV
cbi-29	354	21	be	be	AUX
cbi-29	354	22	proved	prove	VERB
cbi-29	354	23	logically	logically	ADV
cbi-29	354	24	and	and	CCONJ
cbi-29	354	25	not	not	PART
cbi-29	354	26	physically	physically	ADV
cbi-29	354	27	is	be	AUX
cbi-29	354	28	dangerous	dangerous	ADJ
cbi-29	354	29	.	.	PUNCT
cbi-29	355	1	26	26	NUM
cbi-29	355	2	simplifying	simplify	VERB
cbi-29	355	3	and	and	CCONJ
cbi-29	355	4	refactoring	refactoring	NOUN
cbi-29	355	5	introductory	introductory	ADJ
cbi-29	355	6	calculus	calculus	NOUN
cbi-29	355	7	while	while	SCONJ
cbi-29	355	8	these	these	DET
cbi-29	355	9	concerns	concern	NOUN
cbi-29	355	10	are	be	AUX
cbi-29	355	11	understandable	understandable	ADJ
cbi-29	355	12	,	,	PUNCT
cbi-29	355	13	the	the	DET
cbi-29	355	14	long	long	ADJ
cbi-29	355	15	-	-	PUNCT
cbi-29	355	16	term	term	NOUN
cbi-29	355	17	payoff	payoff	NOUN
cbi-29	355	18	will	will	AUX
cbi-29	355	19	come	come	VERB
cbi-29	355	20	from	from	ADP
cbi-29	355	21	helping	help	VERB
cbi-29	355	22	students	student	NOUN
cbi-29	355	23	see	see	VERB
cbi-29	355	24	the	the	DET
cbi-29	355	25	concepts	concept	NOUN
cbi-29	355	26	of	of	ADP
cbi-29	355	27	the	the	DET
cbi-29	355	28	infinite	infinite	ADJ
cbi-29	355	29	and	and	CCONJ
cbi-29	355	30	infinitesimal	infinitesimal	ADJ
cbi-29	355	31	more	more	ADV
cbi-29	355	32	clearly	clearly	ADV
cbi-29	355	33	,	,	PUNCT
cbi-29	355	34	and	and	CCONJ
cbi-29	355	35	that	that	PRON
cbi-29	355	36	will	will	AUX
cbi-29	355	37	only	only	ADV
cbi-29	355	38	come	come	VERB
cbi-29	355	39	from	from	ADP
cbi-29	355	40	practice	practice	NOUN
cbi-29	355	41	and	and	CCONJ
cbi-29	355	42	familiarity	familiarity	NOUN
cbi-29	355	43	with	with	ADP
cbi-29	355	44	the	the	DET
cbi-29	355	45	concepts	concept	NOUN
cbi-29	355	46	.	.	PUNCT
cbi-29	356	1	the	the	DET
cbi-29	356	2	infinite	infinite	NOUN
cbi-29	356	3	should	should	AUX
cbi-29	356	4	not	not	PART
cbi-29	356	5	be	be	AUX
cbi-29	356	6	feared	fear	VERB
cbi-29	356	7	,	,	PUNCT
cbi-29	356	8	in	in	ADP
cbi-29	356	9	fact	fact	NOUN
cbi-29	356	10	,	,	PUNCT
cbi-29	356	11	mathematics	mathematic	NOUN
cbi-29	356	12	is	be	AUX
cbi-29	356	13	one	one	NUM
cbi-29	356	14	area	area	NOUN
cbi-29	356	15	which	which	PRON
cbi-29	356	16	allows	allow	VERB
cbi-29	356	17	us	we	PRON
cbi-29	356	18	to	to	PART
cbi-29	356	19	grapple	grapple	VERB
cbi-29	356	20	with	with	ADP
cbi-29	356	21	the	the	DET
cbi-29	356	22	infinite	infinite	NOUN
cbi-29	356	23	on	on	ADP
cbi-29	356	24	a	a	DET
cbi-29	356	25	much	much	ADV
cbi-29	356	26	more	more	ADV
cbi-29	356	27	rigorous	rigorous	ADJ
cbi-29	356	28	basis	basis	NOUN
cbi-29	356	29	.	.	PUNCT
cbi-29	357	1	13	13	NUM
cbi-29	357	2	conclusion	conclusion	NOUN
cbi-29	357	3	by	by	ADP
cbi-29	357	4	making	make	VERB
cbi-29	357	5	a	a	DET
cbi-29	357	6	few	few	ADJ
cbi-29	357	7	modifications	modification	NOUN
cbi-29	357	8	to	to	ADP
cbi-29	357	9	the	the	DET
cbi-29	357	10	way	way	NOUN
cbi-29	357	11	that	that	PRON
cbi-29	357	12	calculus	calculus	NOUN
cbi-29	357	13	is	be	AUX
cbi-29	357	14	taught	teach	VERB
cbi-29	357	15	,	,	PUNCT
cbi-29	357	16	students	student	NOUN
cbi-29	357	17	can	can	AUX
cbi-29	357	18	be	be	AUX
cbi-29	357	19	presented	present	VERB
cbi-29	357	20	a	a	DET
cbi-29	357	21	more	more	ADV
cbi-29	357	22	unified	unified	ADJ
cbi-29	357	23	,	,	PUNCT
cbi-29	357	24	holistic	holistic	ADJ
cbi-29	357	25	system	system	NOUN
cbi-29	357	26	.	.	PUNCT
cbi-29	358	1	this	this	PRON
cbi-29	358	2	is	be	AUX
cbi-29	358	3	both	both	PRON
cbi-29	358	4	easier	easy	ADJ
cbi-29	358	5	to	to	PART
cbi-29	358	6	use	use	VERB
cbi-29	358	7	and	and	CCONJ
cbi-29	358	8	easier	easy	ADJ
cbi-29	358	9	to	to	PART
cbi-29	358	10	understand	understand	VERB
cbi-29	358	11	.	.	PUNCT
cbi-29	359	1	having	have	VERB
cbi-29	359	2	a	a	DET
cbi-29	359	3	single	single	ADJ
