id	sid	tid	token	lemma	pos
ajst-25566	1	1	academic	academic	ADJ
ajst-25566	1	2	journal	journal	NOUN
ajst-25566	1	3	of	of	ADP
ajst-25566	1	4	science	science	NOUN
ajst-25566	1	5	and	and	CCONJ
ajst-25566	1	6	technology	technology	NOUN
ajst-25566	1	7	issn	issn	NOUN
ajst-25566	1	8	:	:	PUNCT
ajst-25566	1	9	2771	2771	NUM
ajst-25566	1	10	-	-	SYM
ajst-25566	1	11	3032	3032	NUM
ajst-25566	1	12	|	|	NOUN
ajst-25566	1	13	vol	vol	NOUN
ajst-25566	1	14	.	.	PROPN
ajst-25566	2	1	12	12	NUM
ajst-25566	2	2	,	,	PUNCT
ajst-25566	2	3	no	no	INTJ
ajst-25566	2	4	.	.	NOUN
ajst-25566	2	5	2	2	NUM
ajst-25566	2	6	,	,	PUNCT
ajst-25566	2	7	2024	2024	NUM
ajst-25566	2	8	59	59	NUM
ajst-25566	3	1	how	how	SCONJ
ajst-25566	3	2	to	to	PART
ajst-25566	3	3	find	find	VERB
ajst-25566	3	4	the	the	DET
ajst-25566	3	5	maximum	maximum	ADJ
ajst-25566	3	6	difference	difference	NOUN
ajst-25566	3	7	between	between	ADP
ajst-25566	3	8	the	the	DET
ajst-25566	3	9	intervals	interval	NOUN
ajst-25566	3	10	of	of	ADP
ajst-25566	3	11	the	the	DET
ajst-25566	3	12	two	two	NUM
ajst-25566	3	13	closest	close	ADJ
ajst-25566	3	14	intersection	intersection	NOUN
ajst-25566	3	15	points	point	NOUN
ajst-25566	3	16	of	of	ADP
ajst-25566	3	17	two	two	NUM
ajst-25566	3	18	functions	function	NOUN
ajst-25566	3	19	rongzhen	rongzhen	ADV
ajst-25566	3	20	zhu	zhu	PROPN
ajst-25566	3	21	,	,	PUNCT
ajst-25566	3	22	yongtai	yongtai	PROPN
ajst-25566	3	23	hao	hao	PROPN
ajst-25566	3	24	,	,	PUNCT
ajst-25566	3	25	yiwen	yiwen	PROPN
ajst-25566	3	26	liu	liu	PROPN
ajst-25566	3	27	beijing	beijing	PROPN
ajst-25566	3	28	haidian	haidian	PROPN
ajst-25566	3	29	foreign	foreign	PROPN
ajst-25566	3	30	language	language	PROPN
ajst-25566	3	31	shi	shi	PROPN
ajst-25566	3	32	yan	yan	PROPN
ajst-25566	3	33	school	school	PROPN
ajst-25566	3	34	,	,	PUNCT
ajst-25566	3	35	beijing	beijing	PROPN
ajst-25566	3	36	,	,	PUNCT
ajst-25566	3	37	china	china	PROPN
ajst-25566	3	38	abstract	abstract	PROPN
ajst-25566	3	39	:	:	PUNCT
ajst-25566	3	40	a	a	DET
ajst-25566	3	41	new	new	ADJ
ajst-25566	3	42	method	method	NOUN
ajst-25566	3	43	is	be	AUX
ajst-25566	3	44	proposed	propose	VERB
ajst-25566	3	45	in	in	ADP
ajst-25566	3	46	this	this	DET
ajst-25566	3	47	paper	paper	NOUN
ajst-25566	3	48	to	to	PART
ajst-25566	3	49	solve	solve	VERB
ajst-25566	3	50	the	the	DET
ajst-25566	3	51	maximum	maximum	ADJ
ajst-25566	3	52	difference	difference	NOUN
ajst-25566	3	53	between	between	ADP
ajst-25566	3	54	two	two	NUM
ajst-25566	3	55	functions	function	NOUN
ajst-25566	3	56	in	in	ADP
ajst-25566	3	57	the	the	DET
ajst-25566	3	58	two	two	NUM
ajst-25566	3	59	nearest	near	ADJ
ajst-25566	3	60	intersecting	intersecting	ADJ
ajst-25566	3	61	intervals	interval	NOUN
ajst-25566	3	62	by	by	ADP
ajst-25566	3	63	using	use	VERB
ajst-25566	3	64	the	the	DET
ajst-25566	3	65	mean	mean	ADJ
ajst-25566	3	66	value	value	NOUN
ajst-25566	3	67	theorem	theorem	NOUN
ajst-25566	3	68	(	(	PUNCT
ajst-25566	3	69	mvt	mvt	PROPN
ajst-25566	3	70	)	)	PUNCT
ajst-25566	3	71	.	.	PUNCT
ajst-25566	4	1	at	at	ADP
ajst-25566	4	2	the	the	DET
ajst-25566	4	3	same	same	ADJ
ajst-25566	4	4	time	time	NOUN
ajst-25566	4	5	,	,	PUNCT
ajst-25566	4	6	this	this	DET
ajst-25566	4	7	paper	paper	NOUN
ajst-25566	4	8	describes	describe	VERB
ajst-25566	4	9	the	the	DET
ajst-25566	4	10	theoretical	theoretical	ADJ
ajst-25566	4	11	basis	basis	NOUN
ajst-25566	4	12	and	and	CCONJ
ajst-25566	4	13	implementation	implementation	NOUN
ajst-25566	4	14	of	of	ADP
ajst-25566	4	15	the	the	DET
ajst-25566	4	16	method	method	NOUN
ajst-25566	4	17	and	and	CCONJ
ajst-25566	4	18	uses	use	VERB
ajst-25566	4	19	examples	example	NOUN
ajst-25566	4	20	to	to	PART
ajst-25566	4	21	verify	verify	VERB
ajst-25566	4	22	its	its	PRON
ajst-25566	4	23	effectiveness	effectiveness	NOUN
ajst-25566	4	24	.	.	PUNCT
ajst-25566	5	1	the	the	DET
ajst-25566	5	2	goal	goal	NOUN
ajst-25566	5	3	is	be	AUX
ajst-25566	5	4	to	to	PART
ajst-25566	5	5	provide	provide	VERB
ajst-25566	5	6	a	a	DET
ajst-25566	5	7	simplified	simplified	ADJ
ajst-25566	5	8	and	and	CCONJ
ajst-25566	5	9	efficient	efficient	ADJ
ajst-25566	5	10	tool	tool	NOUN
ajst-25566	5	11	for	for	ADP
ajst-25566	5	12	solving	solve	VERB
ajst-25566	5	13	complex	complex	ADJ
ajst-25566	5	14	functional	functional	ADJ
ajst-25566	5	15	analyses	analysis	NOUN
ajst-25566	5	16	.	.	PUNCT
ajst-25566	6	1	keywords	keyword	NOUN
ajst-25566	6	2	:	:	PUNCT
ajst-25566	6	3	mvt	mvt	NOUN
ajst-25566	6	4	;	;	PUNCT
ajst-25566	6	5	new	new	ADJ
ajst-25566	6	6	mathematical	mathematical	ADJ
ajst-25566	6	7	techniques	technique	NOUN
ajst-25566	6	8	;	;	PUNCT
ajst-25566	6	9	absolute	absolute	ADJ
ajst-25566	6	10	maximum	maximum	NOUN
ajst-25566	6	11	.	.	PROPN
ajst-25566	7	1	1	1	X
ajst-25566	7	2	.	.	X
ajst-25566	7	3	introduction	introduction	NOUN
ajst-25566	7	4	the	the	DET
ajst-25566	7	5	research	research	NOUN
ajst-25566	7	6	idea	idea	NOUN
ajst-25566	7	7	of	of	ADP
ajst-25566	7	8	this	this	DET
ajst-25566	7	9	paper	paper	NOUN
ajst-25566	7	10	comes	come	VERB
ajst-25566	7	11	from	from	ADP
ajst-25566	7	12	a	a	DET
ajst-25566	7	13	calculus	calculus	NOUN
ajst-25566	7	14	bc	bc	PROPN
ajst-25566	7	15	exam	exam	PROPN
ajst-25566	7	16	,	,	PUNCT
ajst-25566	7	17	which	which	PRON
ajst-25566	7	18	focuses	focus	VERB
ajst-25566	7	19	on	on	ADP
ajst-25566	7	20	the	the	DET
ajst-25566	7	21	intersection	intersection	NOUN
ajst-25566	7	22	of	of	ADP
ajst-25566	7	23	two	two	NUM
ajst-25566	7	24	functions	function	NOUN
ajst-25566	7	25	[	[	X
ajst-25566	7	26	1	1	NUM
ajst-25566	7	27	]	]	PUNCT
ajst-25566	7	28	.	.	PUNCT
ajst-25566	8	1	for	for	ADP
ajst-25566	8	2	xy	xy	PROPN
ajst-25566	8	3			NOUN
ajst-25566	8	4	1	1	NUM
ajst-25566	8	5	and	and	CCONJ
ajst-25566	8	6	xy	xy	PROPN
ajst-25566	8	7	3	3	NUM
ajst-25566	8	8	2	2	NUM
ajst-25566	8	9	2	2	NUM
ajst-25566	8	10			NOUN
ajst-25566	8	11	,	,	PUNCT
ajst-25566	8	12	we	we	PRON
ajst-25566	8	13	aim	aim	VERB
ajst-25566	8	14	to	to	PART
ajst-25566	8	15	find	find	VERB
ajst-25566	8	16	the	the	DET
ajst-25566	8	17	x	x	NOUN
ajst-25566	8	18	value	value	NOUN
ajst-25566	8	19	that	that	PRON
ajst-25566	8	20	maximizes	maximize	VERB
ajst-25566	8	21	the	the	DET
ajst-25566	8	22	closed	closed	ADJ
ajst-25566	8	23	area	area	NOUN
ajst-25566	8	24	between	between	ADP
ajst-25566	8	25	the	the	DET
ajst-25566	8	26	intersection	intersection	NOUN
ajst-25566	8	27	of	of	ADP
ajst-25566	8	28	these	these	DET
ajst-25566	8	29	two	two	NUM
ajst-25566	8	30	functions	function	NOUN
ajst-25566	8	31	.	.	PUNCT
ajst-25566	9	1	it	it	PRON
ajst-25566	9	2	is	be	AUX
ajst-25566	9	3	noteworthy	noteworthy	ADJ
ajst-25566	9	4	that	that	SCONJ
ajst-25566	9	5	the	the	DET
ajst-25566	9	6	second	second	ADJ
ajst-25566	9	7	derivative	derivative	NOUN
ajst-25566	9	8	of	of	ADP
ajst-25566	9	9	a	a	DET
ajst-25566	9	10	function	function	NOUN
ajst-25566	9	11	does	do	AUX
ajst-25566	9	12	not	not	PART
ajst-25566	9	13	have	have	VERB
ajst-25566	9	14	a	a	DET
ajst-25566	9	15	symbolic	symbolic	ADJ
ajst-25566	9	16	change	change	NOUN
ajst-25566	9	17	in	in	ADP
ajst-25566	9	18	this	this	DET
ajst-25566	9	19	exam	exam	NOUN
ajst-25566	9	20	,	,	PUNCT
ajst-25566	9	21	so	so	SCONJ
ajst-25566	9	22	the	the	DET
ajst-25566	9	23	students	student	NOUN
ajst-25566	9	24	'	'	PART
ajst-25566	9	25	problem	problem	NOUN
ajst-25566	9	26	-	-	PUNCT
ajst-25566	9	27	solving	solve	VERB
ajst-25566	9	28	process	process	NOUN
ajst-25566	9	29	is	be	AUX
ajst-25566	9	30	relatively	relatively	ADV
ajst-25566	9	31	simple	simple	ADJ
ajst-25566	9	32	,	,	PUNCT
ajst-25566	9	33	and	and	CCONJ
ajst-25566	9	34	the	the	DET
ajst-25566	9	35	knowledge	knowledge	NOUN
ajst-25566	9	36	and	and	CCONJ
ajst-25566	9	37	skills	skill	NOUN
ajst-25566	9	38	required	require	VERB
ajst-25566	9	39	to	to	PART
ajst-25566	9	40	solve	solve	VERB
ajst-25566	9	41	the	the	DET
ajst-25566	9	42	problem	problem	NOUN
ajst-25566	9	43	are	be	AUX
ajst-25566	9	44	not	not	PART
ajst-25566	9	45	complex	complex	ADJ
ajst-25566	9	46	.	.	PUNCT
ajst-25566	10	1	they	they	PRON
ajst-25566	10	2	can	can	AUX
ajst-25566	10	3	be	be	AUX
ajst-25566	10	4	understood	understand	VERB
ajst-25566	10	5	by	by	ADP
ajst-25566	10	6	all	all	DET
ajst-25566	10	7	the	the	DET
ajst-25566	10	8	students	student	NOUN
ajst-25566	10	9	.	.	PUNCT
ajst-25566	11	1	however	however	ADV
ajst-25566	11	2	,	,	PUNCT
ajst-25566	11	3	we	we	PRON
ajst-25566	11	4	find	find	VERB
ajst-25566	11	5	a	a	DET
ajst-25566	11	6	universally	universally	ADV
ajst-25566	11	7	applicable	applicable	ADJ
ajst-25566	11	8	mathematical	mathematical	ADJ
ajst-25566	11	9	problem	problem	NOUN
ajst-25566	11	10	by	by	ADP
ajst-25566	11	11	studying	study	VERB
ajst-25566	11	12	these	these	DET
ajst-25566	11	13	problems	problem	NOUN
ajst-25566	11	14	:	:	PUNCT
ajst-25566	11	15	finding	find	VERB
ajst-25566	11	16	their	their	PRON
ajst-25566	11	17	maximum	maximum	ADJ
ajst-25566	11	18	difference	difference	NOUN
ajst-25566	11	19	between	between	ADP
ajst-25566	11	20	the	the	DET
ajst-25566	11	21	closest	close	ADJ
ajst-25566	11	22	intersections	intersection	NOUN
ajst-25566	11	23	of	of	ADP
ajst-25566	11	24	two	two	NUM
ajst-25566	11	25	functions	function	NOUN
ajst-25566	11	26	.	.	PUNCT
ajst-25566	12	1	this	this	DET
ajst-25566	12	2	issue	issue	NOUN
ajst-25566	12	3	is	be	AUX
ajst-25566	12	4	of	of	ADP
ajst-25566	12	5	great	great	ADJ
ajst-25566	12	6	significance	significance	NOUN
ajst-25566	12	7	in	in	ADP
ajst-25566	12	8	both	both	CCONJ
ajst-25566	12	9	reallife	reallife	NOUN
ajst-25566	12	10	and	and	CCONJ
ajst-25566	12	11	academic	academic	ADJ
ajst-25566	12	12	research	research	NOUN
ajst-25566	12	13	.	.	PUNCT
ajst-25566	13	1	figure	figure	NOUN
ajst-25566	13	2	1	1	NUM
ajst-25566	13	3	.	.	PUNCT
ajst-25566	13	4	mathematical	mathematical	ADJ
ajst-25566	13	5	graph	graph	NOUN
ajst-25566	13	6	of	of	ADP
ajst-25566	13	7	function	function	NOUN
ajst-25566	13	8	in	in	ADP
ajst-25566	13	9	modern	modern	ADJ
ajst-25566	13	10	mathematics	mathematic	NOUN
ajst-25566	13	11	education	education	NOUN
ajst-25566	13	12	,	,	PUNCT
ajst-25566	13	13	calculus	calculus	NOUN
ajst-25566	13	14	is	be	AUX
ajst-25566	13	15	a	a	DET
ajst-25566	13	16	basic	basic	ADJ
ajst-25566	13	17	course	course	NOUN
ajst-25566	13	18	that	that	PRON
ajst-25566	13	19	covers	cover	VERB
ajst-25566	13	20	functions	function	NOUN
ajst-25566	13	21	,	,	PUNCT
ajst-25566	13	22	limits	limit	NOUN
ajst-25566	13	23	,	,	PUNCT
ajst-25566	13	24	derivatives	derivative	NOUN
ajst-25566	13	25	,	,	PUNCT
ajst-25566	13	26	and	and	CCONJ
ajst-25566	13	27	integrals	integral	NOUN
ajst-25566	13	28	.	.	PUNCT
ajst-25566	14	1	students	student	NOUN
ajst-25566	14	2	need	need	VERB
ajst-25566	14	3	to	to	PART
ajst-25566	14	4	master	master	VERB
ajst-25566	14	5	these	these	DET
ajst-25566	14	6	concepts	concept	NOUN
ajst-25566	14	7	to	to	PART
ajst-25566	14	8	understand	understand	VERB
ajst-25566	14	9	and	and	CCONJ
ajst-25566	14	10	solve	solve	VERB
ajst-25566	14	11	practical	practical	ADJ
ajst-25566	14	12	problems	problem	NOUN
ajst-25566	14	13	.	.	PUNCT
ajst-25566	15	1	the	the	DET
ajst-25566	15	2	calculus	calculus	NOUN
ajst-25566	15	3	exam	exam	NOUN
ajst-25566	15	4	often	often	ADV
ajst-25566	15	5	involves	involve	VERB
ajst-25566	15	6	the	the	DET
ajst-25566	15	7	intersection	intersection	NOUN
ajst-25566	15	8	of	of	ADP
ajst-25566	15	9	two	two	NUM
ajst-25566	15	10	functions	function	NOUN
ajst-25566	15	11	,	,	PUNCT
ajst-25566	15	12	which	which	PRON
ajst-25566	15	13	requires	require	VERB
ajst-25566	15	14	students	student	NOUN
ajst-25566	15	15	to	to	PART
ajst-25566	15	16	find	find	VERB
ajst-25566	15	17	the	the	DET
ajst-25566	15	18	intersection	intersection	NOUN
ajst-25566	15	19	and	and	CCONJ
ajst-25566	15	20	analyze	analyze	VERB
ajst-25566	15	21	the	the	DET
ajst-25566	15	22	relationship	relationship	NOUN
ajst-25566	15	23	between	between	ADP
ajst-25566	15	24	the	the	DET
ajst-25566	15	25	functions	function	NOUN
ajst-25566	15	26	at	at	ADP
ajst-25566	15	27	the	the	DET
ajst-25566	15	28	intersection	intersection	NOUN
ajst-25566	15	29	.	.	PUNCT
ajst-25566	16	1	traditional	traditional	ADJ
ajst-25566	16	2	methods	method	NOUN
ajst-25566	16	3	usually	usually	ADV
ajst-25566	16	4	require	require	VERB
ajst-25566	16	5	complex	complex	ADJ
ajst-25566	16	6	calculations	calculation	NOUN
ajst-25566	16	7	and	and	CCONJ
ajst-25566	16	8	graphical	graphical	ADJ
ajst-25566	16	9	analysis	analysis	NOUN
ajst-25566	16	10	,	,	PUNCT
ajst-25566	16	11	which	which	PRON
ajst-25566	16	12	is	be	AUX
ajst-25566	16	13	challenging	challenge	VERB
ajst-25566	16	14	for	for	ADP
ajst-25566	16	15	most	most	ADJ
ajst-25566	16	16	students	student	NOUN
ajst-25566	16	17	.	.	PUNCT
ajst-25566	17	1	therefore	therefore	ADV
ajst-25566	17	2	,	,	PUNCT
ajst-25566	17	3	developing	develop	VERB
ajst-25566	17	4	a	a	DET
ajst-25566	17	5	simple	simple	ADJ
ajst-25566	17	6	and	and	CCONJ
ajst-25566	17	7	efficient	efficient	ADJ
ajst-25566	17	8	method	method	NOUN
ajst-25566	17	9	to	to	PART
ajst-25566	17	10	solve	solve	VERB
ajst-25566	17	11	this	this	DET
ajst-25566	17	12	problem	problem	NOUN
ajst-25566	17	13	is	be	AUX
ajst-25566	17	14	particularly	particularly	ADV
ajst-25566	17	15	essential	essential	ADJ
ajst-25566	17	16	.	.	PUNCT
ajst-25566	18	1	2	2	X
ajst-25566	18	2	.	.	X
ajst-25566	18	3	background	background	NOUN
ajst-25566	18	4	of	of	ADP
ajst-25566	18	5	mathematics	mathematics	PROPN
ajst-25566	18	6	education	education	NOUN
ajst-25566	18	7	calculus	calculus	NOUN
ajst-25566	18	8	is	be	AUX
ajst-25566	18	9	an	an	DET
ajst-25566	18	10	essential	essential	ADJ
ajst-25566	18	11	part	part	NOUN
ajst-25566	18	12	of	of	ADP
ajst-25566	18	13	higher	high	ADJ
ajst-25566	18	14	mathematics	mathematic	NOUN
ajst-25566	18	15	and	and	CCONJ
ajst-25566	18	16	is	be	AUX
ajst-25566	18	17	widely	widely	ADV
ajst-25566	18	18	used	use	VERB
ajst-25566	18	19	in	in	ADP
ajst-25566	18	20	science	science	NOUN
ajst-25566	18	21	,	,	PUNCT
ajst-25566	18	22	engineering	engineering	NOUN
ajst-25566	18	23	,	,	PUNCT
ajst-25566	18	24	and	and	CCONJ
ajst-25566	18	25	economics	economic	NOUN
ajst-25566	18	26	.	.	PUNCT
ajst-25566	19	1	the	the	DET
ajst-25566	19	2	goal	goal	NOUN
ajst-25566	19	3	of	of	ADP
ajst-25566	19	4	education	education	NOUN
ajst-25566	19	5	is	be	AUX
ajst-25566	19	6	to	to	PART
ajst-25566	19	7	enable	enable	VERB
ajst-25566	19	8	students	student	NOUN
ajst-25566	19	9	to	to	PART
ajst-25566	19	10	master	master	VERB
ajst-25566	19	11	basic	basic	ADJ
ajst-25566	19	12	concepts	concept	NOUN
ajst-25566	19	13	and	and	CCONJ
ajst-25566	19	14	computational	computational	ADJ
ajst-25566	19	15	skills	skill	NOUN
ajst-25566	19	16	as	as	ADV
ajst-25566	19	17	well	well	ADV
ajst-25566	19	18	as	as	ADP
ajst-25566	19	19	promote	promote	VERB
ajst-25566	19	20	the	the	DET
ajst-25566	19	21	ability	ability	NOUN
ajst-25566	19	22	to	to	PART
ajst-25566	19	23	solve	solve	VERB
ajst-25566	19	24	practical	practical	ADJ
ajst-25566	19	25	problems	problem	NOUN
ajst-25566	19	26	.	.	PUNCT
ajst-25566	20	1	however	however	ADV
ajst-25566	20	2	,	,	PUNCT
ajst-25566	20	3	in	in	ADP
ajst-25566	20	4	traditional	traditional	ADJ
ajst-25566	20	5	calculus	calculus	NOUN
ajst-25566	20	6	teaching	teaching	NOUN
ajst-25566	20	7	,	,	PUNCT
ajst-25566	20	8	students	student	NOUN
ajst-25566	20	9	often	often	ADV
ajst-25566	20	10	have	have	VERB
ajst-25566	20	11	difficulties	difficulty	NOUN
ajst-25566	20	12	in	in	ADP
ajst-25566	20	13	dealing	deal	VERB
ajst-25566	20	14	with	with	ADP
ajst-25566	20	15	the	the	DET
ajst-25566	20	16	intersection	intersection	NOUN
ajst-25566	20	17	and	and	CCONJ
ajst-25566	20	18	difference	difference	NOUN
ajst-25566	20	19	of	of	ADP
ajst-25566	20	20	two	two	NUM
ajst-25566	20	21	functions	function	NOUN
ajst-25566	20	22	.	.	PUNCT
ajst-25566	21	1	the	the	DET
ajst-25566	21	2	difficulty	difficulty	NOUN
ajst-25566	21	3	mainly	mainly	ADV
ajst-25566	21	4	stems	stem	VERB
ajst-25566	21	5	from	from	ADP
ajst-25566	21	6	the	the	DET
ajst-25566	21	7	following	following	ADJ
ajst-25566	21	8	reasons	reason	NOUN
ajst-25566	21	9	:	:	PUNCT
ajst-25566	21	10	(	(	PUNCT
ajst-25566	21	11	1	1	NUM
ajst-25566	21	12	)	)	PUNCT
ajst-25566	21	13	.	.	PUNCT
ajst-25566	22	1	the	the	DET
ajst-25566	22	2	complex	complex	ADJ
ajst-25566	22	3	computation	computation	NOUN
ajst-25566	22	4	:	:	PUNCT
ajst-25566	22	5	we	we	PRON
ajst-25566	22	6	solve	solve	VERB
ajst-25566	22	7	the	the	DET
ajst-25566	22	8	equation	equation	NOUN
ajst-25566	22	9	to	to	PART
ajst-25566	22	10	find	find	VERB
ajst-25566	22	11	the	the	DET
ajst-25566	22	12	intersection	intersection	NOUN
ajst-25566	22	13	of	of	ADP
ajst-25566	22	14	two	two	NUM
ajst-25566	22	15	functions	function	NOUN
ajst-25566	22	16	.	.	PUNCT
ajst-25566	23	1	moreover	moreover	ADV
ajst-25566	23	2	,	,	PUNCT
ajst-25566	23	3	these	these	DET
ajst-25566	23	4	equations	equation	NOUN
ajst-25566	23	5	may	may	AUX
ajst-25566	23	6	be	be	AUX
ajst-25566	23	7	nonlinear	nonlinear	ADJ
ajst-25566	23	8	,	,	PUNCT
ajst-25566	23	9	and	and	CCONJ
ajst-25566	23	10	the	the	DET
ajst-25566	23	11	solution	solution	NOUN
ajst-25566	23	12	process	process	NOUN
ajst-25566	23	13	is	be	AUX
ajst-25566	23	14	cumbersome	cumbersome	ADJ
ajst-25566	23	15	in	in	ADP
ajst-25566	23	16	many	many	ADJ
ajst-25566	23	17	cases	case	NOUN
ajst-25566	23	18	.	.	PUNCT
ajst-25566	24	1	(	(	PUNCT
ajst-25566	24	2	2	2	NUM
ajst-25566	24	3	)	)	PUNCT
ajst-25566	24	4	.	.	PUNCT
ajst-25566	25	1	graphical	graphical	ADJ
ajst-25566	25	2	analysis	analysis	NOUN
ajst-25566	25	3	:	:	PUNCT
ajst-25566	25	4	analyzing	analyze	VERB
ajst-25566	25	5	the	the	DET
ajst-25566	25	6	difference	difference	NOUN
ajst-25566	25	7	between	between	ADP
ajst-25566	25	8	two	two	NUM
ajst-25566	25	9	functions	function	NOUN
ajst-25566	25	10	usually	usually	ADV
ajst-25566	25	11	requires	require	VERB
ajst-25566	25	12	drawing	draw	VERB
ajst-25566	25	13	a	a	DET
ajst-25566	25	14	diagram	diagram	NOUN
ajst-25566	25	15	of	of	ADP
ajst-25566	25	16	the	the	DET
ajst-25566	25	17	function	function	NOUN
ajst-25566	25	18	and	and	CCONJ
ajst-25566	25	19	analyzing	analyze	VERB
ajst-25566	25	20	the	the	DET
ajst-25566	25	21	graph	graph	NOUN
ajst-25566	25	22	,	,	PUNCT
ajst-25566	25	23	which	which	PRON
ajst-25566	25	24	demands	demand	VERB
ajst-25566	25	25	students	student	NOUN
ajst-25566	25	26	'	'	PART
ajst-25566	25	27	spatial	spatial	ADJ
ajst-25566	25	28	imagination	imagination	NOUN
ajst-25566	25	29	and	and	CCONJ
ajst-25566	25	30	analytical	analytical	ADJ
ajst-25566	25	31	abilities	ability	NOUN
ajst-25566	25	32	.	.	PUNCT
ajst-25566	26	1	(	(	PUNCT
ajst-25566	26	2	3	3	NUM
ajst-25566	26	3	)	)	PUNCT
ajst-25566	26	4	.	.	PUNCT
ajst-25566	27	1	multi	multi	ADJ
ajst-25566	27	2	-	-	ADJ
ajst-25566	27	3	step	step	ADJ
ajst-25566	27	4	calculation	calculation	NOUN
ajst-25566	27	5	:	:	PUNCT
ajst-25566	27	6	traditional	traditional	ADJ
ajst-25566	27	7	methods	method	NOUN
ajst-25566	27	8	involve	involve	VERB
ajst-25566	27	9	multiple	multiple	ADJ
ajst-25566	27	10	steps	step	NOUN
ajst-25566	27	11	,	,	PUNCT
ajst-25566	27	12	including	include	VERB
ajst-25566	27	13	derivatives	derivative	NOUN
ajst-25566	27	14	,	,	PUNCT
ajst-25566	27	15	solving	solve	VERB
ajst-25566	27	16	intersection	intersection	NOUN
ajst-25566	27	17	points	point	NOUN
ajst-25566	27	18	,	,	PUNCT
ajst-25566	27	19	comparing	compare	VERB
ajst-25566	27	20	function	function	NOUN
ajst-25566	27	21	values	value	NOUN
ajst-25566	27	22	,	,	PUNCT
ajst-25566	27	23	etc	etc	X
ajst-25566	27	24	.	.	X
ajst-25566	27	25	,	,	PUNCT
ajst-25566	27	26	and	and	CCONJ
ajst-25566	27	27	each	each	DET
ajst-25566	27	28	step	step	NOUN
ajst-25566	27	29	can	can	AUX
ajst-25566	27	30	introduce	introduce	VERB
ajst-25566	27	31	calculation	calculation	NOUN
ajst-25566	27	32	errors	error	NOUN
ajst-25566	27	33	.	.	PUNCT
ajst-25566	28	1	this	this	DET
ajst-25566	28	2	paper	paper	NOUN
ajst-25566	28	3	presents	present	VERB
ajst-25566	28	4	a	a	DET
ajst-25566	28	5	new	new	ADJ
ajst-25566	28	6	method	method	NOUN
ajst-25566	28	7	based	base	VERB
ajst-25566	28	8	on	on	ADP
ajst-25566	28	9	the	the	DET
ajst-25566	28	10	mean	mean	ADJ
ajst-25566	28	11	value	value	NOUN
ajst-25566	28	12	theorem	theorem	VERB
ajst-25566	28	13	to	to	PART
ajst-25566	28	14	help	help	VERB
ajst-25566	28	15	students	student	NOUN
ajst-25566	28	16	better	well	ADV
ajst-25566	28	17	understand	understand	VERB
ajst-25566	28	18	and	and	CCONJ
ajst-25566	28	19	master	master	VERB
ajst-25566	28	20	the	the	DET
ajst-25566	28	21	solution	solution	NOUN
ajst-25566	28	22	to	to	ADP
ajst-25566	28	23	such	such	ADJ
ajst-25566	28	24	problems	problem	NOUN
ajst-25566	28	25	.	.	PUNCT
ajst-25566	29	1	it	it	PRON
ajst-25566	29	2	simplifies	simplify	VERB
ajst-25566	29	3	the	the	DET
ajst-25566	29	4	calculations	calculation	NOUN
ajst-25566	29	5	and	and	CCONJ
ajst-25566	29	6	reduces	reduce	VERB
ajst-25566	29	7	the	the	DET
ajst-25566	29	8	need	need	NOUN
ajst-25566	29	9	for	for	ADP
ajst-25566	29	10	graphic	graphic	ADJ
ajst-25566	29	11	analysis	analysis	NOUN
ajst-25566	29	12	,	,	PUNCT
ajst-25566	29	13	providing	provide	VERB
ajst-25566	29	14	students	student	NOUN
ajst-25566	29	15	with	with	ADP
ajst-25566	29	16	a	a	DET
ajst-25566	29	17	more	more	ADV
ajst-25566	29	18	intuitive	intuitive	ADJ
ajst-25566	29	19	and	and	CCONJ
ajst-25566	29	20	effective	effective	ADJ
ajst-25566	29	21	way	way	NOUN
ajst-25566	29	22	to	to	PART
ajst-25566	29	23	solve	solve	VERB
ajst-25566	29	24	problems	problem	NOUN
ajst-25566	29	25	.	.	PUNCT
ajst-25566	30	1	2.1	2.1	NUM
ajst-25566	30	2	.	.	PUNCT
ajst-25566	30	3	challenges	challenge	NOUN
ajst-25566	30	4	of	of	ADP
ajst-25566	30	5	calculus	calculus	NOUN
ajst-25566	30	6	exams	exam	NOUN
ajst-25566	30	7	in	in	ADP
ajst-25566	30	8	calculus	calculus	NOUN
ajst-25566	30	9	exams	exam	NOUN
ajst-25566	30	10	,	,	PUNCT
ajst-25566	30	11	students	student	NOUN
ajst-25566	30	12	often	often	ADV
ajst-25566	30	13	solve	solve	VERB
ajst-25566	30	14	problems	problem	NOUN
ajst-25566	30	15	about	about	ADP
ajst-25566	30	16	the	the	DET
ajst-25566	30	17	maximum	maximum	ADJ
ajst-25566	30	18	difference	difference	NOUN
ajst-25566	30	19	between	between	ADP
ajst-25566	30	20	the	the	DET
ajst-25566	30	21	intersection	intersection	NOUN
ajst-25566	30	22	points	point	NOUN
ajst-25566	30	23	of	of	ADP
ajst-25566	30	24	two	two	NUM
ajst-25566	30	25	functions	function	NOUN
ajst-25566	30	26	.	.	PUNCT
ajst-25566	31	1	this	this	DET
ajst-25566	31	2	type	type	NOUN
ajst-25566	31	3	of	of	ADP
ajst-25566	31	4	question	question	NOUN
ajst-25566	31	5	not	not	PART
ajst-25566	31	6	only	only	ADV
ajst-25566	31	7	tests	test	VERB
ajst-25566	31	8	students	student	NOUN
ajst-25566	31	9	'	'	PART
ajst-25566	31	10	understanding	understanding	NOUN
ajst-25566	31	11	of	of	ADP
ajst-25566	31	12	fundamental	fundamental	ADJ
ajst-25566	31	13	concepts	concept	NOUN
ajst-25566	31	14	but	but	CCONJ
ajst-25566	31	15	also	also	ADV
ajst-25566	31	16	their	their	PRON
ajst-25566	31	17	ability	ability	NOUN
ajst-25566	31	18	to	to	PART
ajst-25566	31	19	apply	apply	VERB
ajst-25566	31	20	those	those	DET
ajst-25566	31	21	concepts	concept	NOUN
ajst-25566	31	22	comprehensively	comprehensively	ADV
ajst-25566	31	23	.	.	PUNCT
ajst-25566	32	1	specifically	specifically	ADV
ajst-25566	32	2	,	,	PUNCT
ajst-25566	32	3	these	these	DET
ajst-25566	32	4	problems	problem	NOUN
ajst-25566	32	5	usually	usually	ADV
ajst-25566	32	6	include	include	VERB
ajst-25566	32	7	the	the	DET
ajst-25566	32	8	following	follow	VERB
ajst-25566	32	9	aspects	aspect	NOUN
ajst-25566	32	10	:	:	PUNCT
ajst-25566	32	11	(	(	PUNCT
ajst-25566	32	12	1	1	X
ajst-25566	32	13	)	)	PUNCT
ajst-25566	32	14	intersection	intersection	NOUN
ajst-25566	32	15	solution	solution	NOUN
ajst-25566	32	16	:	:	PUNCT
ajst-25566	32	17	students	student	NOUN
ajst-25566	32	18	need	need	VERB
ajst-25566	32	19	to	to	PART
ajst-25566	32	20	find	find	VERB
ajst-25566	32	21	the	the	DET
ajst-25566	32	22	intersection	intersection	NOUN
ajst-25566	32	23	of	of	ADP
ajst-25566	32	24	two	two	NUM
ajst-25566	32	25	functions	function	NOUN
ajst-25566	32	26	,	,	PUNCT
ajst-25566	32	27	which	which	PRON
ajst-25566	32	28	requires	require	VERB
ajst-25566	32	29	them	they	PRON
ajst-25566	32	30	to	to	PART
ajst-25566	32	31	have	have	VERB
ajst-25566	32	32	the	the	DET
ajst-25566	32	33	ability	ability	NOUN
ajst-25566	32	34	to	to	PART
ajst-25566	32	35	solve	solve	VERB
ajst-25566	32	36	equations	equation	NOUN
ajst-25566	32	37	.	.	PUNCT
ajst-25566	33	1	(	(	PUNCT
ajst-25566	33	2	2	2	X
ajst-25566	33	3	)	)	PUNCT
ajst-25566	33	4	function	function	NOUN
ajst-25566	33	5	analysis	analysis	NOUN
ajst-25566	33	6	:	:	PUNCT
ajst-25566	33	7	after	after	ADP
ajst-25566	33	8	finding	find	VERB
ajst-25566	33	9	the	the	DET
ajst-25566	33	10	intersection	intersection	NOUN
ajst-25566	33	11	,	,	PUNCT
ajst-25566	33	12	it	it	PRON
ajst-25566	33	13	is	be	AUX
ajst-25566	33	14	necessary	necessary	ADJ
ajst-25566	33	15	to	to	PART
ajst-25566	33	16	analyze	analyze	VERB
ajst-25566	33	17	the	the	DET
ajst-25566	33	18	relationship	relationship	NOUN
ajst-25566	33	19	between	between	ADP
ajst-25566	33	20	two	two	NUM
ajst-25566	33	21	functions	function	NOUN
ajst-25566	33	22	and	and	CCONJ
ajst-25566	33	23	the	the	DET
ajst-25566	33	24	intersection	intersection	NOUN
ajst-25566	33	25	to	to	PART
ajst-25566	33	26	determine	determine	VERB
ajst-25566	33	27	their	their	PRON
ajst-25566	33	28	maximum	maximum	ADJ
ajst-25566	33	29	difference	difference	NOUN
ajst-25566	33	30	.	.	PUNCT
ajst-25566	34	1	(	(	PUNCT
ajst-25566	34	2	3	3	X
ajst-25566	34	3	)	)	PUNCT
ajst-25566	34	4	graphic	graphic	ADJ
ajst-25566	34	5	interpretation	interpretation	NOUN
ajst-25566	34	6	:	:	PUNCT
ajst-25566	34	7	students	student	NOUN
ajst-25566	34	8	can	can	AUX
ajst-25566	34	9	understand	understand	VERB
ajst-25566	34	10	the	the	DET
ajst-25566	34	11	60	60	NUM
ajst-25566	34	12	relationship	relationship	NOUN
ajst-25566	34	13	between	between	ADP
ajst-25566	34	14	two	two	NUM
ajst-25566	34	15	functions	function	NOUN
ajst-25566	34	16	more	more	ADV
ajst-25566	34	17	intuitively	intuitively	ADV
ajst-25566	34	18	by	by	ADP
ajst-25566	34	19	drawing	draw	VERB
ajst-25566	34	20	function	function	NOUN
ajst-25566	34	21	images	image	NOUN
ajst-25566	34	22	.	.	PUNCT
ajst-25566	35	1	at	at	ADP
ajst-25566	35	2	the	the	DET
ajst-25566	35	3	same	same	ADJ
ajst-25566	35	4	time	time	NOUN
ajst-25566	35	5	,	,	PUNCT
ajst-25566	35	6	it	it	PRON
ajst-25566	35	7	also	also	ADV
ajst-25566	35	8	increases	increase	VERB
ajst-25566	35	9	the	the	DET
ajst-25566	35	10	complexity	complexity	NOUN
ajst-25566	35	11	of	of	ADP
ajst-25566	35	12	the	the	DET
ajst-25566	35	13	problem	problem	NOUN
ajst-25566	35	14	.	.	PUNCT
ajst-25566	36	1	for	for	ADP
ajst-25566	36	2	these	these	DET
ajst-25566	36	3	reasons	reason	NOUN
ajst-25566	36	4	,	,	PUNCT
ajst-25566	36	5	students	student	NOUN
ajst-25566	36	6	often	often	ADV
ajst-25566	36	7	feel	feel	VERB
ajst-25566	36	8	great	great	ADJ
ajst-25566	36	9	pressure	pressure	NOUN
ajst-25566	36	10	when	when	SCONJ
ajst-25566	36	11	dealing	deal	VERB
ajst-25566	36	12	with	with	ADP
ajst-25566	36	13	such	such	ADJ
ajst-25566	36	14	problems	problem	NOUN
ajst-25566	36	15	.	.	PUNCT
ajst-25566	37	1	the	the	DET
ajst-25566	37	2	method	method	NOUN
ajst-25566	37	3	proposed	propose	VERB
ajst-25566	37	4	in	in	ADP
ajst-25566	37	5	this	this	DET
ajst-25566	37	6	paper	paper	NOUN
ajst-25566	37	7	aims	aim	VERB
ajst-25566	37	8	to	to	PART
ajst-25566	37	9	simplify	simplify	VERB
ajst-25566	37	10	this	this	DET
ajst-25566	37	11	process	process	NOUN
ajst-25566	37	12	and	and	CCONJ
ajst-25566	37	13	enable	enable	VERB
ajst-25566	37	14	students	student	NOUN
ajst-25566	37	15	to	to	PART
ajst-25566	37	16	solve	solve	VERB
ajst-25566	37	17	problems	problem	NOUN
ajst-25566	37	18	efficiently	efficiently	ADV
ajst-25566	37	19	.	.	PUNCT
ajst-25566	38	1	2.2	2.2	NUM
ajst-25566	38	2	.	.	PUNCT
ajst-25566	38	3	practical	practical	ADJ
ajst-25566	38	4	significance	significance	NOUN
ajst-25566	38	5	of	of	ADP
ajst-25566	38	6	the	the	DET
ajst-25566	38	7	study	study	NOUN
ajst-25566	38	8	besides	besides	SCONJ
ajst-25566	38	9	the	the	DET
ajst-25566	38	10	application	application	NOUN
ajst-25566	38	11	in	in	ADP
ajst-25566	38	12	the	the	DET
ajst-25566	38	13	field	field	NOUN
ajst-25566	38	14	of	of	ADP
ajst-25566	38	15	education	education	NOUN
ajst-25566	39	1	,	,	PUNCT
ajst-25566	39	2	the	the	DET
ajst-25566	39	3	method	method	NOUN
ajst-25566	39	4	proposed	propose	VERB
ajst-25566	39	5	in	in	ADP
ajst-25566	39	6	this	this	DET
ajst-25566	39	7	paper	paper	NOUN
ajst-25566	39	8	is	be	AUX
ajst-25566	39	9	also	also	ADV
ajst-25566	39	10	of	of	ADP
ajst-25566	39	11	great	great	ADJ
ajst-25566	39	12	significance	significance	NOUN
ajst-25566	39	13	in	in	ADP
ajst-25566	39	14	practical	practical	ADJ
ajst-25566	39	15	application	application	NOUN
ajst-25566	39	16	.	.	PUNCT
ajst-25566	40	1	in	in	ADP
ajst-25566	40	2	engineering	engineering	NOUN
ajst-25566	40	3	design	design	NOUN
ajst-25566	40	4	,	,	PUNCT
ajst-25566	40	5	data	data	VERB
ajst-25566	40	6	analysis	analysis	NOUN
ajst-25566	40	7	and	and	CCONJ
ajst-25566	40	8	economic	economic	ADJ
ajst-25566	40	9	research	research	NOUN
ajst-25566	40	10	,	,	PUNCT
ajst-25566	40	11	it	it	PRON
ajst-25566	40	12	is	be	AUX
ajst-25566	40	13	common	common	ADJ
ajst-25566	40	14	to	to	PART
ajst-25566	40	15	analyze	analyze	VERB
ajst-25566	40	16	the	the	DET
ajst-25566	40	17	maximum	maximum	ADJ
ajst-25566	40	18	difference	difference	NOUN
ajst-25566	40	19	between	between	ADP
ajst-25566	40	20	two	two	NUM
ajst-25566	40	21	functions	function	NOUN
ajst-25566	40	22	.	.	PUNCT
ajst-25566	41	1	for	for	ADP
ajst-25566	41	2	example	example	NOUN
ajst-25566	41	3	:	:	PUNCT
ajst-25566	41	4	(	(	PUNCT
ajst-25566	41	5	1	1	X
ajst-25566	41	6	)	)	PUNCT
ajst-25566	41	7	engineering	engineering	NOUN
ajst-25566	41	8	design	design	NOUN
ajst-25566	41	9	.	.	PUNCT
ajst-25566	42	1	in	in	ADP
ajst-25566	42	2	mechanical	mechanical	ADJ
ajst-25566	42	3	design	design	NOUN
ajst-25566	42	4	,	,	PUNCT
ajst-25566	42	5	the	the	DET
ajst-25566	42	6	difference	difference	NOUN
ajst-25566	42	7	in	in	ADP
ajst-25566	42	8	displacement	displacement	NOUN
ajst-25566	42	9	between	between	ADP
ajst-25566	42	10	two	two	NUM
ajst-25566	42	11	components	component	NOUN
ajst-25566	42	12	can	can	AUX
ajst-25566	42	13	affect	affect	VERB
ajst-25566	42	14	the	the	DET
ajst-25566	42	15	operating	operating	NOUN
ajst-25566	42	16	effect	effect	NOUN
ajst-25566	42	17	of	of	ADP
ajst-25566	42	18	the	the	DET
ajst-25566	42	19	whole	whole	ADJ
ajst-25566	42	20	system	system	NOUN
ajst-25566	42	21	.	.	PUNCT
ajst-25566	43	1	accurately	accurately	ADV
ajst-25566	43	2	calculating	calculate	VERB
ajst-25566	43	3	the	the	DET
ajst-25566	43	4	maximum	maximum	ADJ
ajst-25566	43	5	difference	difference	NOUN
ajst-25566	43	6	between	between	ADP
ajst-25566	43	7	these	these	DET
ajst-25566	43	8	two	two	NUM
ajst-25566	43	9	components	component	NOUN
ajst-25566	43	10	is	be	AUX
ajst-25566	43	11	very	very	ADV
ajst-25566	43	12	important	important	ADJ
ajst-25566	43	13	to	to	PART