cbi-29	359	4	process	process	NOUN
cbi-29	359	5	and	and	CCONJ
cbi-29	359	6	expanding	expand	VERB
cbi-29	359	7	out	out	ADP
cbi-29	359	8	its	its	PRON
cbi-29	359	9	usage	usage	NOUN
cbi-29	359	10	to	to	ADP
cbi-29	359	11	more	more	ADJ
cbi-29	359	12	and	and	CCONJ
cbi-29	359	13	more	more	ADV
cbi-29	359	14	complex	complex	ADJ
cbi-29	359	15	cases	case	NOUN
cbi-29	359	16	is	be	AUX
cbi-29	359	17	much	much	ADV
cbi-29	359	18	more	more	ADV
cbi-29	359	19	straightforward	straightforward	ADJ
cbi-29	359	20	than	than	ADP
cbi-29	359	21	having	have	VERB
cbi-29	359	22	to	to	PART
cbi-29	359	23	reinvent	reinvent	VERB
cbi-29	359	24	the	the	DET
cbi-29	359	25	system	system	NOUN
cbi-29	359	26	at	at	ADP
cbi-29	359	27	every	every	DET
cbi-29	359	28	step	step	NOUN
cbi-29	359	29	,	,	PUNCT
cbi-29	359	30	and	and	CCONJ
cbi-29	359	31	forcing	force	VERB
cbi-29	359	32	students	student	NOUN
cbi-29	359	33	to	to	PART
cbi-29	359	34	memorize	memorize	VERB
cbi-29	359	35	different	different	ADJ
cbi-29	359	36	processes	process	NOUN
cbi-29	359	37	for	for	ADP
cbi-29	359	38	different	different	ADJ
cbi-29	359	39	situations	situation	NOUN
cbi-29	359	40	.	.	PUNCT
cbi-29	360	1	the	the	DET
cbi-29	360	2	changes	change	NOUN
cbi-29	360	3	proposed	propose	VERB
cbi-29	360	4	here	here	ADV
cbi-29	360	5	include	include	VERB
cbi-29	360	6	:	:	PUNCT
cbi-29	360	7	•	•	ADV
cbi-29	360	8	separating	separate	VERB
cbi-29	360	9	differentiation	differentiation	NOUN
cbi-29	360	10	from	from	ADP
cbi-29	360	11	finding	find	VERB
cbi-29	360	12	the	the	DET
cbi-29	360	13	derivative	derivative	NOUN
cbi-29	360	14	.	.	PUNCT
cbi-29	361	1	this	this	PRON
cbi-29	361	2	allows	allow	VERB
cbi-29	361	3	the	the	DET
cbi-29	361	4	unification	unification	NOUN
cbi-29	361	5	of	of	ADP
cbi-29	361	6	explicit	explicit	ADJ
cbi-29	361	7	differentiation	differentiation	NOUN
cbi-29	361	8	,	,	PUNCT
cbi-29	361	9	implicit	implicit	ADJ
cbi-29	361	10	differentiation	differentiation	NOUN
cbi-29	361	11	,	,	PUNCT
cbi-29	361	12	and	and	CCONJ
cbi-29	361	13	multivariable	multivariable	ADJ
cbi-29	361	14	differentiation	differentiation	NOUN
cbi-29	361	15	.	.	PUNCT
cbi-29	362	1	additionally	additionally	ADV
cbi-29	362	2	,	,	PUNCT
cbi-29	362	3	it	it	PRON
cbi-29	362	4	helps	help	VERB
cbi-29	362	5	explain	explain	VERB
cbi-29	362	6	(	(	PUNCT
cbi-29	362	7	and	and	CCONJ
cbi-29	362	8	correct	correct	ADJ
cbi-29	362	9	)	)	PUNCT
cbi-29	362	10	the	the	DET
cbi-29	362	11	notions	notion	NOUN
cbi-29	362	12	of	of	ADP
cbi-29	362	13	higher	high	ADJ
cbi-29	362	14	-	-	PUNCT
cbi-29	362	15	order	order	NOUN
cbi-29	362	16	differentials	differential	NOUN
cbi-29	362	17	.	.	PUNCT
cbi-29	363	1	•	•	NUM
cbi-29	363	2	treating	treat	VERB
cbi-29	363	3	differentials	differential	NOUN
cbi-29	363	4	algebraically	algebraically	ADV
cbi-29	363	5	.	.	PUNCT
cbi-29	364	1	this	this	PRON
cbi-29	364	2	is	be	AUX
cbi-29	364	3	an	an	DET
cbi-29	364	4	extension	extension	NOUN
cbi-29	364	5	of	of	ADP
cbi-29	364	6	the	the	DET
cbi-29	364	7	separation	separation	NOUN
cbi-29	364	8	of	of	ADP
cbi-29	364	9	finding	find	VERB
cbi-29	364	10	differentials	differential	NOUN
cbi-29	364	11	and	and	CCONJ
cbi-29	364	12	derivatives	derivative	NOUN
cbi-29	364	13	.	.	PUNCT
cbi-29	365	1	additionally	additionally	ADV
cbi-29	365	2	,	,	PUNCT
cbi-29	365	3	when	when	SCONJ
cbi-29	365	4	done	do	VERB
cbi-29	365	5	correctly	correctly	ADV
cbi-29	365	6	,	,	PUNCT
cbi-29	365	7	it	it	PRON
cbi-29	365	8	improves	improve	VERB
cbi-29	365	9	the	the	DET
cbi-29	365	10	usability	usability	NOUN
cbi-29	365	11	of	of	ADP
cbi-29	365	12	higher	high	ADJ
cbi-29	365	13	-	-	PUNCT
cbi-29	365	14	order	order	NOUN
cbi-29	365	15	differentials	differential	NOUN
cbi-29	365	16	and	and	CCONJ
cbi-29	365	17	derivatives	derivative	NOUN
cbi-29	365	18	.	.	PUNCT
cbi-29	366	1	•	•	NOUN
cbi-29	366	2	using	use	VERB
cbi-29	366	3	a	a	DET
cbi-29	366	4	rule	rule	NOUN
cbi-29	366	5	for	for	ADP
cbi-29	366	6	uv	uv	NOUN
cbi-29	366	7	instead	instead	ADV
cbi-29	366	8	of	of	ADP
cbi-29	366	9	logarithmic	logarithmic	ADJ
cbi-29	366	10	differentiation	differentiation	NOUN
cbi-29	366	11	.	.	PUNCT
cbi-29	367	1	instead	instead	ADV
cbi-29	367	2	of	of	ADP
cbi-29	367	3	forcing	force	VERB
cbi-29	367	4	students	student	NOUN
cbi-29	367	5	to	to	PART
cbi-29	367	6	use	use	VERB
cbi-29	367	7	different	different	ADJ
cbi-29	367	8	types	type	NOUN
cbi-29	367	9	of	of	ADP
cbi-29	367	10	processes	process	NOUN
cbi-29	367	11	for	for	ADP
cbi-29	367	12	different	different	ADJ
cbi-29	367	13	forms	form	NOUN
cbi-29	367	14	,	,	PUNCT
cbi-29	367	15	teaching	teach	VERB
cbi-29	367	16	the	the	DET
cbi-29	367	17	generalized	generalized	ADJ
cbi-29	367	18	power	power	NOUN
cbi-29	367	19	rule	rule	NOUN
cbi-29	367	20	allows	allow	VERB
cbi-29	367	21	students	student	NOUN
cbi-29	367	22	to	to	PART
cbi-29	367	23	take	take	VERB
cbi-29	367	24	the	the	DET
cbi-29	367	25	differential	differential	NOUN
cbi-29	367	26	of	of	ADP
cbi-29	367	27	uv	uv	NOUN
cbi-29	367	28	directly	directly	ADV
cbi-29	367	29	,	,	PUNCT
cbi-29	367	30	just	just	ADV
cbi-29	367	31	as	as	ADP
cbi-29	367	32	with	with	ADP
cbi-29	367	33	every	every	DET
cbi-29	367	34	other	other	ADJ
cbi-29	367	35	form	form	NOUN
cbi-29	367	36	.	.	PUNCT
cbi-29	368	1	•	•	NUM
cbi-29	368	2	using	use	VERB
cbi-29	368	3	hyperreals	hyperreal	NOUN
cbi-29	368	4	for	for	ADP
cbi-29	368	5	limits	limit	NOUN
cbi-29	368	6	.	.	PUNCT
cbi-29	369	1	hyperreals	hyperreal	NOUN
cbi-29	369	2	allow	allow	VERB
cbi-29	369	3	for	for	ADP
cbi-29	369	4	a	a	DET
cbi-29	369	5	more	more	ADV
cbi-29	369	6	intuitive	intuitive	ADJ
cbi-29	369	7	approach	approach	NOUN
cbi-29	369	8	to	to	ADP
cbi-29	369	9	limits	limit	NOUN
cbi-29	369	10	.	.	PUNCT
cbi-29	370	1	additionally	additionally	ADV
cbi-29	370	2	,	,	PUNCT
cbi-29	370	3	moving	move	VERB
cbi-29	370	4	limits	limit	NOUN
cbi-29	370	5	to	to	ADP
cbi-29	370	6	the	the	DET
cbi-29	370	7	end	end	NOUN
cbi-29	370	8	of	of	ADP
cbi-29	370	9	a	a	DET
cbi-29	370	10	first	first	ADJ
cbi-29	370	11	-	-	PUNCT
cbi-29	370	12	year	year	NOUN
cbi-29	370	13	course	course	NOUN
cbi-29	370	14	allows	allow	VERB
cbi-29	370	15	students	student	NOUN
cbi-29	370	16	to	to	PART
cbi-29	370	17	develop	develop	VERB
cbi-29	370	18	intuitions	intuition	NOUN
cbi-29	370	19	around	around	ADP
cbi-29	370	20	the	the	DET
cbi-29	370	21	derivative	derivative	NOUN
cbi-29	370	22	first	first	ADV
cbi-29	370	23	before	before	ADP
cbi-29	370	24	seeing	see	VERB
cbi-29	370	25	the	the	DET
cbi-29	370	26	formal	formal	ADJ
cbi-29	370	27	proof	proof	NOUN
cbi-29	370	28	of	of	ADP
cbi-29	370	29	their	their	PRON
cbi-29	370	30	validity	validity	NOUN
cbi-29	370	31	.	.	PUNCT
cbi-29	371	1	•	•	NUM
cbi-29	371	2	treating	treat	VERB
cbi-29	371	3	integrals	integral	NOUN
cbi-29	371	4	as	as	ADP
cbi-29	371	5	infinite	infinite	ADJ
cbi-29	371	6	sums	sum	NOUN
cbi-29	371	7	.	.	PUNCT
cbi-29	372	1	treating	treat	VERB
cbi-29	372	2	the	the	DET
cbi-29	372	3	integral	integral	ADJ
cbi-29	372	4	as	as	ADP
cbi-29	372	5	an	an	DET
cbi-29	372	6	infinite	infinite	ADJ
cbi-29	372	7	sum	sum	NOUN
cbi-29	372	8	instead	instead	ADV
cbi-29	372	9	of	of	ADP
cbi-29	372	10	an	an	DET
cbi-29	372	11	area	area	NOUN
cbi-29	372	12	under	under	ADP
cbi-29	372	13	a	a	DET
cbi-29	372	14	curve	curve	NOUN
cbi-29	372	15	allows	allow	VERB
cbi-29	372	16	for	for	ADP
cbi-29	372	17	easier	easy	ADJ
cbi-29	372	18	generalization	generalization	NOUN
cbi-29	372	19	of	of	ADP
cbi-29	372	20	the	the	DET
cbi-29	372	21	concept	concept	NOUN