ajst-25566	43	14	ensure	ensure	VERB
ajst-25566	43	15	the	the	DET
ajst-25566	43	16	normal	normal	ADJ
ajst-25566	43	17	operation	operation	NOUN
ajst-25566	43	18	of	of	ADP
ajst-25566	43	19	the	the	DET
ajst-25566	43	20	device	device	NOUN
ajst-25566	43	21	.	.	PUNCT
ajst-25566	44	1	(	(	PUNCT
ajst-25566	44	2	2	2	X
ajst-25566	44	3	)	)	PUNCT
ajst-25566	44	4	data	datum	NOUN
ajst-25566	44	5	analysis	analysis	NOUN
ajst-25566	44	6	.	.	PUNCT
ajst-25566	45	1	in	in	ADP
ajst-25566	45	2	data	data	NOUN
ajst-25566	45	3	science	science	NOUN
ajst-25566	45	4	,	,	PUNCT
ajst-25566	45	5	comparing	compare	VERB
ajst-25566	45	6	the	the	DET
ajst-25566	45	7	biggest	big	ADJ
ajst-25566	45	8	differences	difference	NOUN
ajst-25566	45	9	between	between	ADP
ajst-25566	45	10	two	two	NUM
ajst-25566	45	11	data	data	NOUN
ajst-25566	45	12	sets	set	NOUN
ajst-25566	45	13	is	be	AUX
ajst-25566	45	14	an	an	DET
ajst-25566	45	15	important	important	ADJ
ajst-25566	45	16	basis	basis	NOUN
ajst-25566	45	17	for	for	ADP
ajst-25566	45	18	helping	help	VERB
ajst-25566	45	19	decision	decision	NOUN
ajst-25566	45	20	makers	maker	NOUN
ajst-25566	45	21	make	make	VERB
ajst-25566	45	22	more	more	ADJ
ajst-25566	45	23	scientific	scientific	ADJ
ajst-25566	45	24	decisions	decision	NOUN
ajst-25566	45	25	.	.	PUNCT
ajst-25566	46	1	(	(	PUNCT
ajst-25566	46	2	3	3	X
ajst-25566	46	3	)	)	PUNCT
ajst-25566	46	4	economic	economic	ADJ
ajst-25566	46	5	research	research	NOUN
ajst-25566	46	6	.	.	PUNCT
ajst-25566	47	1	in	in	ADP
ajst-25566	47	2	economics	economic	NOUN
ajst-25566	47	3	,	,	PUNCT
ajst-25566	47	4	analyzing	analyze	VERB
ajst-25566	47	5	changes	change	NOUN
ajst-25566	47	6	and	and	CCONJ
ajst-25566	47	7	differences	difference	NOUN
ajst-25566	47	8	in	in	ADP
ajst-25566	47	9	various	various	ADJ
ajst-25566	47	10	economic	economic	ADJ
ajst-25566	47	11	indicators	indicator	NOUN
ajst-25566	47	12	can	can	AUX
ajst-25566	47	13	help	help	VERB
ajst-25566	47	14	inform	inform	VERB
ajst-25566	47	15	policy	policy	NOUN
ajst-25566	47	16	making	making	NOUN
ajst-25566	47	17	.	.	PUNCT
ajst-25566	48	1	by	by	ADP
ajst-25566	48	2	studying	study	VERB
ajst-25566	48	3	and	and	CCONJ
ajst-25566	48	4	applying	apply	VERB
ajst-25566	48	5	the	the	DET
ajst-25566	48	6	method	method	NOUN
ajst-25566	48	7	proposed	propose	VERB
ajst-25566	48	8	in	in	ADP
ajst-25566	48	9	this	this	DET
ajst-25566	48	10	paper	paper	NOUN
ajst-25566	48	11	,	,	PUNCT
ajst-25566	48	12	researchers	researcher	NOUN
ajst-25566	48	13	can	can	AUX
ajst-25566	48	14	effectively	effectively	ADV
ajst-25566	48	15	solve	solve	VERB
ajst-25566	48	16	practical	practical	ADJ
ajst-25566	48	17	problems	problem	NOUN
ajst-25566	48	18	and	and	CCONJ
ajst-25566	48	19	improve	improve	VERB
ajst-25566	48	20	the	the	DET
ajst-25566	48	21	efficiency	efficiency	NOUN
ajst-25566	48	22	and	and	CCONJ
ajst-25566	48	23	accuracy	accuracy	NOUN
ajst-25566	48	24	of	of	ADP
ajst-25566	48	25	analysis	analysis	NOUN
ajst-25566	48	26	.	.	PUNCT
ajst-25566	49	1	in	in	ADP
ajst-25566	49	2	mathematics	mathematic	NOUN
ajst-25566	49	3	and	and	CCONJ
ajst-25566	49	4	engineering	engineering	NOUN
ajst-25566	49	5	,	,	PUNCT
ajst-25566	49	6	it	it	PRON
ajst-25566	49	7	is	be	AUX
ajst-25566	49	8	common	common	ADJ
ajst-25566	49	9	to	to	PART
ajst-25566	49	10	analyze	analyze	VERB
ajst-25566	49	11	the	the	DET
ajst-25566	49	12	difference	difference	NOUN
ajst-25566	49	13	between	between	ADP
ajst-25566	49	14	two	two	NUM
ajst-25566	49	15	functions	function	NOUN
ajst-25566	49	16	.	.	PUNCT
ajst-25566	50	1	traditional	traditional	ADJ
ajst-25566	50	2	methods	method	NOUN
ajst-25566	50	3	are	be	AUX
ajst-25566	50	4	complex	complex	ADJ
ajst-25566	50	5	and	and	CCONJ
ajst-25566	50	6	laborious	laborious	ADJ
ajst-25566	50	7	,	,	PUNCT
ajst-25566	50	8	especially	especially	ADV
ajst-25566	50	9	when	when	SCONJ
ajst-25566	50	10	calculating	calculate	VERB
ajst-25566	50	11	the	the	DET
ajst-25566	50	12	maximum	maximum	ADJ
ajst-25566	50	13	difference	difference	NOUN
ajst-25566	50	14	between	between	ADP
ajst-25566	50	15	the	the	DET
ajst-25566	50	16	intersection	intersection	NOUN
ajst-25566	50	17	points	point	NOUN
ajst-25566	50	18	of	of	ADP
ajst-25566	50	19	two	two	NUM
ajst-25566	50	20	functions	function	NOUN
ajst-25566	50	21	.	.	PUNCT
ajst-25566	51	1	the	the	DET
ajst-25566	51	2	aim	aim	NOUN
ajst-25566	51	3	of	of	ADP
ajst-25566	51	4	this	this	DET
ajst-25566	51	5	research	research	NOUN
ajst-25566	51	6	is	be	AUX
ajst-25566	51	7	to	to	PART
ajst-25566	51	8	present	present	VERB
ajst-25566	51	9	a	a	DET
ajst-25566	51	10	new	new	ADJ
ajst-25566	51	11	method	method	NOUN
ajst-25566	51	12	that	that	PRON
ajst-25566	51	13	simplifies	simplify	VERB
ajst-25566	51	14	this	this	DET
ajst-25566	51	15	process	process	NOUN
ajst-25566	51	16	using	use	VERB
ajst-25566	51	17	the	the	DET
ajst-25566	51	18	mean	mean	ADJ
ajst-25566	51	19	value	value	NOUN
ajst-25566	51	20	theorem	theorem	VERB
ajst-25566	51	21	.	.	PUNCT
ajst-25566	52	1	it	it	PRON
ajst-25566	52	2	is	be	AUX
ajst-25566	52	3	suitable	suitable	ADJ
ajst-25566	52	4	for	for	ADP
ajst-25566	52	5	academic	academic	ADJ
ajst-25566	52	6	research	research	NOUN
ajst-25566	52	7	as	as	ADV
ajst-25566	52	8	well	well	ADV
ajst-25566	52	9	as	as	ADP
ajst-25566	52	10	real	real	ADJ
ajst-25566	52	11	technical	technical	ADJ
ajst-25566	52	12	and	and	CCONJ
ajst-25566	52	13	scientific	scientific	ADJ
ajst-25566	52	14	problems	problem	NOUN
ajst-25566	52	15	.	.	PUNCT
ajst-25566	53	1	2.3	2.3	NUM
ajst-25566	53	2	.	.	PUNCT
ajst-25566	53	3	research	research	NOUN
ajst-25566	53	4	background	background	NOUN
ajst-25566	53	5	at	at	ADP
ajst-25566	53	6	home	home	NOUN
ajst-25566	53	7	and	and	CCONJ
ajst-25566	53	8	abroad	abroad	ADV
ajst-25566	53	9	,	,	PUNCT
ajst-25566	53	10	the	the	DET
ajst-25566	53	11	research	research	NOUN
ajst-25566	53	12	on	on	ADP
ajst-25566	53	13	the	the	DET
ajst-25566	53	14	intersection	intersection	NOUN
ajst-25566	53	15	and	and	CCONJ
ajst-25566	53	16	difference	difference	NOUN
ajst-25566	53	17	of	of	ADP
ajst-25566	53	18	two	two	NUM
ajst-25566	53	19	functions	function	NOUN
ajst-25566	53	20	focuses	focus	VERB
ajst-25566	53	21	on	on	ADP
ajst-25566	53	22	numerical	numerical	ADJ
ajst-25566	53	23	analysis	analysis	NOUN
ajst-25566	53	24	,	,	PUNCT
ajst-25566	53	25	computational	computational	ADJ
ajst-25566	53	26	mathematics	mathematic	NOUN
ajst-25566	53	27	,	,	PUNCT
ajst-25566	53	28	and	and	CCONJ
ajst-25566	53	29	application	application	NOUN
ajst-25566	53	30	fields	field	NOUN
ajst-25566	53	31	.	.	PUNCT
ajst-25566	54	1	in	in	ADP
ajst-25566	54	2	numerical	numerical	ADJ
ajst-25566	54	3	analysis	analysis	NOUN
ajst-25566	54	4	,	,	PUNCT
ajst-25566	54	5	foreign	foreign	ADJ
ajst-25566	54	6	scholars	scholar	NOUN
ajst-25566	54	7	have	have	AUX
ajst-25566	54	8	done	do	VERB
ajst-25566	54	9	much	much	ADJ
ajst-25566	54	10	work	work	NOUN
ajst-25566	54	11	on	on	ADP
ajst-25566	54	12	solving	solve	VERB
ajst-25566	54	13	the	the	DET
ajst-25566	54	14	intersection	intersection	NOUN
ajst-25566	54	15	of	of	ADP
ajst-25566	54	16	functions	function	NOUN
ajst-25566	54	17	numerically	numerically	ADV
ajst-25566	54	18	.	.	PUNCT
ajst-25566	55	1	burden	burden	NOUN
ajst-25566	55	2	and	and	CCONJ
ajst-25566	55	3	faires	faire	NOUN
ajst-25566	55	4	introduced	introduce	VERB
ajst-25566	55	5	the	the	DET
ajst-25566	55	6	numerical	numerical	ADJ
ajst-25566	55	7	method	method	NOUN
ajst-25566	55	8	to	to	PART
ajst-25566	55	9	solve	solve	VERB
ajst-25566	55	10	the	the	DET
ajst-25566	55	11	intersection	intersection	NOUN
ajst-25566	55	12	of	of	ADP
ajst-25566	55	13	functions	function	NOUN
ajst-25566	55	14	in	in	ADP
ajst-25566	55	15	detail	detail	NOUN
ajst-25566	55	16	in	in	ADP
ajst-25566	55	17	their	their	PRON
ajst-25566	55	18	classic	classic	ADJ
ajst-25566	55	19	textbook	textbook	NOUN
ajst-25566	55	20	numerical	numerical	ADJ
ajst-25566	55	21	analysis	analysis	NOUN
ajst-25566	55	22	.	.	PUNCT
ajst-25566	56	1	in	in	ADP
ajst-25566	56	2	addition	addition	NOUN
ajst-25566	56	3	,	,	PUNCT
ajst-25566	56	4	they	they	PRON
ajst-25566	56	5	discussed	discuss	VERB
ajst-25566	56	6	the	the	DET
ajst-25566	56	7	convergence	convergence	NOUN
ajst-25566	56	8	and	and	CCONJ
ajst-25566	56	9	stability	stability	NOUN
ajst-25566	56	10	of	of	ADP
ajst-25566	56	11	these	these	DET
ajst-25566	56	12	methods	method	NOUN
ajst-25566	56	13	[	[	X
ajst-25566	56	14	2	2	NUM
ajst-25566	56	15	]	]	PUNCT
ajst-25566	56	16	.	.	PUNCT
ajst-25566	57	1	press	press	NOUN
ajst-25566	57	2	et	et	PROPN
ajst-25566	57	3	al	al	PROPN
ajst-25566	57	4	.	.	PROPN
ajst-25566	58	1	put	put	VERB
ajst-25566	58	2	forward	forward	ADV
ajst-25566	58	3	a	a	DET
ajst-25566	58	4	solution	solution	NOUN
ajst-25566	58	5	based	base	VERB
ajst-25566	58	6	on	on	ADP
ajst-25566	58	7	polynomial	polynomial	ADJ
ajst-25566	58	8	interpolation	interpolation	NOUN
ajst-25566	58	9	and	and	CCONJ
ajst-25566	58	10	numerical	numerical	ADJ
ajst-25566	58	11	integration	integration	NOUN
ajst-25566	58	12	in	in	ADP
ajst-25566	58	13	numerical	numerical	ADJ
ajst-25566	58	14	recipes	recipe	NOUN
ajst-25566	58	15	:	:	PUNCT
ajst-25566	58	16	the	the	DET
ajst-25566	58	17	art	art	NOUN
ajst-25566	58	18	of	of	ADP
ajst-25566	58	19	scientific	scientific	ADJ
ajst-25566	58	20	computing	computing	NOUN
ajst-25566	58	21	.	.	PUNCT
ajst-25566	59	1	experiments	experiment	NOUN
ajst-25566	59	2	verify	verify	VERB
ajst-25566	59	3	its	its	PRON
ajst-25566	59	4	efficiency	efficiency	NOUN
ajst-25566	59	5	and	and	CCONJ
ajst-25566	59	6	accuracy	accuracy	NOUN
ajst-25566	59	7	in	in	ADP
ajst-25566	59	8	dealing	deal	VERB
ajst-25566	59	9	with	with	ADP
ajst-25566	59	10	complex	complex	ADJ
ajst-25566	59	11	functions	function	NOUN
ajst-25566	59	12	[	[	X
ajst-25566	59	13	3	3	NUM
ajst-25566	59	14	]	]	PUNCT
ajst-25566	59	15	.	.	PUNCT
ajst-25566	60	1	in	in	ADP
ajst-25566	60	2	applied	apply	VERB
ajst-25566	60	3	optimization	optimization	NOUN
ajst-25566	60	4	theory	theory	NOUN
ajst-25566	60	5	,	,	PUNCT
ajst-25566	60	6	nocedal	nocedal	NOUN
ajst-25566	60	7	and	and	CCONJ
ajst-25566	60	8	wright	wright	PROPN
ajst-25566	60	9	systematically	systematically	ADV
ajst-25566	60	10	discussed	discuss	VERB
ajst-25566	60	11	nonlinear	nonlinear	ADJ
ajst-25566	60	12	optimization	optimization	NOUN
ajst-25566	60	13	methods	method	NOUN
ajst-25566	60	14	in	in	ADP
ajst-25566	60	15	their	their	PRON
ajst-25566	60	16	book	book	NOUN
ajst-25566	60	17	numerical	numerical	ADJ
ajst-25566	60	18	optimization	optimization	NOUN
ajst-25566	60	19	.	.	PUNCT
ajst-25566	61	1	they	they	PRON
ajst-25566	61	2	proposed	propose	VERB
ajst-25566	61	3	a	a	DET
ajst-25566	61	4	hybrid	hybrid	ADJ
ajst-25566	61	5	algorithm	algorithm	NOUN
ajst-25566	61	6	based	base	VERB
ajst-25566	61	7	on	on	ADP
ajst-25566	61	8	the	the	DET
ajst-25566	61	9	interior	interior	ADJ
ajst-25566	61	10	point	point	NOUN
ajst-25566	61	11	method	method	NOUN
ajst-25566	61	12	and	and	CCONJ
ajst-25566	61	13	constrained	constrained	ADJ
ajst-25566	61	14	optimization	optimization	NOUN
ajst-25566	61	15	to	to	PART
ajst-25566	61	16	solve	solve	VERB
ajst-25566	61	17	the	the	DET
ajst-25566	61	18	optimal	optimal	ADJ
ajst-25566	61	19	solution	solution	NOUN
ajst-25566	61	20	of	of	ADP
ajst-25566	61	21	nonlinear	nonlinear	ADJ
ajst-25566	61	22	functions	function	NOUN
ajst-25566	61	23	[	[	X
ajst-25566	61	24	4	4	NUM
ajst-25566	61	25	]	]	PUNCT
ajst-25566	61	26	.	.	PUNCT
ajst-25566	62	1	this	this	DET
ajst-25566	62	2	algorithm	algorithm	NOUN
ajst-25566	62	3	has	have	VERB
ajst-25566	62	4	high	high	ADJ
ajst-25566	62	5	application	application	NOUN
ajst-25566	62	6	value	value	NOUN
ajst-25566	62	7	in	in	ADP
ajst-25566	62	8	solving	solve	VERB
ajst-25566	62	9	the	the	DET
ajst-25566	62	10	function	function	NOUN
ajst-25566	62	11	difference	difference	NOUN
ajst-25566	62	12	problem	problem	NOUN
ajst-25566	62	13	.	.	PUNCT
ajst-25566	63	1	goldberg	goldberg	PROPN
ajst-25566	63	2	introduced	introduce	VERB
ajst-25566	63	3	an	an	DET
ajst-25566	63	4	optimization	optimization	NOUN
ajst-25566	63	5	method	method	NOUN
ajst-25566	63	6	based	base	VERB
ajst-25566	63	7	on	on	ADP
ajst-25566	63	8	genetic	genetic	ADJ
ajst-25566	63	9	algorithm	algorithm	NOUN
ajst-25566	63	10	in	in	ADP
ajst-25566	63	11	genetic	genetic	ADJ
ajst-25566	63	12	algorithms	algorithm	NOUN
ajst-25566	63	13	in	in	ADP
ajst-25566	63	14	search	search	NOUN
ajst-25566	63	15	,	,	PUNCT
ajst-25566	63	16	optimization	optimization	NOUN
ajst-25566	63	17	,	,	PUNCT
ajst-25566	63	18	and	and	CCONJ
ajst-25566	63	19	machine	machine	NOUN
ajst-25566	63	20	learning	learning	NOUN
ajst-25566	63	21	,	,	PUNCT
ajst-25566	63	22	and	and	CCONJ
ajst-25566	63	23	its	its	PRON
ajst-25566	63	24	effectiveness	effectiveness	NOUN
ajst-25566	63	25	and	and	CCONJ
ajst-25566	63	26	robustness	robustness	NOUN
ajst-25566	63	27	in	in	ADP
ajst-25566	63	28	solving	solve	VERB
ajst-25566	63	29	complex	complex	ADJ
ajst-25566	63	30	optimization	optimization	NOUN
ajst-25566	63	31	problems	problem	NOUN
ajst-25566	63	32	were	be	AUX
ajst-25566	63	33	verified	verify	VERB
ajst-25566	63	34	by	by	ADP
ajst-25566	63	35	experiments	experiment	NOUN
ajst-25566	63	36	[	[	X
ajst-25566	63	37	5	5	NUM
ajst-25566	63	38	]	]	PUNCT
ajst-25566	63	39	.	.	PUNCT
ajst-25566	64	1	in	in	ADP
ajst-25566	64	2	the	the	DET
ajst-25566	64	3	practical	practical	ADJ
ajst-25566	64	4	application	application	NOUN
ajst-25566	64	5	,	,	PUNCT
ajst-25566	64	6	smith	smith	PROPN
ajst-25566	64	7	et	et	PROPN
ajst-25566	64	8	al	al	PROPN
ajst-25566	64	9	.	.	PROPN
ajst-25566	64	10	introduced	introduce	VERB
ajst-25566	64	11	a	a	DET
ajst-25566	64	12	comparison	comparison	NOUN
ajst-25566	64	13	method	method	NOUN
ajst-25566	64	14	of	of	ADP
ajst-25566	64	15	curative	curative	ADJ
ajst-25566	64	16	effect	effect	NOUN
ajst-25566	64	17	based	base	VERB
ajst-25566	64	18	on	on	ADP
ajst-25566	64	19	function	function	NOUN
ajst-25566	64	20	difference	difference	NOUN
ajst-25566	64	21	in	in	ADP
ajst-25566	64	22	data	data	NOUN
ajst-25566	64	23	analysis	analysis	NOUN
ajst-25566	64	24	in	in	ADP
ajst-25566	64	25	medical	medical	ADJ
ajst-25566	64	26	research	research	NOUN
ajst-25566	64	27	,	,	PUNCT
ajst-25566	64	28	verifying	verify	VERB
ajst-25566	64	29	its	its	PRON
ajst-25566	64	30	accuracy	accuracy	NOUN
ajst-25566	64	31	and	and	CCONJ
ajst-25566	64	32	reliability	reliability	NOUN
ajst-25566	64	33	in	in	ADP
ajst-25566	64	34	evaluating	evaluate	VERB
ajst-25566	64	35	different	different	ADJ
ajst-25566	64	36	treatment	treatment	NOUN
ajst-25566	64	37	methods	method	NOUN
ajst-25566	64	38	through	through	ADP
ajst-25566	64	39	experiments	experiment	NOUN
ajst-25566	64	40	[	[	X
ajst-25566	64	41	6	6	NUM
ajst-25566	64	42	]	]	PUNCT
ajst-25566	64	43	.	.	PUNCT
ajst-25566	65	1	jones	jones	PROPN
ajst-25566	65	2	et	et	PROPN
ajst-25566	65	3	al	al	PROPN
ajst-25566	65	4	.	.	PROPN
ajst-25566	65	5	put	put	VERB
ajst-25566	65	6	forward	forward	ADV
ajst-25566	65	7	a	a	DET
ajst-25566	65	8	method	method	NOUN
ajst-25566	65	9	of	of	ADP
ajst-25566	65	10	pollutant	pollutant	ADJ
ajst-25566	65	11	concentration	concentration	NOUN
ajst-25566	65	12	analysis	analysis	NOUN
ajst-25566	65	13	based	base	VERB
ajst-25566	65	14	on	on	ADP
ajst-25566	65	15	function	function	NOUN
ajst-25566	65	16	difference	difference	NOUN
ajst-25566	65	17	in	in	ADP
ajst-25566	65	18	their	their	PRON
ajst-25566	65	19	paper	paper	NOUN
ajst-25566	65	20	application	application	NOUN
ajst-25566	65	21	of	of	ADP
ajst-25566	65	22	function	function	NOUN