cbi-29	372	22	of	of	ADP
cbi-29	372	23	the	the	DET
cbi-29	372	24	integral	integral	ADJ
cbi-29	372	25	into	into	ADP
cbi-29	372	26	various	various	ADJ
cbi-29	372	27	geometric	geometric	ADJ
cbi-29	372	28	situations	situation	NOUN
cbi-29	372	29	(	(	PUNCT
cbi-29	372	30	and	and	CCONJ
cbi-29	372	31	even	even	ADV
cbi-29	372	32	non	non	ADJ
cbi-29	372	33	-	-	ADJ
cbi-29	372	34	geometric	geometric	ADJ
cbi-29	372	35	situations	situation	NOUN
cbi-29	372	36	)	)	PUNCT
cbi-29	372	37	.	.	PUNCT
cbi-29	373	1	additionally	additionally	ADV
cbi-29	373	2	,	,	PUNCT
cbi-29	373	3	this	this	PRON
cbi-29	373	4	allows	allow	VERB
cbi-29	373	5	for	for	ADP
cbi-29	373	6	a	a	DET
cbi-29	373	7	more	more	ADV
cbi-29	373	8	straightforward	straightforward	ADJ
cbi-29	373	9	generalization	generalization	NOUN
cbi-29	373	10	of	of	ADP
cbi-29	373	11	integration	integration	NOUN
cbi-29	373	12	into	into	ADP
cbi-29	373	13	the	the	DET
cbi-29	373	14	inclusion	inclusion	NOUN
cbi-29	373	15	of	of	ADP
cbi-29	373	16	multiple	multiple	ADJ
cbi-29	373	17	variables	variable	NOUN
cbi-29	373	18	.	.	PUNCT
cbi-29	374	1	the	the	DET
cbi-29	374	2	goal	goal	NOUN
cbi-29	374	3	is	be	AUX
cbi-29	374	4	to	to	PART
cbi-29	374	5	simplify	simplify	VERB
cbi-29	374	6	introductory	introductory	ADJ
cbi-29	374	7	calculus	calculus	NOUN
cbi-29	374	8	while	while	SCONJ
cbi-29	374	9	simultaneously	simultaneously	ADV
cbi-29	374	10	making	make	VERB
cbi-29	374	11	it	it	PRON
cbi-29	374	12	more	more	ADV
cbi-29	374	13	powerful	powerful	ADJ
cbi-29	374	14	.	.	PUNCT
cbi-29	375	1	this	this	PRON
cbi-29	375	2	is	be	AUX
cbi-29	375	3	accomplished	accomplish	VERB
cbi-29	375	4	by	by	ADP
cbi-29	375	5	(	(	PUNCT
cbi-29	375	6	using	use	VERB
cbi-29	375	7	computer	computer	NOUN
cbi-29	375	8	science	science	NOUN
cbi-29	375	9	terminology	terminology	NOUN
cbi-29	375	10	)	)	PUNCT
cbi-29	375	11	“	"	PUNCT
cbi-29	375	12	refactoring	refactoring	NOUN
cbi-29	375	13	”	"	PUNCT
cbi-29	375	14	calculus	calculus	NOUN
cbi-29	375	15	into	into	ADP
cbi-29	375	16	pieces	piece	NOUN
cbi-29	375	17	that	that	PRON
cbi-29	375	18	are	be	AUX
cbi-29	375	19	more	more	ADV
cbi-29	375	20	easily	easily	ADV
cbi-29	375	21	recombined	recombined	ADJ
cbi-29	375	22	,	,	PUNCT
cbi-29	375	23	adapted	adapt	VERB
cbi-29	375	24	,	,	PUNCT
cbi-29	375	25	and	and	CCONJ
cbi-29	375	26	applied	apply	VERB
cbi-29	375	27	to	to	ADP
cbi-29	375	28	various	various	ADJ
cbi-29	375	29	situations	situation	NOUN
cbi-29	375	30	.	.	PUNCT
cbi-29	376	1	since	since	SCONJ
cbi-29	376	2	differentials	differential	NOUN
cbi-29	376	3	can	can	AUX
cbi-29	376	4	always	always	ADV
cbi-29	376	5	be	be	AUX
cbi-29	376	6	transformed	transform	VERB
cbi-29	376	7	into	into	ADP
cbi-29	376	8	derivatives	derivative	NOUN
cbi-29	376	9	by	by	ADP
cbi-29	376	10	algebraic	algebraic	ADJ
cbi-29	376	11	rearrangement	rearrangement	NOUN
cbi-29	376	12	,	,	PUNCT
cbi-29	376	13	nothing	nothing	PRON
cbi-29	376	14	is	be	AUX
cbi-29	376	15	lost	lose	VERB
cbi-29	376	16	in	in	ADP
cbi-29	376	17	their	their	PRON
cbi-29	376	18	treatment	treatment	NOUN
cbi-29	376	19	as	as	ADP
cbi-29	376	20	individuated	individuated	ADJ
cbi-29	376	21	entities	entity	NOUN
cbi-29	376	22	.	.	PUNCT
cbi-29	377	1	these	these	DET
cbi-29	377	2	ideas	idea	NOUN
cbi-29	377	3	have	have	AUX
cbi-29	377	4	been	be	AUX
cbi-29	377	5	incorporated	incorporate	VERB
cbi-29	377	6	into	into	ADP
cbi-29	377	7	a	a	DET
cbi-29	377	8	new	new	ADJ
cbi-29	377	9	text	text	NOUN
cbi-29	377	10	on	on	ADP
cbi-29	377	11	calculus	calculus	NOUN
cbi-29	377	12	(	(	PUNCT
cbi-29	377	13	bartlett	bartlett	PROPN
cbi-29	377	14	,	,	PUNCT
cbi-29	377	15	2018	2018	NUM
cbi-29	377	16	)	)	PUNCT
cbi-29	377	17	,	,	PUNCT
cbi-29	377	18	and	and	CCONJ
cbi-29	377	19	future	future	ADJ