ajst-25566	65	23	difference	difference	NOUN
ajst-25566	65	24	in	in	ADP
ajst-25566	65	25	environmental	environmental	ADJ
ajst-25566	65	26	pollutant	pollutant	ADJ
ajst-25566	65	27	concentration	concentration	NOUN
ajst-25566	65	28	analysis	analysis	NOUN
ajst-25566	65	29	.	.	PUNCT
ajst-25566	66	1	experiments	experiment	NOUN
ajst-25566	66	2	verify	verify	VERB
ajst-25566	66	3	its	its	PRON
ajst-25566	66	4	application	application	NOUN
ajst-25566	66	5	value	value	NOUN
ajst-25566	66	6	in	in	ADP
ajst-25566	66	7	environmental	environmental	ADJ
ajst-25566	66	8	monitoring	monitoring	NOUN
ajst-25566	66	9	[	[	X
ajst-25566	66	10	7	7	NUM
ajst-25566	66	11	]	]	PUNCT
ajst-25566	66	12	.	.	PUNCT
ajst-25566	67	1	3	3	X
ajst-25566	67	2	.	.	X
ajst-25566	67	3	research	research	NOUN
ajst-25566	67	4	methodology	methodology	NOUN
ajst-25566	67	5	3.1	3.1	NUM
ajst-25566	67	6	.	.	PUNCT
ajst-25566	68	1	theoretical	theoretical	ADJ
ajst-25566	68	2	basis	basis	NOUN
ajst-25566	68	3	it	it	PRON
ajst-25566	68	4	is	be	AUX
ajst-25566	68	5	vital	vital	ADJ
ajst-25566	68	6	to	to	PART
ajst-25566	68	7	understand	understand	VERB
ajst-25566	68	8	and	and	CCONJ
ajst-25566	68	9	master	master	VERB
ajst-25566	68	10	the	the	DET
ajst-25566	68	11	relevant	relevant	ADJ
ajst-25566	68	12	theoretical	theoretical	ADJ
ajst-25566	68	13	basis	basis	NOUN
ajst-25566	68	14	when	when	SCONJ
ajst-25566	68	15	solving	solve	VERB
ajst-25566	68	16	the	the	DET
ajst-25566	68	17	maximum	maximum	ADJ
ajst-25566	68	18	difference	difference	NOUN
ajst-25566	68	19	between	between	ADP
ajst-25566	68	20	the	the	DET
ajst-25566	68	21	two	two	NUM
ajst-25566	68	22	functions	function	NOUN
ajst-25566	68	23	in	in	ADP
ajst-25566	68	24	the	the	DET
ajst-25566	68	25	two	two	NUM
ajst-25566	68	26	closest	close	ADJ
ajst-25566	68	27	intersection	intersection	NOUN
ajst-25566	68	28	intervals	interval	NOUN
ajst-25566	68	29	.	.	PUNCT
ajst-25566	69	1	the	the	DET
ajst-25566	69	2	methods	method	NOUN
ajst-25566	69	3	used	use	VERB
ajst-25566	69	4	in	in	ADP
ajst-25566	69	5	this	this	DET
ajst-25566	69	6	research	research	NOUN
ajst-25566	69	7	are	be	AUX
ajst-25566	69	8	based	base	VERB
ajst-25566	69	9	on	on	ADP
ajst-25566	69	10	the	the	DET
ajst-25566	69	11	mean	mean	ADJ
ajst-25566	69	12	value	value	NOUN
ajst-25566	69	13	theorem	theorem	NOUN
ajst-25566	69	14	and	and	CCONJ
ajst-25566	69	15	gradient	gradient	ADJ
ajst-25566	69	16	analysis	analysis	NOUN
ajst-25566	69	17	in	in	ADP
ajst-25566	69	18	calculus	calculus	NOUN
ajst-25566	69	19	.	.	PUNCT
ajst-25566	70	1	we	we	PRON
ajst-25566	70	2	will	will	AUX
ajst-25566	70	3	comprehensively	comprehensively	ADV
ajst-25566	70	4	introduce	introduce	VERB
ajst-25566	70	5	the	the	DET
ajst-25566	70	6	theoretical	theoretical	ADJ
ajst-25566	70	7	basis	basis	NOUN
ajst-25566	70	8	in	in	ADP
ajst-25566	70	9	the	the	DET
ajst-25566	70	10	following	follow	VERB
ajst-25566	70	11	sections	section	NOUN
ajst-25566	70	12	.	.	PUNCT
ajst-25566	71	1	3.1.1	3.1.1	X
ajst-25566	71	2	.	.	PUNCT
ajst-25566	72	1	mean	mean	NOUN
ajst-25566	72	2	value	value	NOUN
ajst-25566	72	3	theorem	theorem	NOUN
ajst-25566	72	4	(	(	PUNCT
ajst-25566	72	5	mvt	mvt	X
ajst-25566	72	6	)	)	PUNCT
ajst-25566	72	7	the	the	DET
ajst-25566	72	8	mean	mean	ADJ
ajst-25566	72	9	value	value	NOUN
ajst-25566	72	10	theorem	theorem	NOUN
ajst-25566	72	11	is	be	AUX
ajst-25566	72	12	essential	essential	ADJ
ajst-25566	72	13	in	in	ADP
ajst-25566	72	14	calculus	calculus	NOUN
ajst-25566	72	15	,	,	PUNCT
ajst-25566	72	16	which	which	PRON
ajst-25566	72	17	has	have	VERB
ajst-25566	72	18	a	a	DET
ajst-25566	72	19	broad	broad	ADJ
ajst-25566	72	20	range	range	NOUN
ajst-25566	72	21	of	of	ADP
ajst-25566	72	22	applications	application	NOUN
ajst-25566	72	23	in	in	ADP
ajst-25566	72	24	analyzing	analyze	VERB
ajst-25566	72	25	the	the	DET
ajst-25566	72	26	function	function	NOUN
ajst-25566	72	27	's	's	PART
ajst-25566	72	28	behavior	behavior	NOUN
ajst-25566	72	29	and	and	CCONJ
ajst-25566	72	30	change	change	NOUN
ajst-25566	72	31	rate	rate	NOUN
ajst-25566	72	32	.	.	PUNCT
ajst-25566	73	1	the	the	DET
ajst-25566	73	2	basic	basic	ADJ
ajst-25566	73	3	idea	idea	NOUN
ajst-25566	73	4	of	of	ADP
ajst-25566	73	5	the	the	DET
ajst-25566	73	6	mean	mean	ADJ
ajst-25566	73	7	value	value	NOUN
ajst-25566	73	8	theorem	theorem	NOUN
ajst-25566	73	9	is	be	AUX
ajst-25566	73	10	that	that	SCONJ
ajst-25566	73	11	if	if	SCONJ
ajst-25566	73	12	a	a	DET
ajst-25566	73	13	function	function	NOUN
ajst-25566	73	14	is	be	AUX
ajst-25566	73	15	continuous	continuous	ADJ
ajst-25566	73	16	on	on	ADP
ajst-25566	73	17	a	a	DET
ajst-25566	73	18	closed	closed	ADJ
ajst-25566	73	19	interval	interval	NOUN
ajst-25566	73	20	and	and	CCONJ
ajst-25566	73	21	differentiable	differentiable	VERB
ajst-25566	73	22	on	on	ADP
ajst-25566	73	23	an	an	DET
ajst-25566	73	24	open	open	ADJ
ajst-25566	73	25	interval	interval	NOUN
ajst-25566	73	26	,	,	PUNCT
ajst-25566	73	27	then	then	ADV
ajst-25566	73	28	the	the	DET
ajst-25566	73	29	average	average	ADJ
ajst-25566	73	30	rate	rate	NOUN
ajst-25566	73	31	of	of	ADP
ajst-25566	73	32	change	change	NOUN
ajst-25566	73	33	of	of	ADP
ajst-25566	73	34	the	the	DET
ajst-25566	73	35	function	function	NOUN
ajst-25566	73	36	in	in	ADP
ajst-25566	73	37	the	the	DET
ajst-25566	73	38	interval	interval	NOUN
ajst-25566	73	39	is	be	AUX
ajst-25566	73	40	equal	equal	ADJ
ajst-25566	73	41	to	to	ADP
ajst-25566	73	42	its	its	PRON
ajst-25566	73	43	instantaneous	instantaneous	ADJ
ajst-25566	73	44	rate	rate	NOUN
ajst-25566	73	45	of	of	ADP
ajst-25566	73	46	change	change	NOUN
ajst-25566	73	47	at	at	ADP
ajst-25566	73	48	a	a	DET
ajst-25566	73	49	certain	certain	ADJ
ajst-25566	73	50	point	point	NOUN
ajst-25566	73	51	.	.	PUNCT
ajst-25566	74	1	here	here	ADV
ajst-25566	74	2	are	be	AUX
ajst-25566	74	3	the	the	DET
ajst-25566	74	4	formulas	formula	NOUN
ajst-25566	74	5	and	and	CCONJ
ajst-25566	74	6	conditions	condition	NOUN
ajst-25566	74	7	of	of	ADP
ajst-25566	74	8	the	the	DET
ajst-25566	74	9	mean	mean	ADJ
ajst-25566	74	10	value	value	NOUN
ajst-25566	74	11	theorem	theorem	VERB
ajst-25566	74	12	.	.	PUNCT
ajst-25566	75	1	the	the	DET
ajst-25566	75	2	mean	mean	ADJ
ajst-25566	75	3	value	value	NOUN
ajst-25566	75	4	theorem	theorem	NOUN
ajst-25566	75	5	can	can	AUX
ajst-25566	75	6	be	be	AUX
ajst-25566	75	7	expressed	express	VERB
ajst-25566	75	8	as	as	ADP
ajst-25566	75	9	:	:	PUNCT
ajst-25566	75	10	assume	assume	VERB
ajst-25566	75	11	that	that	SCONJ
ajst-25566	75	12	function	function	NOUN
ajst-25566	75	13	f	f	PROPN
ajst-25566	75	14	is	be	AUX
ajst-25566	75	15	continuous	continuous	ADJ
ajst-25566	75	16	on	on	ADP
ajst-25566	75	17	the	the	DET
ajst-25566	75	18	closed	closed	ADJ
ajst-25566	75	19	interval	interval	NOUN
ajst-25566	75	20	[	[	X
ajst-25566	75	21	a	a	X
ajst-25566	75	22	,	,	PUNCT
ajst-25566	75	23	b	b	NOUN
ajst-25566	75	24	]	]	PUNCT
ajst-25566	75	25	and	and	CCONJ
ajst-25566	75	26	differentiable	differentiable	VERB
ajst-25566	75	27	on	on	ADP
ajst-25566	75	28	the	the	DET
ajst-25566	75	29	open	open	ADJ
ajst-25566	75	30	interval	interval	NOUN
ajst-25566	75	31	(	(	PUNCT
ajst-25566	75	32	a	a	DET
ajst-25566	75	33	,	,	PUNCT
ajst-25566	75	34	b	b	NOUN
ajst-25566	75	35	)	)	PUNCT
ajst-25566	75	36	,	,	PUNCT
ajst-25566	75	37	then	then	ADV
ajst-25566	75	38	there	there	PRON
ajst-25566	75	39	is	be	VERB
ajst-25566	75	40	at	at	ADV
ajst-25566	75	41	least	least	ADV
ajst-25566	75	42	one	one	NUM
ajst-25566	75	43	point	point	NOUN
ajst-25566	75	44	c	c	NOUN
ajst-25566	75	45	in	in	ADP
ajst-25566	75	46	(	(	PUNCT
ajst-25566	75	47	a	a	DET
ajst-25566	75	48	,	,	PUNCT
ajst-25566	75	49	b	b	NOUN
ajst-25566	75	50	)	)	PUNCT
ajst-25566	75	51	such	such	ADJ
ajst-25566	75	52	that	that	PRON
ajst-25566	75	53	:	:	PUNCT
ajst-25566	75	54	(	(	PUNCT
ajst-25566	75	55	)	)	PUNCT
ajst-25566	75	56	(	(	PUNCT
ajst-25566	75	57	)	)	PUNCT
ajst-25566	75	58	'	'	PUNCT
ajst-25566	75	59	(	(	PUNCT
ajst-25566	75	60	)	)	PUNCT
ajst-25566	76	1	f	f	PROPN
ajst-25566	76	2	b	b	X
ajst-25566	76	3	f	f	PROPN
ajst-25566	76	4	a	a	DET
ajst-25566	76	5	f	f	PROPN
ajst-25566	76	6	c	c	PROPN
ajst-25566	76	7	b	b	PROPN
ajst-25566	76	8	a	a	DET
ajst-25566	76	9			PROPN
ajst-25566	76	10			PROPN
ajst-25566	76	11			NOUN
ajst-25566	76	12	  	  	SPACE
ajst-25566	76	13	in	in	ADP
ajst-25566	76	14	the	the	DET
ajst-25566	76	15	formula	formula	NOUN
ajst-25566	76	16	,	,	PUNCT
ajst-25566	76	17	(	(	PUNCT
ajst-25566	76	18	)	)	PUNCT
ajst-25566	76	19	f	f	PROPN
ajst-25566	76	20	a	a	PROPN
ajst-25566	76	21	and	and	CCONJ
ajst-25566	76	22	(	(	PUNCT
ajst-25566	76	23	)	)	PUNCT
ajst-25566	76	24	f	f	PROPN
ajst-25566	76	25	b	b	PROPN
ajst-25566	76	26	are	be	AUX
ajst-25566	76	27	the	the	DET
ajst-25566	76	28	function	function	NOUN
ajst-25566	76	29	values	value	NOUN
ajst-25566	76	30	of	of	ADP
ajst-25566	76	31	function	function	NOUN
ajst-25566	76	32	f	f	PROPN
ajst-25566	76	33	at	at	ADP
ajst-25566	76	34	points	point	NOUN
ajst-25566	76	35	a	a	PRON
ajst-25566	76	36	and	and	CCONJ
ajst-25566	76	37	b	b	NOUN
ajst-25566	76	38	;	;	PUNCT
ajst-25566	76	39	'	'	PUNCT
ajst-25566	76	40	(	(	PUNCT
ajst-25566	76	41	)	)	PUNCT
ajst-25566	76	42	f	f	PROPN
ajst-25566	76	43	c	c	PROPN
ajst-25566	76	44	is	be	AUX
ajst-25566	76	45	the	the	DET
ajst-25566	76	46	derivative	derivative	NOUN
ajst-25566	76	47	of	of	ADP
ajst-25566	76	48	the	the	DET
ajst-25566	76	49	function	function	NOUN
ajst-25566	76	50	at	at	ADP
ajst-25566	76	51	point	point	NOUN
ajst-25566	76	52	c.	c.	PROPN
ajst-25566	76	53	geometric	geometric	ADJ
ajst-25566	76	54	interpretation	interpretation	NOUN
ajst-25566	76	55	of	of	ADP
ajst-25566	76	56	mean	mean	ADJ
ajst-25566	76	57	value	value	NOUN
ajst-25566	76	58	theorem	theorem	VERB
ajst-25566	76	59	:	:	PUNCT
ajst-25566	76	60	geometrically	geometrically	ADV
ajst-25566	76	61	,	,	PUNCT
ajst-25566	76	62	the	the	DET
ajst-25566	76	63	mean	mean	ADJ
ajst-25566	76	64	value	value	NOUN
ajst-25566	76	65	theorem	theorem	VERB
ajst-25566	76	66	states	state	NOUN
ajst-25566	76	67	that	that	SCONJ
ajst-25566	76	68	there	there	PRON
ajst-25566	76	69	exists	exist	VERB
ajst-25566	76	70	a	a	DET
ajst-25566	76	71	point	point	NOUN
ajst-25566	76	72	c	c	ADP
ajst-25566	76	73	such	such	ADJ
ajst-25566	76	74	that	that	SCONJ
ajst-25566	76	75	the	the	DET
ajst-25566	76	76	slope	slope	NOUN
ajst-25566	76	77	of	of	ADP
ajst-25566	76	78	the	the	DET
ajst-25566	76	79	tangent	tangent	ADJ
ajst-25566	76	80	line	line	NOUN
ajst-25566	76	81	to	to	ADP
ajst-25566	76	82	the	the	DET
ajst-25566	76	83	function	function	NOUN
ajst-25566	76	84	f	f	PROPN
ajst-25566	76	85	at	at	ADP
ajst-25566	76	86	that	that	DET
ajst-25566	76	87	point	point	NOUN
ajst-25566	76	88	is	be	AUX
ajst-25566	76	89	equal	equal	ADJ
ajst-25566	76	90	to	to	ADP
ajst-25566	76	91	the	the	DET
ajst-25566	76	92	slope	slope	NOUN
ajst-25566	76	93	of	of	ADP
ajst-25566	76	94	the	the	DET
ajst-25566	76	95	secant	secant	ADJ
ajst-25566	76	96	line	line	NOUN
ajst-25566	76	97	connecting	connect	VERB
ajst-25566	76	98	the	the	DET
ajst-25566	76	99	points	point	NOUN
ajst-25566	76	100	(	(	PUNCT
ajst-25566	76	101	a	a	DET
ajst-25566	76	102	,	,	PUNCT
ajst-25566	76	103	(	(	PUNCT
ajst-25566	76	104	)	)	PUNCT
ajst-25566	76	105	f	f	PROPN
ajst-25566	76	106	a	a	NOUN
ajst-25566	76	107	)	)	PUNCT
ajst-25566	76	108	and	and	CCONJ
ajst-25566	76	109	(	(	PUNCT
ajst-25566	76	110	b	b	NOUN
ajst-25566	76	111	,	,	PUNCT
ajst-25566	76	112	(	(	PUNCT
ajst-25566	76	113	)	)	PUNCT
ajst-25566	76	114	f	f	PROPN
ajst-25566	76	115	b	b	PROPN
ajst-25566	76	116	)	)	PUNCT
ajst-25566	76	117	.	.	PUNCT
ajst-25566	77	1	proof	proof	NOUN
ajst-25566	77	2	of	of	ADP
ajst-25566	77	3	the	the	DET
ajst-25566	77	4	mean	mean	ADJ
ajst-25566	77	5	value	value	NOUN
ajst-25566	77	6	theorem	theorem	VERB
ajst-25566	77	7	:	:	PUNCT
ajst-25566	77	8	the	the	DET
ajst-25566	77	9	proof	proof	NOUN
ajst-25566	77	10	of	of	ADP
ajst-25566	77	11	the	the	DET
ajst-25566	77	12	mean	mean	ADJ
ajst-25566	77	13	value	value	NOUN
ajst-25566	77	14	theorem	theorem	NOUN
ajst-25566	77	15	is	be	AUX
ajst-25566	77	16	usually	usually	ADV
ajst-25566	77	17	based	base	VERB
ajst-25566	77	18	on	on	ADP
ajst-25566	77	19	rolle	rolle	PROPN
ajst-25566	77	20	's	's	PART
ajst-25566	77	21	theorem	theorem	PROPN
ajst-25566	77	22	.	.	PROPN
ajst-25566	77	23	rolle	rolle	PROPN
ajst-25566	77	24	's	's	PART
ajst-25566	77	25	theorem	theorem	NOUN
ajst-25566	77	26	is	be	AUX
ajst-25566	77	27	a	a	DET
ajst-25566	77	28	special	special	ADJ
ajst-25566	77	29	case	case	NOUN
ajst-25566	77	30	of	of	ADP
ajst-25566	77	31	mean	mean	ADJ
ajst-25566	77	32	value	value	NOUN
ajst-25566	77	33	theorem	theorem	NOUN
ajst-25566	77	34	.	.	PROPN
ajst-25566	77	35	rolle	rolle	PROPN
ajst-25566	77	36	's	's	PART
ajst-25566	77	37	theorem	theorem	NOUN
ajst-25566	77	38	:	:	PUNCT
ajst-25566	77	39	let	let	VERB
ajst-25566	77	40	the	the	DET
ajst-25566	77	41	function	function	NOUN
ajst-25566	77	42	be	be	AUX
ajst-25566	77	43	continuous	continuous	ADJ
ajst-25566	77	44	on	on	ADP
ajst-25566	77	45	the	the	DET
ajst-25566	77	46	closed	closed	ADJ
ajst-25566	77	47	interval	interval	NOUN
ajst-25566	77	48	[	[	X
ajst-25566	77	49	a	a	X
ajst-25566	77	50	,	,	PUNCT
ajst-25566	77	51	b	b	NOUN
ajst-25566	77	52	]	]	X
ajst-25566	77	53	,	,	PUNCT
ajst-25566	77	54	differentiable	differentiable	VERB
ajst-25566	77	55	on	on	ADP
ajst-25566	77	56	the	the	DET
ajst-25566	77	57	open	open	ADJ
ajst-25566	77	58	interval	interval	NOUN
ajst-25566	77	59	(	(	PUNCT
ajst-25566	77	60	a	a	DET
ajst-25566	77	61	,	,	PUNCT
ajst-25566	77	62	b	b	NOUN
ajst-25566	77	63	)	)	PUNCT
ajst-25566	77	64	,	,	PUNCT
ajst-25566	77	65	and	and	CCONJ
ajst-25566	77	66	(	(	PUNCT
ajst-25566	77	67	)	)	PUNCT
ajst-25566	77	68	(	(	PUNCT
ajst-25566	77	69	)	)	PUNCT
ajst-25566	77	70	f	f	PROPN
ajst-25566	77	71	a	a	DET
ajst-25566	77	72	f	f	PROPN
ajst-25566	77	73	b	b	PROPN
ajst-25566	77	74	,	,	PUNCT
ajst-25566	77	75	then	then	ADV
ajst-25566	77	76	there	there	PRON
ajst-25566	77	77	exists	exist	VERB
ajst-25566	77	78	a	a	DET
ajst-25566	77	79	point	point	NOUN
ajst-25566	77	80	c	c	NOUN
ajst-25566	77	81	on	on	X
ajst-25566	77	82	(	(	PUNCT
ajst-25566	77	83	a	a	DET
ajst-25566	77	84	,	,	PUNCT
ajst-25566	77	85	b	b	NOUN
ajst-25566	77	86	)	)	PUNCT
ajst-25566	78	1	such	such	ADJ
ajst-25566	78	2	that	that	SCONJ
ajst-25566	78	3	'	'	PUNCT
ajst-25566	78	4	(	(	PUNCT
ajst-25566	78	5	)	)	PUNCT
ajst-25566	78	6	0f	0f	NOUN
ajst-25566	78	7	c	c	NOUN
ajst-25566	79	1			NOUN
ajst-25566	79	2	:	:	PUNCT
ajst-25566	79	3	the	the	DET
ajst-25566	79	4	proof	proof	ADJ
ajst-25566	79	5	steps	step	NOUN
ajst-25566	79	6	of	of	ADP
ajst-25566	79	7	the	the	DET
ajst-25566	79	8	mean	mean	ADJ
ajst-25566	79	9	value	value	NOUN
ajst-25566	79	10	theorem	theorem	NOUN
ajst-25566	79	11	are	be	AUX
ajst-25566	79	12	as	as	SCONJ
ajst-25566	79	13	follows	follow	VERB
ajst-25566	79	14	:	:	PUNCT
ajst-25566	79	15	(	(	PUNCT
ajst-25566	79	16	1	1	NUM
ajst-25566	79	17	)	)	PUNCT
ajst-25566	79	18	.	.	PUNCT
ajst-25566	80	1	define	define	VERB
ajst-25566	80	2	a	a	DET
ajst-25566	80	3	new	new	ADJ
ajst-25566	80	4	function	function	NOUN
ajst-25566	80	5	(	(	PUNCT
ajst-25566	80	6	)	)	PUNCT
ajst-25566	80	7	(	(	PUNCT
ajst-25566	80	8	)	)	PUNCT
ajst-25566	80	9	(	(	PUNCT
ajst-25566	80	10	)	)	PUNCT
ajst-25566	80	11	(	(	PUNCT
ajst-25566	80	12	)	)	PUNCT
ajst-25566	80	13	(	(	PUNCT
ajst-25566	80	14	)	)	PUNCT
ajst-25566	80	15	(	(	PUNCT
ajst-25566	80	16	)	)	PUNCT
ajst-25566	81	1	f	f	PROPN
ajst-25566	81	2	b	b	X
ajst-25566	81	3	f	f	X
ajst-25566	81	4	a	a	DET
ajst-25566	81	5	g	g	NOUN
ajst-25566	81	6	x	x	X