cbi-29	377	20	study	study	NOUN
cbi-29	377	21	is	be	AUX
cbi-29	377	22	needed	need	VERB
cbi-29	377	23	to	to	PART
cbi-29	377	24	fully	fully	ADV
cbi-29	377	25	assess	assess	VERB
cbi-29	377	26	the	the	DET
cbi-29	377	27	impact	impact	NOUN
cbi-29	377	28	of	of	ADP
cbi-29	377	29	these	these	DET
cbi-29	377	30	ideas	idea	NOUN
cbi-29	377	31	(	(	PUNCT
cbi-29	377	32	both	both	CCONJ
cbi-29	377	33	positive	positive	ADJ
cbi-29	377	34	and	and	CCONJ
cbi-29	377	35	negative	negative	ADJ
cbi-29	377	36	)	)	PUNCT
cbi-29	377	37	on	on	ADP
cbi-29	377	38	the	the	DET
cbi-29	377	39	teaching	teaching	NOUN
cbi-29	377	40	of	of	ADP
cbi-29	377	41	calculus	calculus	NOUN
cbi-29	377	42	.	.	PUNCT
cbi-29	378	1	references	reference	NOUN
cbi-29	378	2	bartlett	bartlett	PROPN
cbi-29	378	3	,	,	PUNCT
cbi-29	378	4	j	j	PROPN
cbi-29	378	5	(	(	PUNCT
cbi-29	378	6	2018	2018	NUM
cbi-29	378	7	)	)	PUNCT
cbi-29	378	8	.	.	PUNCT
cbi-29	379	1	calculus	calculus	NOUN
cbi-29	379	2	from	from	ADP
cbi-29	379	3	the	the	DET
cbi-29	379	4	ground	ground	NOUN
cbi-29	379	5	up	up	ADP
cbi-29	379	6	.	.	PUNCT
cbi-29	380	1	broken	break	VERB
cbi-29	380	2	arrow	arrow	NOUN
cbi-29	380	3	,	,	PUNCT
cbi-29	380	4	ok	ok	ADJ
cbi-29	380	5	:	:	PUNCT
cbi-29	380	6	bp	bp	PROPN
cbi-29	380	7	learning	learning	PROPN
cbi-29	380	8	.	.	PUNCT
cbi-29	381	1	bartlett	bartlett	PROPN
cbi-29	381	2	,	,	PUNCT
cbi-29	381	3	j	j	PROPN
cbi-29	381	4	and	and	CCONJ
cbi-29	381	5	a	a	DET
cbi-29	381	6	z	z	NOUN
cbi-29	381	7	khurshudyan	khurshudyan	NOUN
cbi-29	381	8	(	(	PUNCT
cbi-29	381	9	2018	2018	NUM
cbi-29	381	10	)	)	PUNCT
cbi-29	381	11	.	.	PUNCT
cbi-29	382	1	“	"	PUNCT
cbi-29	382	2	extending	extend	VERB
cbi-29	382	3	the	the	DET
cbi-29	382	4	algebraic	algebraic	ADJ
cbi-29	382	5	manipulability	manipulability	NOUN
cbi-29	382	6	of	of	ADP
cbi-29	382	7	differentials	differential	NOUN
cbi-29	382	8	”	"	PUNCT
cbi-29	382	9	.	.	PUNCT
cbi-29	383	1	in	in	ADP
cbi-29	383	2	:	:	PUNCT
cbi-29	383	3	arxiv	arxiv	PROPN
cbi-29	383	4	1801.09553	1801.09553	PROPN
cbi-29	383	5	.	.	PUNCT
cbi-29	384	1	in	in	ADP
cbi-29	384	2	review	review	PROPN
cbi-29	384	3	.	.	PUNCT
cbi-29	385	1	url	url	PROPN
cbi-29	385	2	:	:	PUNCT
cbi-29	385	3	https://arxiv.org/	https://arxiv.org/	PROPN
cbi-29	385	4	abs/1801.09553	abs/1801.09553	PROPN
cbi-29	385	5	.	.	PUNCT
cbi-29	386	1	berkeley	berkeley	PROPN
cbi-29	386	2	,	,	PUNCT
cbi-29	386	3	g	g	PROPN
cbi-29	386	4	(	(	PUNCT
cbi-29	386	5	1734	1734	NUM
cbi-29	386	6	)	)	PUNCT
cbi-29	386	7	.	.	PUNCT
cbi-29	387	1	the	the	DET
cbi-29	387	2	analyst	analyst	NOUN
cbi-29	387	3	.	.	PUNCT
cbi-29	388	1	bos	bos	PROPN
cbi-29	388	2	,	,	PUNCT
cbi-29	388	3	h	h	NOUN
cbi-29	389	1	j	j	PROPN
cbi-29	389	2	m	m	PROPN
cbi-29	389	3	(	(	PUNCT
cbi-29	389	4	1974	1974	NUM
cbi-29	389	5	)	)	PUNCT
cbi-29	389	6	.	.	PUNCT
cbi-29	390	1	“	"	PUNCT
cbi-29	390	2	differentials	differential	NOUN
cbi-29	390	3	,	,	PUNCT
cbi-29	390	4	higher	high	ADJ
cbi-29	390	5	-	-	PUNCT
cbi-29	390	6	order	order	NOUN
cbi-29	390	7	differentials	differential	NOUN
cbi-29	390	8	,	,	PUNCT
cbi-29	390	9	and	and	CCONJ
cbi-29	390	10	the	the	DET
cbi-29	390	11	derivative	derivative	NOUN
cbi-29	390	12	in	in	ADP
cbi-29	390	13	the	the	DET
cbi-29	390	14	leibnizian	leibnizian	PROPN
cbi-29	390	15	calculus	calculus	NOUN
cbi-29	390	16	”	"	PUNCT
cbi-29	390	17	.	.	PUNCT
cbi-29	391	1	in	in	ADP
cbi-29	391	2	:	:	PUNCT
cbi-29	391	3	archive	archive	NOUN
cbi-29	391	4	for	for	ADP
cbi-29	391	5	history	history	NOUN
cbi-29	391	6	of	of	ADP
cbi-29	391	7	exact	exact	ADJ
cbi-29	391	8	sciences	science	NOUN
cbi-29	391	9	14.1	14.1	NUM
cbi-29	391	10	,	,	PUNCT
cbi-29	391	11	pp	pp	ADJ
cbi-29	391	12	.	.	PUNCT
cbi-29	391	13	1	1	NUM
cbi-29	391	14	–	–	SYM
cbi-29	391	15	90	90	NUM
cbi-29	391	16	.	.	PUNCT