ajst-25566	81	7	f	f	NOUN
ajst-25566	81	8	x	x	X
ajst-25566	81	9	x	x	X
ajst-25566	81	10	a	a	PRON
ajst-25566	81	11	f	f	NOUN
ajst-25566	81	12	a	a	DET
ajst-25566	81	13	b	b	NOUN
ajst-25566	81	14	a	a	DET
ajst-25566	81	15			PROPN
ajst-25566	81	16			X
ajst-25566	81	17			PROPN
ajst-25566	81	18			PROPN
ajst-25566	81	19			PROPN
ajst-25566	81	20			NOUN
ajst-25566	81	21			NOUN
ajst-25566	81	22	that	that	PRON
ajst-25566	81	23	represents	represent	VERB
ajst-25566	81	24	(	(	PUNCT
ajst-25566	81	25	)	)	PUNCT
ajst-25566	81	26	f	f	PROPN
ajst-25566	81	27	x	x	PUNCT
ajst-25566	81	28	minus	minus	ADP
ajst-25566	81	29	the	the	DET
ajst-25566	81	30	secant	secant	ADJ
ajst-25566	81	31	equation	equation	NOUN
ajst-25566	81	32	.	.	PUNCT
ajst-25566	82	1	(	(	PUNCT
ajst-25566	82	2	2	2	NUM
ajst-25566	82	3	)	)	PUNCT
ajst-25566	82	4	.	.	PUNCT
ajst-25566	83	1	since	since	SCONJ
ajst-25566	83	2	(	(	PUNCT
ajst-25566	83	3	)	)	PUNCT
ajst-25566	83	4	(	(	PUNCT
ajst-25566	83	5	)	)	PUNCT
ajst-25566	83	6	0	0	NUM
ajst-25566	83	7	g	g	PROPN
ajst-25566	83	8	a	a	DET
ajst-25566	83	9	g	g	NOUN
ajst-25566	83	10	b	b	NOUN
ajst-25566	83	11			PROPN
ajst-25566	83	12	,	,	PUNCT
ajst-25566	83	13	according	accord	VERB
ajst-25566	83	14	to	to	ADP
ajst-25566	83	15	rolle	rolle	PROPN
ajst-25566	83	16	's	's	PART
ajst-25566	83	17	theorem	theorem	NOUN
ajst-25566	83	18	,	,	PUNCT
ajst-25566	83	19	there	there	PRON
ajst-25566	83	20	exists	exist	VERB
ajst-25566	83	21	(	(	PUNCT
ajst-25566	83	22	,	,	PUNCT
ajst-25566	83	23	)	)	PUNCT
ajst-25566	83	24	c	c	PROPN
ajst-25566	83	25	a	a	DET
ajst-25566	83	26	b	b	NOUN
ajst-25566	83	27	such	such	ADJ
ajst-25566	83	28	that	that	SCONJ
ajst-25566	83	29	g	g	NOUN
ajst-25566	83	30	'	'	PUNCT
ajst-25566	83	31	(	(	PUNCT
ajst-25566	83	32	)	)	PUNCT
ajst-25566	83	33	0c	0c	NOUN
ajst-25566	83	34			PRON
ajst-25566	83	35	.	.	PUNCT
ajst-25566	84	1	(	(	PUNCT
ajst-25566	84	2	3	3	NUM
ajst-25566	84	3	)	)	PUNCT
ajst-25566	84	4	.	.	PUNCT
ajst-25566	85	1	calculate	calculate	NOUN
ajst-25566	85	2	(	(	PUNCT
ajst-25566	85	3	)	)	PUNCT
ajst-25566	85	4	(	(	PUNCT
ajst-25566	85	5	)	)	PUNCT
ajst-25566	85	6	(	(	PUNCT
ajst-25566	85	7	)	)	PUNCT
ajst-25566	85	8	(	(	PUNCT
ajst-25566	85	9	)	)	PUNCT
ajst-25566	86	1	f	f	PROPN
ajst-25566	86	2	b	b	X
ajst-25566	86	3	f	f	X
ajst-25566	86	4	a	a	DET
ajst-25566	86	5	g	g	NOUN
ajst-25566	86	6	x	x	SYM
ajst-25566	86	7	f	f	PROPN
ajst-25566	86	8	x	x	SYM
ajst-25566	86	9	b	b	X
ajst-25566	86	10	a	a	DET
ajst-25566	86	11			NOUN
ajst-25566	86	12			PROPN
ajst-25566	86	13			ADJ
ajst-25566	86	14			PROPN
ajst-25566	86	15			PROPN
ajst-25566	86	16			ADV
ajst-25566	86	17	.	.	PUNCT
ajst-25566	87	1	and	and	CCONJ
ajst-25566	87	2	61	61	NUM
ajst-25566	87	3	g	g	NOUN
ajst-25566	87	4	'	'	PUNCT
ajst-25566	87	5	(	(	PUNCT
ajst-25566	87	6	)	)	PUNCT
ajst-25566	87	7	0c	0c	PROPN
ajst-25566	88	1			PROPN
ajst-25566	88	2	means	mean	VERB
ajst-25566	88	3	(	(	PUNCT
ajst-25566	88	4	)	)	PUNCT
ajst-25566	88	5	(	(	PUNCT
ajst-25566	88	6	)	)	PUNCT
ajst-25566	88	7	'	'	PUNCT
ajst-25566	88	8	(	(	PUNCT
ajst-25566	88	9	)	)	PUNCT
ajst-25566	89	1	f	f	PROPN
ajst-25566	89	2	b	b	X
ajst-25566	89	3	f	f	PROPN
ajst-25566	89	4	a	a	DET
ajst-25566	89	5	f	f	PROPN
ajst-25566	89	6	c	c	PROPN
ajst-25566	89	7	b	b	PROPN
ajst-25566	89	8	a	a	DET
ajst-25566	89	9			PROPN
ajst-25566	89	10			PROPN
ajst-25566	89	11			NOUN
ajst-25566	89	12	.	.	PUNCT
ajst-25566	90	1	3.1.2	3.1.2	X
ajst-25566	90	2	.	.	PUNCT
ajst-25566	90	3	gradient	gradient	ADJ
ajst-25566	90	4	analysis	analysis	NOUN
ajst-25566	90	5	gradient	gradient	ADJ
ajst-25566	90	6	analysis	analysis	NOUN
ajst-25566	90	7	plays	play	VERB
ajst-25566	90	8	a	a	DET
ajst-25566	90	9	key	key	ADJ
ajst-25566	90	10	role	role	NOUN
ajst-25566	90	11	in	in	ADP
ajst-25566	90	12	function	function	NOUN
ajst-25566	90	13	comparison	comparison	NOUN
ajst-25566	90	14	and	and	CCONJ
ajst-25566	90	15	optimization	optimization	NOUN
ajst-25566	90	16	.	.	PUNCT
ajst-25566	91	1	when	when	SCONJ
ajst-25566	91	2	studying	study	VERB
ajst-25566	91	3	the	the	DET
ajst-25566	91	4	maximum	maximum	ADJ
ajst-25566	91	5	difference	difference	NOUN
ajst-25566	91	6	between	between	ADP
ajst-25566	91	7	two	two	NUM
ajst-25566	91	8	functions	function	NOUN
ajst-25566	91	9	(	(	PUNCT
ajst-25566	91	10	)	)	PUNCT
ajst-25566	91	11	f	f	NOUN
ajst-25566	91	12	x	x	X
ajst-25566	91	13	and	and	CCONJ
ajst-25566	91	14	(	(	PUNCT
ajst-25566	91	15	)	)	PUNCT
ajst-25566	91	16	g	g	NOUN
ajst-25566	91	17	x	x	SYM
ajst-25566	91	18	,	,	PUNCT
ajst-25566	91	19	the	the	DET
ajst-25566	91	20	extreme	extreme	ADJ
ajst-25566	91	21	points	point	NOUN
ajst-25566	91	22	of	of	ADP
ajst-25566	91	23	the	the	DET
ajst-25566	91	24	function	function	NOUN
ajst-25566	91	25	within	within	ADP
ajst-25566	91	26	a	a	DET
ajst-25566	91	27	certain	certain	ADJ
ajst-25566	91	28	interval	interval	NOUN
ajst-25566	91	29	can	can	AUX
ajst-25566	91	30	be	be	AUX
ajst-25566	91	31	determined	determine	VERB
ajst-25566	91	32	by	by	ADP
ajst-25566	91	33	analyzing	analyze	VERB
ajst-25566	91	34	their	their	PRON
ajst-25566	91	35	derivatives	derivative	NOUN
ajst-25566	91	36	(	(	PUNCT
ajst-25566	91	37	gradients	gradient	NOUN
ajst-25566	91	38	)	)	PUNCT
ajst-25566	91	39	.	.	PUNCT
ajst-25566	92	1	the	the	DET
ajst-25566	92	2	meaning	meaning	NOUN
ajst-25566	92	3	of	of	ADP
ajst-25566	92	4	the	the	DET
ajst-25566	92	5	derivative	derivative	NOUN
ajst-25566	92	6	:	:	PUNCT
ajst-25566	92	7	the	the	DET
ajst-25566	92	8	derivative	derivative	ADJ
ajst-25566	92	9	'	'	PUNCT
ajst-25566	92	10	(	(	PUNCT
ajst-25566	92	11	)	)	PUNCT
ajst-25566	92	12	f	f	X
ajst-25566	93	1	x	x	PRON
ajst-25566	93	2	represents	represent	VERB
ajst-25566	93	3	the	the	DET
ajst-25566	93	4	instantaneous	instantaneous	ADJ
ajst-25566	93	5	rate	rate	NOUN
ajst-25566	93	6	of	of	ADP
ajst-25566	93	7	change	change	NOUN
ajst-25566	93	8	or	or	CCONJ
ajst-25566	93	9	slope	slope	NOUN
ajst-25566	93	10	of	of	ADP
ajst-25566	93	11	the	the	DET
ajst-25566	93	12	function	function	NOUN
ajst-25566	93	13	f	f	PROPN
ajst-25566	93	14	at	at	ADP
ajst-25566	93	15	a	a	DET
ajst-25566	93	16	point	point	NOUN
ajst-25566	93	17	x.	x.	NOUN
ajst-25566	93	18	for	for	ADP
ajst-25566	93	19	two	two	NUM
ajst-25566	93	20	functions	function	NOUN
ajst-25566	93	21	(	(	PUNCT
ajst-25566	93	22	)	)	PUNCT
ajst-25566	93	23	f	f	NOUN
ajst-25566	93	24	x	x	X
ajst-25566	93	25	and	and	CCONJ
ajst-25566	93	26	(	(	PUNCT
ajst-25566	93	27	)	)	PUNCT
ajst-25566	93	28	g	g	NOUN
ajst-25566	93	29	x	x	SYM
ajst-25566	93	30	,	,	PUNCT
ajst-25566	93	31	comparing	compare	VERB
ajst-25566	93	32	their	their	PRON
ajst-25566	93	33	derivatives	derivative	NOUN
ajst-25566	93	34	can	can	AUX
ajst-25566	93	35	reveal	reveal	VERB
ajst-25566	93	36	their	their	PRON
ajst-25566	93	37	relative	relative	ADJ
ajst-25566	93	38	rate	rate	NOUN
ajst-25566	93	39	of	of	ADP
ajst-25566	93	40	change	change	NOUN
ajst-25566	93	41	:	:	PUNCT
ajst-25566	93	42	(	(	PUNCT
ajst-25566	93	43	1	1	X
ajst-25566	93	44	)	)	PUNCT
ajst-25566	93	45	derivatives	derivative	NOUN
ajst-25566	93	46	are	be	AUX
ajst-25566	93	47	equal	equal	ADJ
ajst-25566	93	48	:	:	PUNCT
ajst-25566	93	49	if	if	SCONJ
ajst-25566	93	50	at	at	ADP
ajst-25566	93	51	a	a	DET
ajst-25566	93	52	point	point	NOUN
ajst-25566	93	53	x	x	NOUN
ajst-25566	93	54	,	,	PUNCT
ajst-25566	93	55	'	'	PUNCT
ajst-25566	93	56	(	(	PUNCT
ajst-25566	93	57	)	)	PUNCT
ajst-25566	93	58	'	'	PUNCT
ajst-25566	93	59	(	(	PUNCT
ajst-25566	93	60	)	)	PUNCT
ajst-25566	93	61	f	f	X
ajst-25566	94	1	x	x	X
ajst-25566	94	2	g	g	PROPN
ajst-25566	94	3	x	x	PROPN
ajst-25566	94	4	,	,	PUNCT
ajst-25566	94	5	then	then	ADV
ajst-25566	94	6	the	the	DET
ajst-25566	94	7	rates	rate	NOUN
ajst-25566	94	8	of	of	ADP
ajst-25566	94	9	change	change	NOUN
ajst-25566	94	10	of	of	ADP
ajst-25566	94	11	the	the	DET
ajst-25566	94	12	two	two	NUM
ajst-25566	94	13	functions	function	NOUN
ajst-25566	94	14	at	at	ADP
ajst-25566	94	15	that	that	DET
ajst-25566	94	16	point	point	NOUN
ajst-25566	94	17	are	be	AUX
ajst-25566	94	18	the	the	DET
ajst-25566	94	19	same	same	ADJ
ajst-25566	94	20	.	.	PUNCT
ajst-25566	95	1	(	(	PUNCT
ajst-25566	95	2	2	2	X
ajst-25566	95	3	)	)	PUNCT
ajst-25566	95	4	comparison	comparison	NOUN
ajst-25566	95	5	of	of	ADP
ajst-25566	95	6	derivatives	derivative	NOUN
ajst-25566	95	7	:	:	PUNCT
ajst-25566	95	8	if	if	SCONJ
ajst-25566	95	9	'	'	PUNCT
ajst-25566	95	10	(	(	PUNCT
ajst-25566	95	11	)	)	PUNCT
ajst-25566	95	12	'	'	PUNCT
ajst-25566	95	13	(	(	PUNCT
ajst-25566	95	14	)	)	PUNCT
ajst-25566	95	15	f	f	X
ajst-25566	95	16	x	x	PUNCT
ajst-25566	95	17	g	g	NOUN
ajst-25566	95	18	x	x	ADV
ajst-25566	95	19	,	,	PUNCT
ajst-25566	95	20	it	it	PRON
ajst-25566	95	21	means	mean	VERB
ajst-25566	95	22	that	that	SCONJ
ajst-25566	95	23	at	at	ADP
ajst-25566	95	24	this	this	DET
ajst-25566	95	25	point	point	NOUN
ajst-25566	95	26	(	(	PUNCT
ajst-25566	95	27	)	)	PUNCT
ajst-25566	95	28	f	f	X
ajst-25566	95	29	x	x	PUNCT
ajst-25566	95	30	grows	grow	VERB
ajst-25566	95	31	faster	fast	ADV
ajst-25566	95	32	than	than	ADP
ajst-25566	95	33	(	(	PUNCT
ajst-25566	95	34	)	)	PUNCT
ajst-25566	95	35	g	g	NOUN
ajst-25566	95	36	x	x	X
ajst-25566	95	37	;	;	PUNCT
ajst-25566	95	38	if	if	SCONJ
ajst-25566	95	39	'	'	PUNCT
ajst-25566	95	40	(	(	PUNCT
ajst-25566	95	41	)	)	PUNCT
ajst-25566	95	42	'	'	PUNCT
ajst-25566	95	43	(	(	PUNCT
ajst-25566	95	44	)	)	PUNCT
ajst-25566	95	45	f	f	NOUN
ajst-25566	95	46	x	x	SYM
ajst-25566	95	47	g	g	PROPN
ajst-25566	95	48	x	x	INTJ
ajst-25566	95	49	,	,	PUNCT
ajst-25566	95	50	it	it	PRON
ajst-25566	95	51	means	mean	VERB
ajst-25566	95	52	that	that	SCONJ
ajst-25566	95	53	(	(	PUNCT
ajst-25566	95	54	)	)	PUNCT
ajst-25566	95	55	f	f	X
ajst-25566	95	56	x	x	PUNCT
ajst-25566	95	57	grows	grow	VERB
ajst-25566	95	58	slower	slow	ADJ
ajst-25566	95	59	than	than	ADP
ajst-25566	95	60	(	(	PUNCT
ajst-25566	95	61	)	)	PUNCT
ajst-25566	95	62	g	g	NOUN
ajst-25566	95	63	x	x	X
ajst-25566	95	64	.	.	PUNCT
ajst-25566	96	1	3.1.3	3.1.3	NUM
ajst-25566	96	2	.	.	PUNCT
ajst-25566	96	3	determination	determination	NOUN
ajst-25566	96	4	of	of	ADP
ajst-25566	96	5	extreme	extreme	ADJ
ajst-25566	96	6	points	point	NOUN
ajst-25566	96	7	by	by	ADP
ajst-25566	96	8	solving	solve	VERB
ajst-25566	96	9	the	the	DET
ajst-25566	96	10	equations	equation	NOUN
ajst-25566	96	11	for	for	ADP
ajst-25566	96	12	derivatives	derivative	NOUN
ajst-25566	96	13	equal	equal	ADJ
ajst-25566	96	14	to	to	ADP
ajst-25566	96	15	zero	zero	NUM
ajst-25566	96	16	,	,	PUNCT
ajst-25566	96	17	'	'	PUNCT
ajst-25566	96	18	(	(	PUNCT
ajst-25566	96	19	)	)	PUNCT
ajst-25566	96	20	0f	0f	NOUN
ajst-25566	96	21	x	x	SYM
ajst-25566	96	22			PROPN
ajst-25566	96	23	and	and	CCONJ
ajst-25566	96	24	'	'	PUNCT
ajst-25566	96	25	(	(	PUNCT
ajst-25566	96	26	)	)	PUNCT
ajst-25566	96	27	0	0	NUM
ajst-25566	96	28	g	g	NOUN
ajst-25566	96	29	x	x	X
ajst-25566	96	30			NOUN
ajst-25566	96	31	,	,	PUNCT
ajst-25566	96	32	we	we	PRON
ajst-25566	96	33	can	can	AUX
ajst-25566	96	34	find	find	VERB
ajst-25566	96	35	the	the	DET
ajst-25566	96	36	extreme	extreme	ADJ
ajst-25566	96	37	points	point	NOUN
ajst-25566	96	38	of	of	ADP
ajst-25566	96	39	the	the	DET
ajst-25566	96	40	function	function	NOUN
ajst-25566	96	41	.	.	PUNCT
ajst-25566	97	1	at	at	ADP
ajst-25566	97	2	these	these	DET
ajst-25566	97	3	points	point	NOUN
ajst-25566	97	4	,	,	PUNCT
ajst-25566	97	5	the	the	DET
ajst-25566	97	6	function	function	NOUN
ajst-25566	97	7	may	may	AUX
ajst-25566	97	8	reach	reach	VERB
ajst-25566	97	9	a	a	DET
ajst-25566	97	10	local	local	ADJ
ajst-25566	97	11	maximum	maximum	NOUN
ajst-25566	97	12	or	or	CCONJ
ajst-25566	97	13	minimum	minimum	NOUN
ajst-25566	97	14	.	.	PUNCT
ajst-25566	98	1	by	by	ADP
ajst-25566	98	2	comparing	compare	VERB
ajst-25566	98	3	the	the	DET
ajst-25566	98	4	values	value	NOUN
ajst-25566	98	5	of	of	ADP
ajst-25566	98	6	the	the	DET
ajst-25566	98	7	two	two	NUM
ajst-25566	98	8	functions	function	NOUN
ajst-25566	98	9	at	at	ADP
ajst-25566	98	10	these	these	DET
ajst-25566	98	11	extreme	extreme	ADJ
ajst-25566	98	12	points	point	NOUN
ajst-25566	98	13	,	,	PUNCT
ajst-25566	98	14	the	the	DET
ajst-25566	98	15	maximum	maximum	ADJ
ajst-25566	98	16	difference	difference	NOUN
ajst-25566	98	17	between	between	ADP
ajst-25566	98	18	them	they	PRON
ajst-25566	98	19	can	can	AUX
ajst-25566	98	20	be	be	AUX
ajst-25566	98	21	found	find	VERB
ajst-25566	98	22	.	.	PUNCT
ajst-25566	99	1	3.2	3.2	NUM
ajst-25566	99	2	.	.	PUNCT
ajst-25566	99	3	specific	specific	ADJ
ajst-25566	99	4	steps	step	NOUN
ajst-25566	99	5	the	the	DET
ajst-25566	99	6	method	method	NOUN
ajst-25566	99	7	in	in	ADP
ajst-25566	99	8	this	this	DET
ajst-25566	99	9	paper	paper	NOUN
ajst-25566	99	10	combines	combine	VERB
ajst-25566	99	11	the	the	DET
ajst-25566	99	12	mean	mean	ADJ
ajst-25566	99	13	value	value	NOUN
ajst-25566	99	14	theorem	theorem	NOUN
ajst-25566	99	15	and	and	CCONJ
ajst-25566	99	16	gradient	gradient	ADJ
ajst-25566	99	17	analysis	analysis	NOUN
ajst-25566	99	18	to	to	PART
ajst-25566	99	19	systematically	systematically	ADV
ajst-25566	99	20	find	find	VERB
ajst-25566	99	21	the	the	DET
ajst-25566	99	22	maximum	maximum	ADJ
ajst-25566	99	23	difference	difference	NOUN
ajst-25566	99	24	between	between	ADP
ajst-25566	99	25	two	two	NUM
ajst-25566	99	26	functions	function	NOUN
ajst-25566	99	27	in	in	ADP
ajst-25566	99	28	the	the	DET
ajst-25566	99	29	two	two	NUM
ajst-25566	99	30	nearest	near	ADJ
ajst-25566	99	31	intersection	intersection	NOUN
ajst-25566	99	32	intervals	interval	NOUN
ajst-25566	99	33	.	.	PUNCT
ajst-25566	100	1	the	the	DET
ajst-25566	100	2	specific	specific	ADJ
ajst-25566	100	3	steps	step	NOUN
ajst-25566	100	4	are	be	AUX
ajst-25566	100	5	as	as	SCONJ
ajst-25566	100	6	follows	follow	VERB
ajst-25566	100	7	:	:	PUNCT
ajst-25566	100	8	step	step	NOUN
ajst-25566	100	9	1	1	NUM
ajst-25566	100	10	:	:	PUNCT
ajst-25566	100	11	determine	determine	VERB
ajst-25566	100	12	the	the	DET
ajst-25566	100	13	intersection	intersection	NOUN
ajst-25566	100	14	of	of	ADP
ajst-25566	100	15	the	the	DET
ajst-25566	100	16	two	two	NUM
ajst-25566	100	17	functions	function	NOUN
ajst-25566	100	18	:	:	PUNCT
ajst-25566	100	19	first	first	ADV
ajst-25566	100	20	,	,	PUNCT
ajst-25566	100	21	we	we	PRON
ajst-25566	100	22	need	need	VERB
ajst-25566	100	23	to	to	PART
ajst-25566	100	24	determine	determine	VERB
ajst-25566	100	25	all	all	DET
ajst-25566	100	26	the	the	DET
ajst-25566	100	27	points	point	NOUN
ajst-25566	100	28	where	where	SCONJ
ajst-25566	100	29	the	the	DET
ajst-25566	100	30	functions	function	NOUN
ajst-25566	100	31	(	(	PUNCT
ajst-25566	100	32	)	)	PUNCT
ajst-25566	100	33	f	f	NOUN
ajst-25566	100	34	x	x	X
ajst-25566	100	35	and	and	CCONJ
ajst-25566	100	36	(	(	PUNCT
ajst-25566	100	37	)	)	PUNCT
ajst-25566	100	38	g	g	NOUN
ajst-25566	100	39	x	x	SYM
ajst-25566	100	40	intersect	intersect	ADJ
ajst-25566	100	41	.	.	PUNCT
ajst-25566	101	1	an	an	DET
ajst-25566	101	2	intersection	intersection	NOUN
ajst-25566	101	3	point	point	NOUN
ajst-25566	101	4	is	be	AUX
ajst-25566	101	5	a	a	DET
ajst-25566	101	6	point	point	NOUN
ajst-25566	101	7	where	where	SCONJ
ajst-25566	101	8	the	the	DET
ajst-25566	101	9	values	value	NOUN
ajst-25566	101	10	of	of	ADP
ajst-25566	101	11	the	the	DET
ajst-25566	101	12	two	two	NUM
ajst-25566	101	13	functions	function	NOUN
ajst-25566	101	14	are	be	AUX
ajst-25566	101	15	equal	equal	ADJ
ajst-25566	101	16	,	,	PUNCT
ajst-25566	101	17	i.e.	i.e.	X
ajst-25566	101	18	(	(	PUNCT
ajst-25566	101	19	)	)	PUNCT
ajst-25566	101	20	(	(	PUNCT
ajst-25566	101	21	)	)	PUNCT
ajst-25566	101	22	f	f	X
ajst-25566	101	23	x	x	X