cbi-29	391	17	url	url	PROPN
cbi-29	391	18	:	:	PUNCT
cbi-29	391	19	https://link.springer.com/article/10	https://link.springer.com/article/10	X
cbi-29	391	20	.	.	PUNCT
cbi-29	391	21	1007	1007	NUM
cbi-29	391	22	/	/	SYM
cbi-29	391	23	bf00327456	bf00327456	PROPN
cbi-29	391	24	.	.	PUNCT
cbi-29	392	1	cantor	cantor	PROPN
cbi-29	392	2	,	,	PUNCT
cbi-29	392	3	g	g	PROPN
cbi-29	392	4	(	(	PUNCT
cbi-29	392	5	1915	1915	NUM
cbi-29	392	6	)	)	PUNCT
cbi-29	392	7	.	.	PUNCT
cbi-29	393	1	contributions	contribution	NOUN
cbi-29	393	2	to	to	ADP
cbi-29	393	3	the	the	DET
cbi-29	393	4	founding	founding	NOUN
cbi-29	393	5	of	of	ADP
cbi-29	393	6	the	the	DET
cbi-29	393	7	theory	theory	NOUN
cbi-29	393	8	of	of	ADP
cbi-29	393	9	transfinite	transfinite	ADJ
cbi-29	393	10	numbers	number	NOUN
cbi-29	393	11	.	.	PUNCT
cbi-29	394	1	trans	tran	NOUN
cbi-29	394	2	.	.	PUNCT
cbi-29	395	1	by	by	ADP
cbi-29	395	2	p	p	PROPN
cbi-29	395	3	e	e	PROPN
cbi-29	395	4	b	b	PROPN
cbi-29	395	5	jourdain	jourdain	NOUN
cbi-29	395	6	.	.	PUNCT
cbi-29	396	1	dover	dover	PROPN
cbi-29	396	2	publications	publication	NOUN
cbi-29	396	3	.	.	PUNCT
cbi-29	397	1	url	url	PROPN
cbi-29	397	2	:	:	PUNCT
cbi-29	397	3	https://www.maths	https://www.math	NOUN
cbi-29	397	4	.	.	PUNCT
cbi-29	398	1	ed.ac.uk/~v1ranick/papers/cantor1.pdf	ed.ac.uk/~v1ranick/papers/cantor1.pdf	PROPN
cbi-29	398	2	.	.	PUNCT
cbi-29	399	1	dauben	dauben	PROPN
cbi-29	399	2	,	,	PUNCT
cbi-29	399	3	j	j	PROPN
cbi-29	399	4	w	w	PROPN
cbi-29	399	5	(	(	PUNCT
cbi-29	399	6	1990	1990	NUM
cbi-29	399	7	)	)	PUNCT
cbi-29	399	8	.	.	PUNCT
cbi-29	400	1	georg	georg	PROPN
cbi-29	400	2	cantor	cantor	PROPN
cbi-29	400	3	:	:	PUNCT
cbi-29	400	4	his	his	PRON
cbi-29	400	5	mathematics	mathematic	NOUN
cbi-29	400	6	and	and	CCONJ
cbi-29	400	7	philosophy	philosophy	NOUN
cbi-29	400	8	of	of	ADP
cbi-29	400	9	the	the	DET
cbi-29	400	10	infinite	infinite	NOUN
cbi-29	400	11	.	.	PUNCT
cbi-29	400	12	princeton	princeton	PROPN
cbi-29	400	13	university	university	PROPN
cbi-29	400	14	press	press	NOUN
cbi-29	400	15	.	.	PUNCT
cbi-29	401	1	dray	dray	PROPN
cbi-29	401	2	,	,	PUNCT
cbi-29	401	3	t	t	PROPN
cbi-29	401	4	and	and	CCONJ
cbi-29	401	5	c	c	PROPN
cbi-29	401	6	a	a	DET
cbi-29	401	7	manogue	manogue	NOUN
cbi-29	401	8	(	(	PUNCT
cbi-29	401	9	2010	2010	NUM
cbi-29	401	10	)	)	PUNCT
cbi-29	401	11	.	.	PUNCT
cbi-29	402	1	“	"	PUNCT
cbi-29	402	2	putting	put	VERB
cbi-29	402	3	differentials	differential	NOUN
cbi-29	402	4	back	back	ADV
cbi-29	402	5	into	into	ADP
cbi-29	402	6	calculus	calculus	NOUN
cbi-29	402	7	”	"	PUNCT
cbi-29	402	8	.	.	PUNCT
cbi-29	403	1	in	in	ADP
cbi-29	403	2	:	:	PUNCT
cbi-29	403	3	the	the	DET
cbi-29	403	4	college	college	NOUN
cbi-29	403	5	mathematics	mathematics	PROPN
cbi-29	403	6	journal	journal	PROPN
cbi-29	403	7	41.2	41.2	NUM
cbi-29	403	8	,	,	PUNCT
cbi-29	403	9	pp	pp	ADJ
cbi-29	403	10	.	.	PUNCT
cbi-29	404	1	90–100	90–100	NUM
cbi-29	404	2	.	.	PUNCT
cbi-29	405	1	gonzález	gonzález	PROPN
cbi-29	405	2	-	-	PUNCT
cbi-29	405	3	lloret	lloret	PROPN
cbi-29	405	4	,	,	PUNCT
cbi-29	405	5	m	m	VERB
cbi-29	405	6	and	and	CCONJ
cbi-29	405	7	k	k	PROPN
cbi-29	405	8	b	b	PROPN
cbi-29	405	9	nielson	nielson	PROPN
cbi-29	405	10	(	(	PUNCT
cbi-29	405	11	2015	2015	NUM
cbi-29	405	12	)	)	PUNCT
cbi-29	405	13	.	.	PUNCT
cbi-29	406	1	“	"	PUNCT
cbi-29	406	2	evaluating	evaluate	VERB
cbi-29	406	3	tblt	tblt	NOUN
cbi-29	406	4	:	:	PUNCT
cbi-29	406	5	the	the	DET
cbi-29	406	6	case	case	NOUN
cbi-29	406	7	of	of	ADP
cbi-29	406	8	a	a	DET
cbi-29	406	9	task	task	NOUN
cbi-29	406	10	-	-	PUNCT
cbi-29	406	11	based	base	VERB
cbi-29	406	12	spanish	spanish	ADJ
cbi-29	406	13	program	program	NOUN
cbi-29	406	14	”	"	PUNCT
cbi-29	406	15	.	.	PUNCT
cbi-29	407	1	in	in	ADP
cbi-29	407	2	:	:	PUNCT