ajst-25566	101	24	g	g	PROPN
ajst-25566	101	25	x	x	PROPN
ajst-25566	101	26	.	.	PUNCT
ajst-25566	102	1	here	here	ADV
ajst-25566	102	2	are	be	AUX
ajst-25566	102	3	the	the	DET
ajst-25566	102	4	specific	specific	ADJ
ajst-25566	102	5	steps	step	NOUN
ajst-25566	102	6	:	:	PUNCT
ajst-25566	102	7	(	(	PUNCT
ajst-25566	102	8	1	1	NUM
ajst-25566	102	9	)	)	PUNCT
ajst-25566	102	10	.	.	PUNCT
ajst-25566	103	1	solving	solve	VERB
ajst-25566	103	2	equations	equation	NOUN
ajst-25566	103	3	:	:	PUNCT
ajst-25566	103	4	for	for	ADP
ajst-25566	103	5	simple	simple	ADJ
ajst-25566	103	6	functions	function	NOUN
ajst-25566	103	7	,	,	PUNCT
ajst-25566	103	8	the	the	DET
ajst-25566	103	9	equation	equation	NOUN
ajst-25566	103	10	(	(	PUNCT
ajst-25566	103	11	)	)	PUNCT
ajst-25566	103	12	(	(	PUNCT
ajst-25566	103	13	)	)	PUNCT
ajst-25566	103	14	f	f	X
ajst-25566	103	15	x	x	X
ajst-25566	103	16	g	g	PROPN
ajst-25566	103	17	x	x	PROPN
ajst-25566	103	18	can	can	AUX
ajst-25566	103	19	be	be	AUX
ajst-25566	103	20	solved	solve	VERB
ajst-25566	103	21	by	by	ADP
ajst-25566	103	22	analytical	analytical	ADJ
ajst-25566	103	23	method	method	NOUN
ajst-25566	103	24	.	.	PUNCT
ajst-25566	104	1	for	for	ADP
ajst-25566	104	2	complex	complex	ADJ
ajst-25566	104	3	functions	function	NOUN
ajst-25566	104	4	,	,	PUNCT
ajst-25566	104	5	it	it	PRON
ajst-25566	104	6	may	may	AUX
ajst-25566	104	7	be	be	AUX
ajst-25566	104	8	necessary	necessary	ADJ
ajst-25566	104	9	to	to	PART
ajst-25566	104	10	use	use	VERB
ajst-25566	104	11	numerical	numerical	ADJ
ajst-25566	104	12	methods	method	NOUN
ajst-25566	104	13	,	,	PUNCT
ajst-25566	104	14	such	such	ADJ
ajst-25566	104	15	as	as	ADP
ajst-25566	104	16	newton	newton	PROPN
ajst-25566	104	17	iterative	iterative	NOUN
ajst-25566	104	18	method	method	NOUN
ajst-25566	104	19	or	or	CCONJ
ajst-25566	104	20	dichotomy	dichotomy	NOUN
ajst-25566	104	21	,	,	PUNCT
ajst-25566	104	22	to	to	PART
ajst-25566	104	23	solve	solve	VERB
ajst-25566	104	24	the	the	DET
ajst-25566	104	25	intersection	intersection	NOUN
ajst-25566	104	26	point	point	NOUN
ajst-25566	104	27	.	.	PUNCT
ajst-25566	105	1	(	(	PUNCT
ajst-25566	105	2	2	2	NUM
ajst-25566	105	3	)	)	PUNCT
ajst-25566	105	4	.	.	PUNCT
ajst-25566	106	1	verify	verify	VERB
ajst-25566	106	2	the	the	DET
ajst-25566	106	3	intersection	intersection	NOUN
ajst-25566	106	4	point	point	NOUN
ajst-25566	106	5	:	:	PUNCT
ajst-25566	106	6	we	we	PRON
ajst-25566	106	7	confirm	confirm	VERB
ajst-25566	106	8	that	that	SCONJ
ajst-25566	106	9	the	the	DET
ajst-25566	106	10	solved	solved	ADJ
ajst-25566	106	11	point	point	NOUN
ajst-25566	106	12	is	be	AUX
ajst-25566	106	13	the	the	DET
ajst-25566	106	14	actual	actual	ADJ
ajst-25566	106	15	intersection	intersection	NOUN
ajst-25566	106	16	point	point	NOUN
ajst-25566	106	17	of	of	ADP
ajst-25566	106	18	the	the	DET
ajst-25566	106	19	two	two	NUM
ajst-25566	106	20	functions	function	NOUN
ajst-25566	106	21	,	,	PUNCT
ajst-25566	106	22	not	not	PART
ajst-25566	106	23	the	the	DET
ajst-25566	106	24	false	false	ADJ
ajst-25566	106	25	solution	solution	NOUN
ajst-25566	106	26	.	.	PUNCT
ajst-25566	107	1	example	example	NOUN
ajst-25566	107	2	:	:	PUNCT
ajst-25566	107	3	suppose	suppose	VERB
ajst-25566	107	4	there	there	PRON
ajst-25566	107	5	are	be	VERB
ajst-25566	107	6	two	two	NUM
ajst-25566	107	7	functions	function	NOUN
ajst-25566	107	8	2	2	NUM
ajst-25566	107	9	(	(	PUNCT
ajst-25566	107	10	)	)	PUNCT
ajst-25566	107	11	f	f	NOUN
ajst-25566	108	1	x	x	X
ajst-25566	108	2	x	x	PROPN
ajst-25566	108	3	and	and	CCONJ
ajst-25566	108	4	(	(	PUNCT
ajst-25566	108	5	)	)	PUNCT
ajst-25566	108	6	sin	sin	NOUN
ajst-25566	108	7	(	(	PUNCT
ajst-25566	108	8	)	)	PUNCT
ajst-25566	108	9	g	g	NOUN
ajst-25566	108	10	x	x	X
ajst-25566	108	11	x	x	X
ajst-25566	108	12	,	,	PUNCT
ajst-25566	108	13	and	and	CCONJ
ajst-25566	108	14	we	we	PRON
ajst-25566	108	15	need	need	VERB
ajst-25566	108	16	to	to	PART
ajst-25566	108	17	solve	solve	VERB
ajst-25566	108	18	the	the	DET
ajst-25566	108	19	equation	equation	NOUN
ajst-25566	108	20	:	:	PUNCT
ajst-25566	108	21	2	2	NUM
ajst-25566	108	22	sin	sin	NOUN
ajst-25566	108	23	(	(	PUNCT
ajst-25566	108	24	)	)	PUNCT
ajst-25566	108	25	x	x	X
ajst-25566	108	26	x	x	PROPN
ajst-25566	108	27	,	,	PUNCT
ajst-25566	108	28	let	let	VERB
ajst-25566	108	29	1x	1x	PRON
ajst-25566	108	30	and	and	CCONJ
ajst-25566	108	31	2x	2x	NUM
ajst-25566	108	32	be	be	AUX
ajst-25566	108	33	the	the	DET
ajst-25566	108	34	two	two	NUM
ajst-25566	108	35	intersection	intersection	NOUN
ajst-25566	108	36	points	point	NOUN
ajst-25566	108	37	.	.	PUNCT
ajst-25566	109	1	step	step	NOUN
ajst-25566	109	2	2	2	NUM
ajst-25566	109	3	:	:	PUNCT
ajst-25566	109	4	calculate	calculate	VERB
ajst-25566	109	5	the	the	DET
ajst-25566	109	6	secant	secant	NOUN
ajst-25566	109	7	and	and	CCONJ
ajst-25566	109	8	tangent	tangent	NOUN
ajst-25566	109	9	after	after	ADP
ajst-25566	109	10	finding	find	VERB
ajst-25566	109	11	the	the	DET
ajst-25566	109	12	two	two	NUM
ajst-25566	109	13	nearest	near	ADJ
ajst-25566	109	14	intersection	intersection	NOUN
ajst-25566	109	15	points	point	NOUN
ajst-25566	109	16	1x	1x	NUM
ajst-25566	109	17	and	and	CCONJ
ajst-25566	109	18	2x	2x	NUM
ajst-25566	109	19	,	,	PUNCT
ajst-25566	109	20	we	we	PRON
ajst-25566	109	21	calculate	calculate	VERB
ajst-25566	109	22	the	the	DET
ajst-25566	109	23	secant	secant	NOUN
ajst-25566	109	24	between	between	ADP
ajst-25566	109	25	the	the	DET
ajst-25566	109	26	two	two	NUM
ajst-25566	109	27	points	point	NOUN
ajst-25566	109	28	and	and	CCONJ
ajst-25566	109	29	find	find	VERB
ajst-25566	109	30	the	the	DET
ajst-25566	109	31	tangent	tangent	NOUN
ajst-25566	109	32	parallel	parallel	NOUN
ajst-25566	109	33	to	to	ADP
ajst-25566	109	34	the	the	DET
ajst-25566	109	35	secant	secant	NOUN
ajst-25566	109	36	.	.	PUNCT
ajst-25566	110	1	here	here	ADV
ajst-25566	110	2	are	be	AUX
ajst-25566	110	3	the	the	DET
ajst-25566	110	4	specific	specific	ADJ
ajst-25566	110	5	steps	step	NOUN
ajst-25566	110	6	:	:	PUNCT
ajst-25566	110	7	(	(	PUNCT
ajst-25566	110	8	1	1	NUM
ajst-25566	110	9	)	)	PUNCT
ajst-25566	110	10	.	.	PUNCT
ajst-25566	111	1	compute	compute	VERB
ajst-25566	111	2	the	the	DET
ajst-25566	111	3	slope	slope	NOUN
ajst-25566	111	4	of	of	ADP
ajst-25566	111	5	the	the	DET
ajst-25566	111	6	secant	secant	ADJ
ajst-25566	111	7	line	line	NOUN
ajst-25566	111	8	:	:	PUNCT
ajst-25566	111	9	2	2	NUM
ajst-25566	111	10	1	1	NUM
ajst-25566	111	11	2	2	NUM
ajst-25566	111	12	1	1	NUM
ajst-25566	111	13	(	(	PUNCT
ajst-25566	111	14	)	)	PUNCT
ajst-25566	111	15	(	(	PUNCT
ajst-25566	111	16	)	)	PUNCT
ajst-25566	111	17	f	f	X
ajst-25566	112	1	x	x	PUNCT
ajst-25566	112	2	f	f	NOUN
ajst-25566	112	3	x	x	X
ajst-25566	112	4	m	m	VERB
ajst-25566	112	5	x	x	X
ajst-25566	112	6	x	x	PUNCT
ajst-25566	112	7			NOUN
ajst-25566	112	8			NUM
ajst-25566	112	9			PROPN
ajst-25566	112	10	.	.	PUNCT
ajst-25566	113	1	the	the	DET
ajst-25566	113	2	equation	equation	NOUN
ajst-25566	113	3	of	of	ADP
ajst-25566	113	4	the	the	DET
ajst-25566	113	5	secant	secant	ADJ
ajst-25566	113	6	line	line	NOUN
ajst-25566	113	7	is	be	AUX
ajst-25566	113	8	l	l	NOUN
ajst-25566	113	9	:	:	PUNCT
ajst-25566	113	10	1	1	NUM
ajst-25566	113	11	1	1	NUM
ajst-25566	113	12	(	(	PUNCT
ajst-25566	113	13	)	)	PUNCT
ajst-25566	113	14	(	(	PUNCT
ajst-25566	113	15	)	)	PUNCT
ajst-25566	114	1	y	y	PROPN
ajst-25566	114	2	m	m	VERB
ajst-25566	114	3	x	x	PUNCT
ajst-25566	114	4	x	x	X
ajst-25566	114	5	f	f	X
ajst-25566	114	6	x	x	PROPN
ajst-25566	114	7			PROPN
ajst-25566	114	8			X
ajst-25566	114	9	(	(	PUNCT
ajst-25566	114	10	2	2	NUM
ajst-25566	114	11	)	)	PUNCT
ajst-25566	114	12	.	.	PUNCT
ajst-25566	115	1	applying	apply	VERB
ajst-25566	115	2	the	the	DET
ajst-25566	115	3	mean	mean	ADJ
ajst-25566	115	4	value	value	NOUN
ajst-25566	115	5	theorem	theorem	VERB
ajst-25566	115	6	:	:	PUNCT
ajst-25566	115	7	according	accord	VERB
ajst-25566	115	8	to	to	ADP
ajst-25566	115	9	the	the	DET
ajst-25566	115	10	mean	mean	ADJ
ajst-25566	115	11	value	value	NOUN
ajst-25566	115	12	theorem	theorem	VERB
ajst-25566	115	13	,	,	PUNCT
ajst-25566	115	14	there	there	PRON
ajst-25566	115	15	exists	exist	VERB
ajst-25566	115	16	a	a	DET
ajst-25566	115	17	point	point	NOUN
ajst-25566	115	18	c	c	NOUN
ajst-25566	115	19	(	(	PUNCT
ajst-25566	115	20	1	1	NUM
ajst-25566	115	21	2	2	NUM
ajst-25566	115	22	(	(	PUNCT
ajst-25566	115	23	,	,	PUNCT
ajst-25566	115	24	)	)	PUNCT
ajst-25566	115	25	c	c	NOUN
ajst-25566	115	26	x	x	X
ajst-25566	115	27	x	x	PROPN
ajst-25566	115	28	)	)	PUNCT
ajst-25566	115	29	,	,	PUNCT
ajst-25566	115	30	such	such	ADJ
ajst-25566	115	31	that	that	SCONJ
ajst-25566	115	32	:	:	PUNCT
ajst-25566	115	33	'	'	PUNCT
ajst-25566	115	34	(	(	PUNCT
ajst-25566	115	35	)	)	PUNCT
ajst-25566	115	36	f	f	PROPN
ajst-25566	115	37	c	c	NOUN
ajst-25566	115	38	m	m	NOUN
ajst-25566	115	39	.	.	PUNCT
ajst-25566	116	1	similarly	similarly	ADV
ajst-25566	116	2	,	,	PUNCT
ajst-25566	116	3	for	for	ADP
ajst-25566	116	4	(	(	PUNCT
ajst-25566	116	5	)	)	PUNCT
ajst-25566	116	6	g	g	NOUN
ajst-25566	116	7	x	x	SYM
ajst-25566	116	8	,	,	PUNCT
ajst-25566	116	9	'	'	PUNCT
ajst-25566	116	10	(	(	PUNCT
ajst-25566	116	11	)	)	PUNCT
ajst-25566	116	12	g	g	NOUN
ajst-25566	116	13	d	d	NOUN
ajst-25566	116	14	m	m	NOUN
ajst-25566	116	15	,	,	PUNCT
ajst-25566	116	16	and	and	CCONJ
ajst-25566	116	17	we	we	PRON
ajst-25566	116	18	can	can	AUX
ajst-25566	116	19	find	find	VERB
ajst-25566	116	20	the	the	DET
ajst-25566	116	21	points	point	NOUN
ajst-25566	116	22	c	c	NOUN
ajst-25566	116	23	and	and	CCONJ
ajst-25566	116	24	d	d	X
ajst-25566	116	25	such	such	ADJ
ajst-25566	116	26	that	that	SCONJ
ajst-25566	116	27	the	the	DET
ajst-25566	116	28	derivative	derivative	NOUN
ajst-25566	116	29	is	be	AUX
ajst-25566	116	30	equal	equal	ADJ
ajst-25566	116	31	to	to	ADP
ajst-25566	116	32	the	the	DET
ajst-25566	116	33	slope	slope	NOUN
ajst-25566	116	34	of	of	ADP
ajst-25566	116	35	the	the	DET
ajst-25566	116	36	secant	secant	ADJ
ajst-25566	116	37	line	line	NOUN
ajst-25566	116	38	.	.	PUNCT
ajst-25566	117	1	example	example	NOUN
ajst-25566	117	2	:	:	PUNCT
ajst-25566	117	3	using	use	VERB
ajst-25566	117	4	the	the	DET
ajst-25566	117	5	above	above	ADJ
ajst-25566	117	6	example	example	NOUN
ajst-25566	117	7	,	,	PUNCT
ajst-25566	117	8	assuming	assume	VERB
ajst-25566	117	9	1x	1x	PRON
ajst-25566	117	10	and	and	CCONJ
ajst-25566	117	11	2x	2x	NUM
ajst-25566	117	12	are	be	AUX
ajst-25566	117	13	0.5	0.5	NUM
ajst-25566	117	14	and	and	CCONJ
ajst-25566	117	15	0.15	0.15	NUM
ajst-25566	117	16	,	,	PUNCT
ajst-25566	117	17	the	the	DET
ajst-25566	117	18	slope	slope	NOUN
ajst-25566	117	19	of	of	ADP
ajst-25566	117	20	the	the	DET
ajst-25566	117	21	secant	secant	ADJ
ajst-25566	117	22	line	line	NOUN
ajst-25566	117	23	is	be	AUX
ajst-25566	117	24	:	:	PUNCT
ajst-25566	117	25	2	2	NUM
ajst-25566	117	26	2(1.5	2(1.5	NUM
ajst-25566	117	27	)	)	PUNCT
ajst-25566	117	28	(	(	PUNCT
ajst-25566	117	29	0.5	0.5	NUM
ajst-25566	117	30	)	)	PUNCT
ajst-25566	117	31	2.25	2.25	NUM
ajst-25566	117	32	0.25	0.25	NUM
ajst-25566	117	33	2	2	NUM
ajst-25566	117	34	1.5	1.5	NUM
ajst-25566	117	35	0.5	0.5	NUM
ajst-25566	117	36	1	1	NUM
ajst-25566	117	37	m	m	PROPN
ajst-25566	117	38			PROPN
ajst-25566	117	39			VERB
ajst-25566	117	40			NUM
ajst-25566	117	41			NUM
ajst-25566	118	1			PROPN
ajst-25566	118	2			NOUN
ajst-25566	118	3	,	,	PUNCT
ajst-25566	118	4	  	  	SPACE
ajst-25566	118	5	the	the	DET
ajst-25566	118	6	equation	equation	NOUN
ajst-25566	118	7	of	of	ADP
ajst-25566	118	8	the	the	DET
ajst-25566	118	9	secant	secant	ADJ
ajst-25566	118	10	line	line	NOUN
ajst-25566	118	11	is	be	AUX
ajst-25566	118	12	l	l	NOUN
ajst-25566	118	13	:	:	PUNCT
ajst-25566	118	14	2	2	NUM
ajst-25566	118	15	(	(	PUNCT
ajst-25566	118	16	0.5	0.5	NUM
ajst-25566	118	17	)	)	PUNCT
ajst-25566	118	18	0.25y	0.25y	PROPN
ajst-25566	118	19	x	x	PUNCT
ajst-25566	119	1			PROPN
ajst-25566	119	2			ADV
ajst-25566	119	3	step	step	VERB
ajst-25566	119	4	3	3	NUM
ajst-25566	119	5	:	:	PUNCT
ajst-25566	119	6	determine	determine	VERB
ajst-25566	119	7	the	the	DET
ajst-25566	119	8	relative	relative	ADJ
ajst-25566	119	9	extreme	extreme	ADJ
ajst-25566	119	10	points	point	NOUN
ajst-25566	119	11	after	after	ADP
ajst-25566	119	12	finding	find	VERB
ajst-25566	119	13	the	the	DET
ajst-25566	119	14	points	point	NOUN
ajst-25566	119	15	under	under	ADP
ajst-25566	119	16	the	the	DET
ajst-25566	119	17	mean	mean	ADJ
ajst-25566	119	18	value	value	NOUN
ajst-25566	119	19	theorem	theorem	VERB
ajst-25566	119	20	,	,	PUNCT
ajst-25566	119	21	it	it	PRON
ajst-25566	119	22	is	be	AUX
ajst-25566	119	23	necessary	necessary	ADJ
ajst-25566	119	24	to	to	PART
ajst-25566	119	25	determine	determine	VERB
ajst-25566	119	26	the	the	DET
ajst-25566	119	27	relative	relative	ADJ
ajst-25566	119	28	extreme	extreme	ADJ
ajst-25566	119	29	points	point	NOUN
ajst-25566	119	30	of	of	ADP
ajst-25566	119	31	the	the	DET
ajst-25566	119	32	functions	function	NOUN
ajst-25566	119	33	(	(	PUNCT
ajst-25566	119	34	)	)	PUNCT
ajst-25566	119	35	f	f	NOUN
ajst-25566	119	36	x	x	X
ajst-25566	119	37	and	and	CCONJ
ajst-25566	119	38	(	(	PUNCT
ajst-25566	119	39	)	)	PUNCT
ajst-25566	119	40	g	g	NOUN
ajst-25566	119	41	x	x	X
ajst-25566	119	42	in	in	ADP
ajst-25566	119	43	the	the	DET
ajst-25566	119	44	intersection	intersection	NOUN
ajst-25566	119	45	interval	interval	NOUN
ajst-25566	119	46	,	,	PUNCT
ajst-25566	119	47	which	which	PRON
ajst-25566	119	48	may	may	AUX
ajst-25566	119	49	be	be	AUX
ajst-25566	119	50	the	the	DET
ajst-25566	119	51	candidate	candidate	NOUN
ajst-25566	119	52	points	point	NOUN
ajst-25566	119	53	of	of	ADP
ajst-25566	119	54	the	the	DET
ajst-25566	119	55	maximum	maximum	ADJ
ajst-25566	119	56	difference	difference	NOUN
ajst-25566	119	57	.	.	PUNCT
ajst-25566	120	1	here	here	ADV
ajst-25566	120	2	are	be	AUX
ajst-25566	120	3	the	the	DET
ajst-25566	120	4	specific	specific	ADJ
ajst-25566	120	5	steps	step	NOUN
ajst-25566	120	6	:	:	PUNCT
ajst-25566	120	7	(	(	PUNCT
ajst-25566	120	8	1	1	NUM
ajst-25566	120	9	)	)	PUNCT
ajst-25566	120	10	.	.	PUNCT
ajst-25566	121	1	solve	solve	VERB
ajst-25566	121	2	the	the	DET
ajst-25566	121	3	point	point	NOUN
ajst-25566	121	4	where	where	SCONJ
ajst-25566	121	5	the	the	DET
ajst-25566	121	6	derivative	derivative	NOUN
ajst-25566	121	7	is	be	AUX
ajst-25566	121	8	zero	zero	NUM
ajst-25566	121	9	:	:	PUNCT
ajst-25566	121	10	derivate	derivate	NOUN
ajst-25566	121	11	(	(	PUNCT
ajst-25566	121	12	)	)	PUNCT
ajst-25566	121	13	f	f	PROPN
ajst-25566	121	14	x	x	X
ajst-25566	121	15	and	and	CCONJ
ajst-25566	121	16	(	(	PUNCT
ajst-25566	121	17	)	)	PUNCT
ajst-25566	121	18	g	g	NOUN
ajst-25566	121	19	x	x	PUNCT
ajst-25566	121	20	respectively	respectively	ADV
ajst-25566	121	21	,	,	PUNCT
ajst-25566	121	22	and	and	CCONJ
ajst-25566	121	23	solve	solve	VERB
ajst-25566	121	24	the	the	DET
ajst-25566	121	25	equations	equation	NOUN
ajst-25566	121	26	'	'	PUNCT
ajst-25566	121	27	(	(	PUNCT
ajst-25566	121	28	)	)	PUNCT
ajst-25566	121	29	0f	0f	NOUN
ajst-25566	121	30	x	x	SYM
ajst-25566	122	1			PROPN
ajst-25566	122	2	and	and	CCONJ
ajst-25566	122	3	'	'	PUNCT
ajst-25566	122	4	(	(	PUNCT
ajst-25566	122	5	)	)	PUNCT
ajst-25566	122	6	0	0	NUM
ajst-25566	122	7	g	g	NOUN
ajst-25566	122	8	x	x	NOUN
ajst-25566	122	9			NOUN
ajst-25566	122	10	to	to	PART
ajst-25566	122	11	find	find	VERB
ajst-25566	122	12	the	the	DET
ajst-25566	122	13	extreme	extreme	ADJ
ajst-25566	122	14	point	point	NOUN
ajst-25566	122	15	.	.	PUNCT
ajst-25566	123	1	(	(	PUNCT
ajst-25566	123	2	2	2	NUM
ajst-25566	123	3	)	)	PUNCT
ajst-25566	123	4	.	.	PUNCT
ajst-25566	124	1	calculate	calculate	VERB
ajst-25566	124	2	the	the	DET
ajst-25566	124	3	difference	difference	NOUN
ajst-25566	124	4	in	in	ADP
ajst-25566	124	5	function	function	NOUN
ajst-25566	124	6	values	value	NOUN
ajst-25566	124	7	:	:	PUNCT
ajst-25566	124	8	calculate	calculate	VERB
ajst-25566	124	9	the	the	DET
ajst-25566	124	10	values	value	NOUN
ajst-25566	124	11	of	of	ADP
ajst-25566	124	12	the	the	DET
ajst-25566	124	13	two	two	NUM
ajst-25566	124	14	functions	function	NOUN
ajst-25566	124	15	at	at	ADP
ajst-25566	124	16	these	these	DET
ajst-25566	124	17	extremes	extreme	NOUN
ajst-25566	124	18	and	and	CCONJ
ajst-25566	124	19	intersections	intersection	NOUN
ajst-25566	124	20	and	and	CCONJ
ajst-25566	124	21	record	record	VERB
ajst-25566	124	22	the	the	DET
ajst-25566	124	23	difference	difference	NOUN
ajst-25566	124	24	.	.	PUNCT
ajst-25566	125	1	example	example	NOUN
ajst-25566	125	2	:	:	PUNCT
ajst-25566	125	3	after	after	ADP
ajst-25566	125	4	taking	take	VERB
ajst-25566	125	5	the	the	DET
ajst-25566	125	6	derivative	derivative	NOUN
ajst-25566	125	7	with	with	ADP
ajst-25566	125	8	respect	respect	NOUN
ajst-25566	125	9	to	to	ADP
ajst-25566	125	10	2	2	NUM
ajst-25566	125	11	(	(	PUNCT
ajst-25566	125	12	)	)	PUNCT
ajst-25566	125	13	f	f	NOUN
ajst-25566	125	14	x	x	X
ajst-25566	125	15	x	x	PROPN
ajst-25566	125	16	,	,	PUNCT
ajst-25566	125	17	the	the	DET
ajst-25566	125	18	result	result	NOUN
ajst-25566	125	19	is	be	AUX
ajst-25566	125	20	'	'	PUNCT
ajst-25566	125	21	(	(	PUNCT
ajst-25566	125	22	)	)	PUNCT
ajst-25566	125	23	2f	2f	NUM
ajst-25566	125	24	x	x	X
ajst-25566	126	1	x	x	X
ajst-25566	127	1	;	;	PUNCT
ajst-25566	127	2	after	after	ADP
ajst-25566	127	3	taking	take	VERB
ajst-25566	127	4	the	the	DET
ajst-25566	127	5	derivative	derivative	NOUN
ajst-25566	127	6	with	with	ADP
ajst-25566	127	7	respect	respect	NOUN
ajst-25566	127	8	to	to	ADP
ajst-25566	127	9	(	(	PUNCT
ajst-25566	127	10	)	)	PUNCT
ajst-25566	127	11	sin	sin	NOUN
ajst-25566	127	12	(	(	PUNCT
ajst-25566	127	13	)	)	PUNCT
ajst-25566	127	14	g	g	NOUN
ajst-25566	127	15	x	x	X
ajst-25566	127	16	x	x	PROPN
ajst-25566	127	17	,	,	PUNCT
ajst-25566	127	18	the	the	DET
ajst-25566	127	19	result	result	NOUN
ajst-25566	127	20	is	be	AUX
ajst-25566	127	21	'	'	PUNCT
ajst-25566	127	22	(	(	PUNCT
ajst-25566	127	23	)	)	PUNCT
ajst-25566	127	24	cos	cos	PROPN
ajst-25566	127	25	(	(	PUNCT
ajst-25566	127	26	)	)	PUNCT
ajst-25566	127	27	g	g	NOUN
ajst-25566	127	28	x	x	X
ajst-25566	127	29	x	x	PROPN
ajst-25566	127	30	.	.	PUNCT
ajst-25566	128	1	then	then	ADV
ajst-25566	128	2	,	,	PUNCT
ajst-25566	128	3	solving	solve	VERB
ajst-25566	128	4	the	the	DET
ajst-25566	128	5	equation	equation	NOUN
ajst-25566	128	6	'	'	PUNCT
ajst-25566	128	7	(	(	PUNCT
ajst-25566	128	8	)	)	PUNCT
ajst-25566	128	9	2	2	NUM
ajst-25566	128	10	0f	0f	NOUN
ajst-25566	128	11	x	x	X
ajst-25566	129	1	x	x	PROPN
ajst-25566	129	2			NUM
ajst-25566	129	3	,	,	PUNCT
ajst-25566	129	4	we	we	PRON
ajst-25566	129	5	get	get	VERB
ajst-25566	129	6	the	the	DET
ajst-25566	129	7	extreme	extreme	ADJ
ajst-25566	129	8	point	point	NOUN
ajst-25566	129	9	0x	0x	NOUN
ajst-25566	129	10			NOUN
ajst-25566	129	11	;	;	PUNCT
ajst-25566	129	12	similarly	similarly	ADV
ajst-25566	129	13	,	,	PUNCT
ajst-25566	129	14	'	'	PUNCT
ajst-25566	129	15	(	(	PUNCT
ajst-25566	129	16	)	)	PUNCT
ajst-25566	129	17	cos	cos	PROPN
ajst-25566	129	18	(	(	PUNCT
ajst-25566	129	19	)	)	PUNCT
ajst-25566	129	20	0	0	NUM
ajst-25566	129	21	g	g	NOUN
ajst-25566	129	22	x	x	X
ajst-25566	130	1	x	x	NOUN
ajst-25566	130	2			NUM
ajst-25566	130	3	,	,	PUNCT
ajst-25566	130	4	we	we	PRON
ajst-25566	130	5	get	get	VERB
ajst-25566	130	6	the	the	DET
ajst-25566	130	7	extreme	extreme	ADJ
ajst-25566	130	8	point	point	NOUN
ajst-25566	130	9	2	2	NUM
ajst-25566	130	10	x	x	SYM
ajst-25566	130	11			PROPN
ajst-25566	130	12			NOUN
ajst-25566	130	13	.	.	PUNCT
ajst-25566	131	1	step	step	NOUN
ajst-25566	131	2	4	4	NUM
ajst-25566	131	3	:	:	PUNCT
ajst-25566	131	4	compare	compare	VERB
ajst-25566	131	5	the	the	DET
ajst-25566	131	6	differences	difference	NOUN
ajst-25566	131	7	and	and	CCONJ
ajst-25566	131	8	find	find	VERB
ajst-25566	131	9	the	the	DET
ajst-25566	131	10	maximum	maximum	ADJ
ajst-25566	131	11	difference	difference	NOUN
ajst-25566	131	12	calculate	calculate	NOUN
ajst-25566	131	13	the	the	DET
ajst-25566	131	14	difference	difference	NOUN
ajst-25566	131	15	between	between	ADP
ajst-25566	131	16	(	(	PUNCT
ajst-25566	131	17	)	)	PUNCT
ajst-25566	131	18	f	f	PROPN
ajst-25566	131	19	x	x	X
ajst-25566	131	20	and	and	CCONJ
ajst-25566	131	21	(	(	PUNCT
ajst-25566	131	22	)	)	PUNCT
ajst-25566	131	23	g	g	NOUN
ajst-25566	131	24	x	x	X
ajst-25566	131	25	at	at	ADV
ajst-25566	131	26	all	all	PRON
ajst-25566	131	27	extreme	extreme	ADJ
ajst-25566	131	28	points	point	NOUN
ajst-25566	131	29	and	and	CCONJ
ajst-25566	131	30	intersections	intersection	NOUN
ajst-25566	131	31	.	.	PUNCT
ajst-25566	132	1	compare	compare	VERB
ajst-25566	132	2	these	these	DET
ajst-25566	132	3	differences	difference	NOUN
ajst-25566	132	4	to	to	PART
ajst-25566	132	5	find	find	VERB
ajst-25566	132	6	the	the	DET
ajst-25566	132	7	maximum	maximum	NOUN
ajst-25566	132	8	.	.	PUNCT
ajst-25566	133	1	here	here	ADV
ajst-25566	133	2	are	be	AUX
ajst-25566	133	3	the	the	DET
ajst-25566	133	4	specific	specific	ADJ
ajst-25566	133	5	steps	step	NOUN
ajst-25566	133	6	:	:	PUNCT
ajst-25566	133	7	(	(	PUNCT
ajst-25566	133	8	1	1	NUM
ajst-25566	133	9	)	)	PUNCT
ajst-25566	133	10	.	.	PUNCT
ajst-25566	134	1	calculate	calculate	VERB
ajst-25566	134	2	the	the	DET
ajst-25566	134	3	difference	difference	NOUN
ajst-25566	134	4	:	:	PUNCT
ajst-25566	134	5	calculate	calculate	VERB
ajst-25566	134	6	the	the	DET
ajst-25566	134	7	difference	difference	NOUN
ajst-25566	134	8	at	at	ADP
ajst-25566	134	9	each	each	DET
ajst-25566	134	10	extreme	extreme	ADJ
ajst-25566	134	11	point	point	NOUN
ajst-25566	134	12	and	and	CCONJ
ajst-25566	134	13	intersection	intersection	NOUN
ajst-25566	134	14	point	point	NOUN
ajst-25566	134	15	ix	ix	X
ajst-25566	134	16	:	:	PUNCT
ajst-25566	134	17			NOUN
ajst-25566	135	1			SYM
ajst-25566	135	2			NOUN
ajst-25566	135	3			SYM
ajst-25566	135	4			NOUN
ajst-25566	136	1	δ	δ	NOUN
ajst-25566	137	1	i	i	PRON
ajst-25566	137	2	i	i	PRON
ajst-25566	138	1	ix	ix	INTJ
ajst-25566	138	2	f	f	PROPN
ajst-25566	139	1	x	x	X
ajst-25566	139	2	g	g	PROPN
ajst-25566	139	3	x	x	PROPN
ajst-25566	139	4			PROPN
ajst-25566	139	5	(	(	PUNCT
ajst-25566	139	6	2	2	NUM
ajst-25566	139	7	)	)	PUNCT
ajst-25566	139	8	.	.	PUNCT
ajst-25566	140	1	find	find	VERB
ajst-25566	140	2	the	the	DET
ajst-25566	140	3	maximum	maximum	ADJ
ajst-25566	140	4	difference	difference	NOUN
ajst-25566	140	5	:	:	PUNCT
ajst-25566	140	6	compare	compare	VERB
ajst-25566	140	7	all	all	DET
ajst-25566	140	8	the	the	DET
ajst-25566	140	9	differences	difference	NOUN
ajst-25566	140	10	to	to	PART
ajst-25566	140	11	determine	determine	VERB
ajst-25566	140	12	the	the	DET
ajst-25566	140	13	maximum	maximum	ADJ
ajst-25566	140	14	difference	difference	NOUN
ajst-25566	140	15	and	and	CCONJ
ajst-25566	140	16	the	the	DET
ajst-25566	140	17	corresponding	corresponding	ADJ
ajst-25566	140	18	points	point	NOUN
ajst-25566	140	19	.	.	PUNCT
ajst-25566	141	1	for	for	ADP
ajst-25566	141	2	example	example	NOUN
ajst-25566	141	3	,	,	PUNCT
ajst-25566	141	4	compute	compute	VERB
ajst-25566	141	5	the	the	DET
ajst-25566	141	6	difference	difference	NOUN
ajst-25566	141	7	between	between	ADP
ajst-25566	141	8	2	2	NUM
ajst-25566	141	9	(	(	PUNCT
ajst-25566	141	10	)	)	PUNCT
ajst-25566	141	11	f	f	NOUN
ajst-25566	142	1	x	x	X
ajst-25566	142	2	x	x	PROPN
ajst-25566	142	3	and	and	CCONJ
ajst-25566	142	4	(	(	PUNCT
ajst-25566	142	5	)	)	PUNCT
ajst-25566	142	6	sin	sin	NOUN
ajst-25566	142	7	(	(	PUNCT
ajst-25566	142	8	)	)	PUNCT
ajst-25566	142	9	g	g	NOUN
ajst-25566	142	10	x	x	X
ajst-25566	142	11	x	x	PROPN
ajst-25566	143	1	at	at	ADP
ajst-25566	143	2	1	1	NUM
ajst-25566	143	3	0.5x	0.5x	NUM
ajst-25566	143	4			NOUN
ajst-25566	143	5	and	and	CCONJ
ajst-25566	143	6	2	2	NUM
ajst-25566	143	7	1.5x	1.5x	NUM
ajst-25566	143	8			NOUN
ajst-25566	143	9	,	,	PUNCT
ajst-25566	143	10	and	and	CCONJ
ajst-25566	143	11	the	the	DET
ajst-25566	143	12	extreme	extreme	ADJ
ajst-25566	143	13	points	point	NOUN
ajst-25566	143	14	0x	0x	NOUN
ajst-25566	143	15			NOUN
ajst-25566	143	16	and	and	CCONJ
ajst-25566	143	17	2	2	NUM
ajst-25566	143	18	x	x	SYM
ajst-25566	143	19			PROPN
ajst-25566	143	20			NOUN
ajst-25566	143	21	:	:	SYM
ajst-25566	143	22	1	1	NUM
ajst-25566	143	23	0.5	0.5	NUM
ajst-25566	143	24	:	:	PUNCT
ajst-25566	143	25	(	(	PUNCT
ajst-25566	143	26	0.5	0.5	NUM
ajst-25566	143	27	)	)	PUNCT
ajst-25566	143	28	0.25	0.25	NUM
ajst-25566	143	29	,	,	PUNCT
ajst-25566	143	30	(	(	PUNCT
ajst-25566	143	31	0.5	0.5	NUM
ajst-25566	143	32	)	)	PUNCT
ajst-25566	143	33	sin(0.5	sin(0.5	NUM
ajst-25566	143	34	)	)	PUNCT
ajst-25566	143	35	0.479x	0.479x	NOUN
ajst-25566	143	36	f	f	PROPN
ajst-25566	144	1	g	g	PROPN
ajst-25566	145	1			NUM
ajst-25566	145	2			NOUN
ajst-25566	145	3			PUNCT
ajst-25566	145	4	  	  	SPACE
ajst-25566	145	5	difference	difference	NOUN
ajst-25566	145	6	δ(0.5	δ(0.5	NOUN
ajst-25566	145	7	)	)	PUNCT
ajst-25566	145	8	|	|	ADV
ajst-25566	145	9	0.25	0.25	NUM
ajst-25566	145	10	0.479	0.479	NUM
ajst-25566	146	1	|	|	ADV
ajst-25566	146	2	0.229	0.229	PROPN
ajst-25566	146	3			NOUN
ajst-25566	146	4			NOUN
ajst-25566	146	5	。	。	NUM
ajst-25566	146	6	62	62	NUM
ajst-25566	146	7	2	2	NUM
ajst-25566	146	8	1.5	1.5	NUM
ajst-25566	146	9	:	:	PUNCT
ajst-25566	146	10	(	(	PUNCT
ajst-25566	146	11	1.5	1.5	NUM
ajst-25566	146	12	)	)	PUNCT
ajst-25566	146	13	2.25	2.25	NUM
ajst-25566	146	14	,	,	PUNCT
ajst-25566	146	15	(	(	PUNCT
ajst-25566	146	16	1.5	1.5	NUM
ajst-25566	146	17	)	)	PUNCT
ajst-25566	146	18	sin(1.5	sin(1.5	NUM
ajst-25566	146	19	)	)	PUNCT
ajst-25566	146	20	0.997x	0.997x	NUM
ajst-25566	147	1	f	f	NOUN
ajst-25566	147	2	g	g	PROPN
ajst-25566	148	1			NUM
ajst-25566	148	2			NOUN
ajst-25566	148	3			NOUN
ajst-25566	148	4	difference	difference	NOUN
ajst-25566	148	5	|	|	ADV
ajst-25566	148	6	2.25	2.25	NUM
ajst-25566	148	7	0.997	0.997	NUM
ajst-25566	148	8	|	|	ADV
ajst-25566	148	9	1	1	NUM
ajst-25566	148	10	.	.	NOUN
ajst-25566	148	11	3(1.5	3(1.5	NUM
ajst-25566	148	12	)	)	PUNCT
ajst-25566	148	13	25	25	NUM
ajst-25566	148	14			NOUN
ajst-25566	148	15			X
ajst-25566	148	16	.	.	PUNCT
ajst-25566	148	17	0	0	NUM
ajst-25566	148	18	:	:	PUNCT
ajst-25566	148	19	(	(	PUNCT
ajst-25566	148	20	0	0	NUM
ajst-25566	148	21	)	)	PUNCT
ajst-25566	148	22	0	0	NUM
ajst-25566	148	23	,	,	PUNCT
ajst-25566	148	24	(	(	PUNCT
ajst-25566	148	25	0	0	NUM
ajst-25566	148	26	)	)	PUNCT
ajst-25566	148	27	sin(0	sin(0	NOUN
ajst-25566	148	28	)	)	PUNCT
ajst-25566	149	1	0x	0x	NOUN
ajst-25566	149	2	f	f	PROPN
ajst-25566	149	3	g	g	PROPN
ajst-25566	150	1			NUM
ajst-25566	151	1			NUM
ajst-25566	151	2			NOUN
ajst-25566	151	3	,	,	PUNCT
ajst-25566	151	4	difference	difference	NOUN
ajst-25566	151	5	(	(	PUNCT
ajst-25566	151	6	0	0	NUM
ajst-25566	151	7	)	)	PUNCT
ajst-25566	151	8	0	0	NOUN
ajst-25566	152	1			PROPN
ajst-25566	152	2	.	.	PUNCT
ajst-25566	153	1	:	:	PUNCT
ajst-25566	153	2	(	(	PUNCT
ajst-25566	153	3	)	)	PUNCT
ajst-25566	153	4	2.47	2.47	NUM
ajst-25566	153	5	,	,	PUNCT
ajst-25566	153	6	(	(	PUNCT
ajst-25566	153	7	)	)	PUNCT
ajst-25566	153	8	1	1	NUM
ajst-25566	153	9	2	2	NUM
ajst-25566	153	10	2	2	NUM
ajst-25566	153	11	2	2	NUM
ajst-25566	153	12	x	x	SYM
ajst-25566	153	13	f	f	PROPN
ajst-25566	153	14	g	g	PROPN
ajst-25566	153	15			PROPN
ajst-25566	153	16			PROPN
ajst-25566	153	17			ADJ
ajst-25566	153	18			PROPN
ajst-25566	153	19			NOUN
ajst-25566	153	20			NOUN
ajst-25566	153	21	,	,	PUNCT
ajst-25566	153	22	difference	difference	NOUN
ajst-25566	153	23	|	|	ADV
ajst-25566	153	24	2.47	2.47	NUM
ajst-25566	153	25	1|	1|	NUM
ajst-25566	153	26	1.47	1.47	NUM
ajst-25566	153	27	(	(	PUNCT
ajst-25566	153	28	)	)	PUNCT
ajst-25566	153	29	2	2	NUM
ajst-25566	153	30			NOUN
ajst-25566	153	31			ADJ
ajst-25566	153	32			NOUN
ajst-25566	153	33	compare	compare	VERB
ajst-25566	153	34	the	the	DET
ajst-25566	153	35	above	above	ADJ
ajst-25566	153	36	differences	difference	NOUN
ajst-25566	153	37	and	and	CCONJ
ajst-25566	153	38	get	get	VERB
ajst-25566	153	39	the	the	DET
ajst-25566	153	40	maximum	maximum	ADJ
ajst-25566	153	41	difference	difference	NOUN
ajst-25566	153	42	:	:	PUNCT
ajst-25566	153	43	(	(	PUNCT
ajst-25566	153	44	)	)	PUNCT
ajst-25566	153	45	1.47	1.47	NUM
ajst-25566	153	46	2	2	NUM
ajst-25566	153	47			NOUN
ajst-25566	153	48			NOUN
ajst-25566	153	49			X
ajst-25566	153	50	.	.	PUNCT
ajst-25566	154	1	4	4	X
ajst-25566	154	2	.	.	NOUN
ajst-25566	154	3	practical	practical	ADJ
ajst-25566	154	4	application	application	NOUN
ajst-25566	154	5	the	the	DET
ajst-25566	154	6	method	method	NOUN
ajst-25566	154	7	proposed	propose	VERB
ajst-25566	154	8	in	in	ADP
ajst-25566	154	9	this	this	DET
ajst-25566	154	10	paper	paper	NOUN
ajst-25566	154	11	to	to	PART
ajst-25566	154	12	solve	solve	VERB
ajst-25566	154	13	the	the	DET
ajst-25566	154	14	maximum	maximum	ADJ
ajst-25566	154	15	difference	difference	NOUN
ajst-25566	154	16	between	between	ADP
ajst-25566	154	17	two	two	NUM
ajst-25566	154	18	functions	function	NOUN
ajst-25566	154	19	in	in	ADP
ajst-25566	154	20	their	their	PRON
ajst-25566	154	21	two	two	NUM
ajst-25566	154	22	closest	close	ADJ
ajst-25566	154	23	intersection	intersection	NOUN
ajst-25566	154	24	intervals	interval	NOUN
ajst-25566	154	25	is	be	AUX
ajst-25566	154	26	of	of	ADP
ajst-25566	154	27	great	great	ADJ
ajst-25566	154	28	theoretical	theoretical	ADJ
ajst-25566	154	29	importance	importance	NOUN
ajst-25566	154	30	and	and	CCONJ
ajst-25566	154	31	is	be	AUX
ajst-25566	154	32	widely	widely	ADV
ajst-25566	154	33	used	use	VERB
ajst-25566	154	34	in	in	ADP
ajst-25566	154	35	practice	practice	NOUN
ajst-25566	154	36	.	.	PUNCT
ajst-25566	155	1	the	the	DET
ajst-25566	155	2	following	follow	VERB
ajst-25566	155	3	are	be	AUX
ajst-25566	155	4	several	several	ADJ
ajst-25566	155	5	typical	typical	ADJ
ajst-25566	155	6	application	application	NOUN
ajst-25566	155	7	cases	case	NOUN
ajst-25566	155	8	:	:	PUNCT
ajst-25566	155	9	different	different	ADJ
ajst-25566	155	10	asset	asset	NOUN
ajst-25566	155	11	prices	price	NOUN
ajst-25566	155	12	(	(	PUNCT
ajst-25566	155	13	such	such	ADJ
ajst-25566	155	14	as	as	ADP
ajst-25566	155	15	stocks	stock	NOUN
ajst-25566	155	16	,	,	PUNCT
ajst-25566	155	17	bonds	bond	NOUN
ajst-25566	155	18	,	,	PUNCT
ajst-25566	155	19	futures	future	NOUN
ajst-25566	155	20	,	,	PUNCT
ajst-25566	155	21	etc	etc	X
ajst-25566	155	22	.	.	X
ajst-25566	155	23	)	)	PUNCT
ajst-25566	155	24	often	often	ADV
ajst-25566	155	25	show	show	VERB
ajst-25566	155	26	different	different	ADJ
ajst-25566	155	27	fluctuation	fluctuation	NOUN
ajst-25566	155	28	patterns	pattern	NOUN
ajst-25566	155	29	in	in	ADP
ajst-25566	155	30	the	the	DET
ajst-25566	155	31	financial	financial	ADJ
ajst-25566	155	32	market	market	NOUN
ajst-25566	155	33	.	.	PUNCT
ajst-25566	156	1	by	by	ADP
ajst-25566	156	2	analyzing	analyze	VERB
ajst-25566	156	3	the	the	DET
ajst-25566	156	4	price	price	NOUN
ajst-25566	156	5	fluctuation	fluctuation	NOUN
ajst-25566	156	6	of	of	ADP
ajst-25566	156	7	these	these	DET
ajst-25566	156	8	assets	asset	NOUN
ajst-25566	156	9	,	,	PUNCT
ajst-25566	156	10	we	we	PRON
ajst-25566	156	11	can	can	AUX
ajst-25566	156	12	help	help	VERB
ajst-25566	156	13	investors	investor	NOUN
ajst-25566	156	14	make	make	VERB
ajst-25566	156	15	more	more	ADJ
ajst-25566	156	16	reasonable	reasonable	ADJ