cbi-29	407	3	language	language	NOUN
cbi-29	407	4	teaching	teaching	NOUN
cbi-29	407	5	research	research	NOUN
cbi-29	407	6	19.5	19.5	NUM
cbi-29	407	7	.	.	PUNCT
cbi-29	408	1	url	url	PROPN
cbi-29	408	2	:	:	PUNCT
cbi-29	409	1	https://	https://	PROPN
cbi-29	409	2	www.academia.edu/6763175/evaluating_tblt_the	www.academia.edu/6763175/evaluating_tblt_the	PROPN
cbi-29	409	3	_	_	PROPN
cbi-29	409	4	case_of_a_task	case_of_a_task	NOUN
cbi-29	409	5	-	-	PUNCT
cbi-29	409	6	based_spanish_program	based_spanish_program	PROPN
cbi-29	409	7	.	.	PUNCT
cbi-29	409	8	henle	henle	PROPN
cbi-29	409	9	,	,	PUNCT
cbi-29	409	10	j	j	PROPN
cbi-29	409	11	m	m	PROPN
cbi-29	409	12	and	and	CCONJ
cbi-29	409	13	e	e	PROPN
cbi-29	409	14	m	m	PROPN
cbi-29	409	15	kleinberg	kleinberg	PROPN
cbi-29	409	16	(	(	PUNCT
cbi-29	409	17	2003	2003	NUM
cbi-29	409	18	)	)	PUNCT
cbi-29	409	19	.	.	PUNCT
cbi-29	410	1	infinitesimal	infinitesimal	ADJ
cbi-29	410	2	calculus	calculus	NOUN
cbi-29	410	3	.	.	PUNCT
cbi-29	411	1	dover	dover	PROPN
cbi-29	411	2	publications	publications	PROPN
cbi-29	411	3	.	.	PUNCT
cbi-29	412	1	katz	katz	PROPN
cbi-29	412	2	,	,	PUNCT
cbi-29	412	3	m	m	PROPN
cbi-29	412	4	and	and	CCONJ
cbi-29	412	5	l	l	PROPN
cbi-29	412	6	polev	polev	NOUN
cbi-29	412	7	(	(	PUNCT
cbi-29	412	8	2017	2017	NUM
cbi-29	412	9	)	)	PUNCT
cbi-29	412	10	.	.	PUNCT
cbi-29	413	1	“	"	PUNCT
cbi-29	413	2	from	from	ADP
cbi-29	413	3	pythagoreans	pythagorean	NOUN
cbi-29	413	4	and	and	CCONJ
cbi-29	413	5	weierstrassians	weierstrassian	NOUN
cbi-29	413	6	to	to	ADP
cbi-29	413	7	true	true	ADJ
cbi-29	413	8	infinitesimal	infinitesimal	ADJ
cbi-29	413	9	calculus	calculus	NOUN
cbi-29	413	10	”	"	PUNCT
cbi-29	413	11	.	.	PUNCT
cbi-29	414	1	in	in	ADP
cbi-29	414	2	:	:	PUNCT
cbi-29	414	3	journal	journal	NOUN
cbi-29	414	4	of	of	ADP
cbi-29	414	5	humanistic	humanistic	ADJ
cbi-29	414	6	mathematics	mathematic	NOUN
cbi-29	414	7	7.1	7.1	NUM
cbi-29	414	8	.	.	PUNCT
cbi-29	414	9	url	url	PROPN
cbi-29	414	10	:	:	PUNCT
cbi-29	414	11	http	http	ADJ
cbi-29	414	12	:	:	PUNCT
cbi-29	414	13	//scholarship.claremont.edu	//scholarship.claremont.edu	ADJ
cbi-29	414	14	/	/	SYM
cbi-29	414	15	cgi	cgi	NOUN
cbi-29	414	16	/	/	SYM
cbi-29	414	17	viewcontent	viewcontent	NOUN
cbi-29	414	18	.	.	PUNCT
cbi-29	414	19	cgi?article=1368%5c&context	cgi?article=1368%5c&context	PROPN
cbi-29	414	20	=	=	SYM
cbi-29	414	21	jhm	jhm	PROPN
cbi-29	414	22	.	.	PUNCT
cbi-29	414	23	keisler	keisler	PROPN
cbi-29	414	24	,	,	PUNCT
cbi-29	414	25	h	h	PROPN
cbi-29	414	26	j	j	PROPN
cbi-29	414	27	(	(	PUNCT
cbi-29	414	28	2012	2012	NUM
cbi-29	414	29	)	)	PUNCT
cbi-29	414	30	.	.	PUNCT
cbi-29	415	1	elementary	elementary	PROPN
cbi-29	415	2	calculus	calculus	PROPN
cbi-29	415	3	:	:	PUNCT
cbi-29	415	4	an	an	DET
cbi-29	415	5	infinitesimal	infinitesimal	ADJ
cbi-29	415	6	approach	approach	NOUN
cbi-29	415	7	.	.	PUNCT
cbi-29	416	1	dover	dover	PROPN
cbi-29	416	2	publications	publication	NOUN
cbi-29	416	3	.	.	PUNCT
cbi-29	417	1	volume	volume	NOUN
cbi-29	417	2	1	1	NUM
cbi-29	417	3	,	,	PUNCT
cbi-29	417	4	issue	issue	NOUN
cbi-29	417	5	1	1	NUM
cbi-29	417	6	references	reference	NOUN
cbi-29	417	7	27	27	NUM
cbi-29	417	8	knuth	knuth	NOUN
cbi-29	417	9	,	,	PUNCT
cbi-29	417	10	d	d	X
cbi-29	417	11	(	(	PUNCT
cbi-29	417	12	1974	1974	NUM
cbi-29	417	13	)	)	PUNCT
cbi-29	417	14	.	.	PUNCT
cbi-29	418	1	surreal	surreal	ADJ
cbi-29	418	2	numbers	number	NOUN
cbi-29	418	3	.	.	PUNCT
cbi-29	419	1	addison	addison	PROPN
cbi-29	419	2	-	-	PUNCT
cbi-29	419	3	wesley	wesley	PROPN
cbi-29	419	4	professional	professional	PROPN
cbi-29	419	5	.	.	PUNCT
cbi-29	420	1	robinson	robinson	PROPN
cbi-29	420	2	,	,	PUNCT
cbi-29	420	3	a	a	DET
cbi-29	420	4	(	(	PUNCT
cbi-29	420	5	1974	1974	NUM
cbi-29	420	6	)	)	PUNCT
cbi-29	420	7	.	.	PUNCT
cbi-29	421	1	non	non	ADJ
cbi-29	421	2	-	-	ADJ
cbi-29	421	3	standard	standard	ADJ
cbi-29	421	4	analysis	analysis	NOUN
cbi-29	421	5	.	.	PUNCT
cbi-29	422	1	north	north	NOUN
cbi-29	422	2	-	-	PUNCT
cbi-29	422	3	holland	holland	PROPN
cbi-29	422	4	publishing	publishing	PROPN
cbi-29	422	5	company	company	NOUN
cbi-29	422	6	.	.	PUNCT
cbi-29	423	1	thomson	thomson	PROPN
cbi-29	423	2	,	,	PUNCT
cbi-29	423	3	s	s	PART
cbi-29	423	4	p	p	X
cbi-29	423	5	(	(	PUNCT
cbi-29	423	6	1910	1910	NUM
cbi-29	423	7	)	)	PUNCT
cbi-29	423	8	.	.	PUNCT
cbi-29	424	1	calculus	calculus	NOUN
cbi-29	424	2	made	make	VERB
cbi-29	424	3	easy	easy	ADJ
cbi-29	424	4	.	.	PUNCT
cbi-29	425	1	new	new	PROPN
cbi-29	425	2	york	york	PROPN
cbi-29	425	3	:	:	PUNCT
cbi-29	425	4	macmillan	macmillan	PROPN
cbi-29	425	5	company	company	PROPN
cbi-29	425	6	.	.	PUNCT
cbi-29	426	1	url	url	PROPN
cbi-29	426	2	:	:	PUNCT
cbi-29	427	1	http://www.gutenberg	http://www.gutenberg	PROPN
cbi-29	427	2	.	.	PUNCT
cbi-29	427	3	org	org	PROPN
cbi-29	427	4	/	/	SYM
cbi-29	427	5	ebooks/33283	ebooks/33283	PROPN
cbi-29	427	6	.	.	PUNCT
cbi-29	428	1	wolfe	wolfe	PROPN
cbi-29	428	2	,	,	PUNCT
cbi-29	428	3	alan	alan	PROPN
cbi-29	428	4	(	(	PUNCT
cbi-29	428	5	2014	2014	NUM
cbi-29	428	6	)	)	PUNCT
cbi-29	428	7	.	.	PUNCT
cbi-29	429	1	“	"	PUNCT
cbi-29	429	2	dual	dual	ADJ
cbi-29	429	3	numbers	number	NOUN
cbi-29	429	4	and	and	CCONJ
cbi-29	429	5	automatic	automatic	ADJ
cbi-29	429	6	differentiation	differentiation	NOUN
cbi-29	429	7	”	"	PUNCT
cbi-29	429	8	.	.	PUNCT
cbi-29	430	1	in	in	ADP
cbi-29	430	2	:	:	PUNCT
cbi-29	430	3	the	the	DET
cbi-29	430	4	blog	blog	NOUN
cbi-29	430	5	at	at	ADP
cbi-29	430	6	the	the	DET
cbi-29	430	7	bottom	bottom	NOUN
cbi-29	430	8	of	of	ADP
cbi-29	430	9	the	the	DET
cbi-29	430	10	sea	sea	PROPN
cbi-29	430	11	.	.	PUNCT
cbi-29	430	12	url	url	PROPN
cbi-29	430	13	:	:	PUNCT
cbi-29	430	14	https://blog.demofox.org/2014/12/30/dualnumbers-automatic-differentiation/.	https://blog.demofox.org/2014/12/30/dualnumbers-automatic-differentiation/.	PROPN
cbi-29	430	15	zach	zach	PROPN
cbi-29	430	16	,	,	PUNCT
cbi-29	430	17	r	r	NOUN
cbi-29	430	18	(	(	PUNCT
cbi-29	430	19	2016	2016	NUM
cbi-29	430	20	)	)	PUNCT
cbi-29	430	21	.	.	PUNCT
cbi-29	431	1	“	"	PUNCT
cbi-29	431	2	hilbert	hilbert	PROPN
cbi-29	431	3	’s	’s	PART
cbi-29	431	4	program	program	NOUN
cbi-29	431	5	”	"	PUNCT
cbi-29	431	6	.	.	PUNCT
cbi-29	432	1	in	in	ADP
cbi-29	432	2	:	:	PUNCT
cbi-29	432	3	the	the	DET
cbi-29	432	4	stanford	stanford	PROPN
cbi-29	432	5	encyclopedia	encyclopedia	NOUN
cbi-29	432	6	of	of	ADP
cbi-29	432	7	philosophy	philosophy	NOUN
cbi-29	432	8	.	.	PUNCT
cbi-29	433	1	ed	ed	NOUN
cbi-29	433	2	.	.	PUNCT
cbi-29	434	1	by	by	ADP
cbi-29	434	2	edward	edward	PROPN
cbi-29	434	3	n.	n.	PROPN
cbi-29	434	4	zalta	zalta	PROPN
cbi-29	434	5	.	.	PUNCT
cbi-29	435	1	spring	spring	NOUN
cbi-29	435	2	2016	2016	NUM
cbi-29	435	3	.	.	PUNCT
cbi-29	436	1	metaphysics	metaphysics	PROPN
cbi-29	436	2	research	research	NOUN
cbi-29	436	3	lab	lab	PROPN
cbi-29	436	4	,	,	PUNCT
cbi-29	436	5	stanford	stanford	PROPN
cbi-29	436	6	university	university	PROPN
cbi-29	436	7	.	.	PUNCT
cbi-29	437	1	url	url	PROPN
cbi-29	437	2	:	:	PUNCT
cbi-29	437	3	https	https	NOUN
cbi-29	437	4	:	:	PUNCT
cbi-29	437	5	/	/	SYM
cbi-29	437	6	/	/	SYM
cbi-29	437	7	plato	plato	PROPN
cbi-29	437	8	.	.	PUNCT
cbi-29	438	1	stanford	stanford	PROPN
cbi-29	438	2	.	.	PUNCT
cbi-29	439	1	edu	edu	PROPN
cbi-29	439	2	/	/	SYM
cbi-29	439	3	archives	archive	NOUN
cbi-29	439	4	/	/	SYM
cbi-29	439	5	spr2016	spr2016	ADJ
cbi-29	439	6	/	/	SYM
cbi-29	439	7	entries	entry	NOUN
cbi-29	439	8	/	/	SYM
cbi-29	439	9	hilbert	hilbert	NOUN
cbi-29	439	10	-	-	PUNCT
cbi-29	439	11	program/.	program/.	ADJ