ajst-25566	156	17	investment	investment	NOUN
ajst-25566	156	18	strategies	strategy	NOUN
ajst-25566	156	19	.	.	PUNCT
ajst-25566	157	1	the	the	DET
ajst-25566	157	2	method	method	NOUN
ajst-25566	157	3	proposed	propose	VERB
ajst-25566	157	4	in	in	ADP
ajst-25566	157	5	this	this	DET
ajst-25566	157	6	paper	paper	NOUN
ajst-25566	157	7	allows	allow	VERB
ajst-25566	157	8	us	we	PRON
ajst-25566	157	9	to	to	PART
ajst-25566	157	10	compare	compare	VERB
ajst-25566	157	11	the	the	DET
ajst-25566	157	12	maximum	maximum	ADJ
ajst-25566	157	13	difference	difference	NOUN
ajst-25566	157	14	between	between	ADP
ajst-25566	157	15	two	two	NUM
ajst-25566	157	16	asset	asset	NOUN
ajst-25566	157	17	prices	price	NOUN
ajst-25566	157	18	within	within	ADP
ajst-25566	157	19	a	a	DET
ajst-25566	157	20	certain	certain	ADJ
ajst-25566	157	21	period	period	NOUN
ajst-25566	157	22	,	,	PUNCT
ajst-25566	157	23	thus	thus	ADV
ajst-25566	157	24	identifying	identify	VERB
ajst-25566	157	25	extreme	extreme	ADJ
ajst-25566	157	26	market	market	NOUN
ajst-25566	157	27	fluctuations	fluctuation	NOUN
ajst-25566	157	28	.	.	PUNCT
ajst-25566	158	1	for	for	ADP
ajst-25566	158	2	the	the	DET
ajst-25566	158	3	engineering	engineering	NOUN
ajst-25566	158	4	field	field	NOUN
ajst-25566	158	5	,	,	PUNCT
ajst-25566	158	6	accuracy	accuracy	NOUN
ajst-25566	158	7	and	and	CCONJ
ajst-25566	158	8	error	error	NOUN
ajst-25566	158	9	analysis	analysis	NOUN
ajst-25566	158	10	are	be	AUX
ajst-25566	158	11	very	very	ADV
ajst-25566	158	12	important	important	ADJ
ajst-25566	158	13	.	.	PUNCT
ajst-25566	159	1	the	the	DET
ajst-25566	159	2	accuracy	accuracy	NOUN
ajst-25566	159	3	and	and	CCONJ
ajst-25566	159	4	stability	stability	NOUN
ajst-25566	159	5	of	of	ADP
ajst-25566	159	6	a	a	DET
ajst-25566	159	7	measurement	measurement	NOUN
ajst-25566	159	8	method	method	NOUN
ajst-25566	159	9	can	can	AUX
ajst-25566	159	10	be	be	AUX
ajst-25566	159	11	assessed	assess	VERB
ajst-25566	159	12	by	by	ADP
ajst-25566	159	13	comparing	compare	VERB
ajst-25566	159	14	the	the	DET
ajst-25566	159	15	maximum	maximum	ADJ
ajst-25566	159	16	difference	difference	NOUN
ajst-25566	159	17	in	in	ADP
ajst-25566	159	18	a	a	DET
ajst-25566	159	19	specific	specific	ADJ
ajst-25566	159	20	interval	interval	NOUN
ajst-25566	159	21	for	for	ADP
ajst-25566	159	22	data	datum	NOUN
ajst-25566	159	23	obtained	obtain	VERB
ajst-25566	159	24	from	from	ADP
ajst-25566	159	25	two	two	NUM
ajst-25566	159	26	different	different	ADJ
ajst-25566	159	27	measurement	measurement	NOUN
ajst-25566	159	28	methods	method	NOUN
ajst-25566	159	29	.	.	PUNCT
ajst-25566	160	1	the	the	DET
ajst-25566	160	2	method	method	NOUN
ajst-25566	160	3	proposed	propose	VERB
ajst-25566	160	4	in	in	ADP
ajst-25566	160	5	this	this	DET
ajst-25566	160	6	paper	paper	NOUN
ajst-25566	160	7	can	can	AUX
ajst-25566	160	8	be	be	AUX
ajst-25566	160	9	used	use	VERB
ajst-25566	160	10	to	to	PART
ajst-25566	160	11	determine	determine	VERB
ajst-25566	160	12	the	the	DET
ajst-25566	160	13	maximum	maximum	ADJ
ajst-25566	160	14	error	error	NOUN
ajst-25566	160	15	of	of	ADP
ajst-25566	160	16	two	two	NUM
ajst-25566	160	17	measurement	measurement	NOUN
ajst-25566	160	18	results	result	NOUN
ajst-25566	160	19	in	in	ADP
ajst-25566	160	20	the	the	DET
ajst-25566	160	21	intersection	intersection	NOUN
ajst-25566	160	22	interval	interval	NOUN
ajst-25566	160	23	,	,	PUNCT
ajst-25566	160	24	thus	thus	ADV
ajst-25566	160	25	evaluating	evaluate	VERB
ajst-25566	160	26	the	the	DET
ajst-25566	160	27	reliability	reliability	NOUN
ajst-25566	160	28	of	of	ADP
ajst-25566	160	29	the	the	DET
ajst-25566	160	30	measurement	measurement	NOUN
ajst-25566	160	31	method	method	NOUN
ajst-25566	160	32	.	.	PUNCT
ajst-25566	161	1	for	for	ADP
ajst-25566	161	2	medical	medical	ADJ
ajst-25566	161	3	research	research	NOUN
ajst-25566	161	4	,	,	PUNCT
ajst-25566	161	5	it	it	PRON
ajst-25566	161	6	is	be	AUX
ajst-25566	161	7	a	a	DET
ajst-25566	161	8	common	common	ADJ
ajst-25566	161	9	demand	demand	NOUN
ajst-25566	161	10	to	to	PART
ajst-25566	161	11	compare	compare	VERB
ajst-25566	161	12	the	the	DET
ajst-25566	161	13	efficacy	efficacy	NOUN
ajst-25566	161	14	of	of	ADP
ajst-25566	161	15	treatment	treatment	NOUN
ajst-25566	161	16	methods	method	NOUN
ajst-25566	161	17	.	.	PUNCT
ajst-25566	162	1	by	by	ADP
ajst-25566	162	2	analyzing	analyze	VERB
ajst-25566	162	3	the	the	DET
ajst-25566	162	4	effect	effect	NOUN
ajst-25566	162	5	curves	curve	NOUN
ajst-25566	162	6	of	of	ADP
ajst-25566	162	7	different	different	ADJ
ajst-25566	162	8	treatment	treatment	NOUN
ajst-25566	162	9	methods	method	NOUN
ajst-25566	162	10	,	,	PUNCT
ajst-25566	162	11	we	we	PRON
ajst-25566	162	12	can	can	AUX
ajst-25566	162	13	find	find	VERB
ajst-25566	162	14	the	the	DET
ajst-25566	162	15	maximum	maximum	ADJ
ajst-25566	162	16	difference	difference	NOUN
ajst-25566	162	17	between	between	ADP
ajst-25566	162	18	the	the	DET
ajst-25566	162	19	two	two	NUM
ajst-25566	162	20	treatment	treatment	NOUN
ajst-25566	162	21	methods	method	NOUN
ajst-25566	162	22	in	in	ADP
ajst-25566	162	23	a	a	DET
ajst-25566	162	24	specific	specific	ADJ
ajst-25566	162	25	period	period	NOUN
ajst-25566	162	26	and	and	CCONJ
ajst-25566	162	27	help	help	VERB
ajst-25566	162	28	doctors	doctor	NOUN
ajst-25566	162	29	choose	choose	VERB
ajst-25566	162	30	the	the	DET
ajst-25566	162	31	most	most	ADV
ajst-25566	162	32	effective	effective	ADJ
ajst-25566	162	33	treatment	treatment	NOUN
ajst-25566	162	34	scheme	scheme	NOUN
ajst-25566	162	35	.	.	PUNCT
ajst-25566	163	1	when	when	SCONJ
ajst-25566	163	2	comparing	compare	VERB
ajst-25566	163	3	the	the	DET
ajst-25566	163	4	maximum	maximum	ADJ
ajst-25566	163	5	difference	difference	NOUN
ajst-25566	163	6	between	between	ADP
ajst-25566	163	7	the	the	DET
ajst-25566	163	8	two	two	NUM
ajst-25566	163	9	curative	curative	ADJ
ajst-25566	163	10	effect	effect	NOUN
ajst-25566	163	11	curves	curve	NOUN
ajst-25566	163	12	,	,	PUNCT
ajst-25566	163	13	we	we	PRON
ajst-25566	163	14	can	can	AUX
ajst-25566	163	15	use	use	VERB
ajst-25566	163	16	the	the	DET
ajst-25566	163	17	method	method	NOUN
ajst-25566	163	18	in	in	ADP
ajst-25566	163	19	this	this	DET
ajst-25566	163	20	paper	paper	NOUN
ajst-25566	163	21	to	to	PART
ajst-25566	163	22	evaluate	evaluate	VERB
ajst-25566	163	23	the	the	DET
ajst-25566	163	24	difference	difference	NOUN
ajst-25566	163	25	in	in	ADP
ajst-25566	163	26	therapeutic	therapeutic	ADJ
ajst-25566	163	27	effect	effect	NOUN
ajst-25566	163	28	.	.	PUNCT
ajst-25566	164	1	for	for	ADP
ajst-25566	164	2	environmental	environmental	ADJ
ajst-25566	164	3	science	science	NOUN
ajst-25566	164	4	research	research	NOUN
ajst-25566	164	5	,	,	PUNCT
ajst-25566	164	6	changes	change	NOUN
ajst-25566	164	7	in	in	ADP
ajst-25566	164	8	the	the	DET
ajst-25566	164	9	concentration	concentration	NOUN
ajst-25566	164	10	of	of	ADP
ajst-25566	164	11	pollutants	pollutant	NOUN
ajst-25566	164	12	can	can	AUX
ajst-25566	164	13	reflect	reflect	VERB
ajst-25566	164	14	changes	change	NOUN
ajst-25566	164	15	in	in	ADP
ajst-25566	164	16	the	the	DET
ajst-25566	164	17	quality	quality	NOUN
ajst-25566	164	18	of	of	ADP
ajst-25566	164	19	the	the	DET
ajst-25566	164	20	environment	environment	NOUN
ajst-25566	164	21	.	.	PUNCT
ajst-25566	165	1	by	by	ADP
ajst-25566	165	2	comparing	compare	VERB
ajst-25566	165	3	the	the	DET
ajst-25566	165	4	maximum	maximum	ADJ
ajst-25566	165	5	concentration	concentration	NOUN
ajst-25566	165	6	differences	difference	NOUN
ajst-25566	165	7	of	of	ADP
ajst-25566	165	8	different	different	ADJ
ajst-25566	165	9	pollutants	pollutant	NOUN
ajst-25566	165	10	over	over	ADP
ajst-25566	165	11	some	some	DET
ajst-25566	165	12	time	time	NOUN
ajst-25566	165	13	,	,	PUNCT
ajst-25566	165	14	the	the	DET
ajst-25566	165	15	main	main	ADJ
ajst-25566	165	16	causes	cause	NOUN
ajst-25566	165	17	of	of	ADP
ajst-25566	165	18	environmental	environmental	ADJ
ajst-25566	165	19	pollution	pollution	NOUN
ajst-25566	165	20	can	can	AUX
ajst-25566	165	21	be	be	AUX
ajst-25566	165	22	identified	identify	VERB
ajst-25566	165	23	.	.	PUNCT
ajst-25566	166	1	when	when	SCONJ
ajst-25566	166	2	comparing	compare	VERB
ajst-25566	166	3	the	the	DET
ajst-25566	166	4	maximum	maximum	ADJ
ajst-25566	166	5	difference	difference	NOUN
ajst-25566	166	6	between	between	ADP
ajst-25566	166	7	two	two	NUM
ajst-25566	166	8	pollutant	pollutant	ADJ
ajst-25566	166	9	concentration	concentration	NOUN
ajst-25566	166	10	curves	curve	NOUN
ajst-25566	166	11	,	,	PUNCT
ajst-25566	166	12	the	the	DET
ajst-25566	166	13	method	method	NOUN
ajst-25566	166	14	in	in	ADP
ajst-25566	166	15	this	this	DET
ajst-25566	166	16	paper	paper	NOUN
ajst-25566	166	17	can	can	AUX
ajst-25566	166	18	be	be	AUX
ajst-25566	166	19	used	use	VERB
ajst-25566	166	20	to	to	PART
ajst-25566	166	21	evaluate	evaluate	VERB
ajst-25566	166	22	the	the	DET
ajst-25566	166	23	impact	impact	NOUN
ajst-25566	166	24	of	of	ADP
ajst-25566	166	25	pollutants	pollutant	NOUN
ajst-25566	166	26	on	on	ADP
ajst-25566	166	27	the	the	DET
ajst-25566	166	28	environment	environment	NOUN
ajst-25566	166	29	.	.	PUNCT
ajst-25566	167	1	5	5	X
ajst-25566	167	2	.	.	X
ajst-25566	167	3	conclusion	conclusion	NOUN
ajst-25566	167	4	a	a	DET
ajst-25566	167	5	new	new	ADJ
ajst-25566	167	6	method	method	NOUN
ajst-25566	167	7	based	base	VERB
ajst-25566	167	8	on	on	ADP
ajst-25566	167	9	the	the	DET
ajst-25566	167	10	mean	mean	ADJ
ajst-25566	167	11	value	value	NOUN
ajst-25566	167	12	theorem	theorem	NOUN
ajst-25566	167	13	is	be	AUX
ajst-25566	167	14	proposed	propose	VERB
ajst-25566	167	15	in	in	ADP
ajst-25566	167	16	this	this	DET
ajst-25566	167	17	paper	paper	NOUN
ajst-25566	167	18	to	to	PART
ajst-25566	167	19	solve	solve	VERB
ajst-25566	167	20	the	the	DET
ajst-25566	167	21	maximum	maximum	ADJ
ajst-25566	167	22	difference	difference	NOUN
ajst-25566	167	23	between	between	ADP
ajst-25566	167	24	two	two	NUM
ajst-25566	167	25	functions	function	NOUN
ajst-25566	167	26	in	in	ADP
ajst-25566	167	27	the	the	DET
ajst-25566	167	28	interval	interval	NOUN
ajst-25566	167	29	closest	close	ADJ
ajst-25566	167	30	to	to	ADP
ajst-25566	167	31	the	the	DET
ajst-25566	167	32	intersection	intersection	NOUN
ajst-25566	167	33	point	point	NOUN
ajst-25566	167	34	.	.	PUNCT
ajst-25566	168	1	through	through	ADP
ajst-25566	168	2	detailed	detailed	ADJ
ajst-25566	168	3	theoretical	theoretical	ADJ
ajst-25566	168	4	analysis	analysis	NOUN
ajst-25566	168	5	and	and	CCONJ
ajst-25566	168	6	practical	practical	ADJ
ajst-25566	168	7	example	example	NOUN
ajst-25566	168	8	checks	check	NOUN
ajst-25566	168	9	,	,	PUNCT
ajst-25566	168	10	we	we	PRON
ajst-25566	168	11	prove	prove	VERB
ajst-25566	168	12	the	the	DET
ajst-25566	168	13	effectiveness	effectiveness	NOUN
ajst-25566	168	14	and	and	CCONJ
ajst-25566	168	15	practicality	practicality	NOUN
ajst-25566	168	16	of	of	ADP
ajst-25566	168	17	our	our	PRON
ajst-25566	168	18	method	method	NOUN
ajst-25566	168	19	.	.	PUNCT
ajst-25566	169	1	future	future	ADJ
ajst-25566	169	2	research	research	NOUN
ajst-25566	169	3	can	can	AUX
ajst-25566	169	4	further	far	ADV
ajst-25566	169	5	optimize	optimize	VERB
ajst-25566	169	6	our	our	PRON
ajst-25566	169	7	method	method	NOUN
ajst-25566	169	8	and	and	CCONJ
ajst-25566	169	9	explore	explore	VERB
ajst-25566	169	10	its	its	PRON
ajst-25566	169	11	application	application	NOUN
ajst-25566	169	12	to	to	ADP
ajst-25566	169	13	more	more	ADV
ajst-25566	169	14	practical	practical	ADJ
ajst-25566	169	15	problems	problem	NOUN
ajst-25566	169	16	.	.	PUNCT
ajst-25566	170	1	acknowledgments	acknowledgment	NOUN
ajst-25566	170	2	thank	thank	VERB
ajst-25566	170	3	mr	mr	PROPN
ajst-25566	170	4	.	.	PROPN
ajst-25566	170	5	zhang	zhang	PROPN
ajst-25566	170	6	and	and	CCONJ
ajst-25566	170	7	mr	mr	PROPN
ajst-25566	170	8	.	.	PROPN
ajst-25566	170	9	wang	wang	PROPN
ajst-25566	170	10	for	for	ADP
ajst-25566	170	11	their	their	PRON
ajst-25566	170	12	guidance	guidance	NOUN
ajst-25566	170	13	and	and	CCONJ
ajst-25566	170	14	help	help	NOUN
ajst-25566	170	15	in	in	ADP
ajst-25566	170	16	the	the	DET
ajst-25566	170	17	research	research	NOUN
ajst-25566	170	18	process	process	NOUN
ajst-25566	170	19	of	of	ADP
ajst-25566	170	20	this	this	DET
ajst-25566	170	21	paper	paper	NOUN
ajst-25566	170	22	.	.	PUNCT
ajst-25566	171	1	references	reference	NOUN
ajst-25566	171	2	[	[	X
ajst-25566	171	3	1	1	NUM
ajst-25566	171	4	]	]	PUNCT
ajst-25566	171	5	thomas	thomas	PROPN
ajst-25566	171	6	hyun	hyun	PROPN
ajst-25566	171	7	,	,	PUNCT
ajst-25566	171	8	ap	ap	PROPN
ajst-25566	171	9	calculus	calculus	PROPN
ajst-25566	171	10	ab	ab	PROPN
ajst-25566	171	11	and	and	CCONJ
ajst-25566	171	12	bc	bc	PROPN
ajst-25566	171	13	.	.	PUNCT
ajst-25566	172	1	[	[	X
ajst-25566	172	2	2	2	NUM
ajst-25566	172	3	]	]	PUNCT
ajst-25566	172	4	burden	burden	NOUN
ajst-25566	172	5	r	r	NOUN
ajst-25566	172	6	l	l	NOUN
ajst-25566	172	7	,	,	PUNCT
ajst-25566	172	8	faires	fair	VERB
ajst-25566	172	9	j	j	PROPN
ajst-25566	172	10	d.	d.	PROPN
ajst-25566	172	11	numerical	numerical	PROPN
ajst-25566	172	12	analysis	analysis	PROPN
ajst-25566	172	13	.	.	PUNCT
ajst-25566	173	1	brooks	brooks	PROPN
ajst-25566	173	2	/	/	SYM
ajst-25566	173	3	cole	cole	PROPN
ajst-25566	173	4	,	,	PUNCT
ajst-25566	173	5	cengagelearning[j	cengagelearning[j	NOUN
ajst-25566	173	6	]	]	PUNCT
ajst-25566	173	7	.	.	PUNCT
ajst-25566	174	1	boston	boston	PROPN
ajst-25566	174	2	,	,	PUNCT
ajst-25566	174	3	usa	usa	PROPN
ajst-25566	174	4	,	,	PUNCT
ajst-25566	174	5	2011	2011	NUM
ajst-25566	174	6	.	.	PUNCT
ajst-25566	175	1	[	[	X
ajst-25566	175	2	3	3	NUM
ajst-25566	175	3	]	]	X
ajst-25566	175	4	press	press	NOUN
ajst-25566	175	5	,	,	PUNCT
ajst-25566	175	6	w.	w.	PROPN
ajst-25566	175	7	h.	h.	PROPN
ajst-25566	175	8	,	,	PUNCT
ajst-25566	175	9	teukolsky	teukolsky	PROPN
ajst-25566	175	10	,	,	PUNCT
ajst-25566	175	11	s.	s.	PROPN
ajst-25566	175	12	a.	a.	PROPN
ajst-25566	175	13	,	,	PUNCT
ajst-25566	175	14	vetterling	vetterle	VERB
ajst-25566	175	15	,	,	PUNCT
ajst-25566	175	16	w.	w.	PROPN
ajst-25566	175	17	t.	t.	PROPN
ajst-25566	175	18	,	,	PUNCT
ajst-25566	175	19	&	&	CCONJ
ajst-25566	175	20	flannery	flannery	PROPN
ajst-25566	175	21	,	,	PUNCT
ajst-25566	175	22	b.	b.	PROPN
ajst-25566	175	23	p.	p.	PROPN
ajst-25566	175	24	(	(	PUNCT
ajst-25566	175	25	2007	2007	NUM
ajst-25566	175	26	)	)	PUNCT
ajst-25566	175	27	.	.	PUNCT
ajst-25566	176	1	numerical	numerical	ADJ
ajst-25566	176	2	recipes	recipe	NOUN
ajst-25566	176	3	:	:	PUNCT
ajst-25566	176	4	the	the	DET
ajst-25566	176	5	art	art	NOUN
ajst-25566	176	6	of	of	ADP
ajst-25566	176	7	scientific	scientific	ADJ
ajst-25566	176	8	computing	computing	NOUN
ajst-25566	176	9	.	.	PUNCT
ajst-25566	177	1	cambridge	cambridge	PROPN
ajst-25566	177	2	university	university	PROPN
ajst-25566	177	3	press	press	NOUN
ajst-25566	177	4	.	.	PUNCT
ajst-25566	178	1	[	[	X
ajst-25566	178	2	4	4	NUM
ajst-25566	178	3	]	]	X
ajst-25566	178	4	nocedal	nocedal	NOUN
ajst-25566	178	5	,	,	PUNCT
ajst-25566	178	6	j.	j.	PROPN
ajst-25566	178	7	,	,	PUNCT
ajst-25566	178	8	&	&	CCONJ
ajst-25566	178	9	wright	wright	PROPN
ajst-25566	178	10	,	,	PUNCT
ajst-25566	178	11	s.	s.	PROPN
ajst-25566	178	12	j.	j.	PROPN
ajst-25566	178	13	(	(	PUNCT
ajst-25566	178	14	2006	2006	NUM
ajst-25566	178	15	)	)	PUNCT
ajst-25566	178	16	.	.	PUNCT
ajst-25566	179	1	numerical	numerical	PROPN
ajst-25566	179	2	optimization	optimization	PROPN
ajst-25566	179	3	.	.	PUNCT
ajst-25566	180	1	springer	springer	NOUN
ajst-25566	180	2	.	.	PUNCT
ajst-25566	181	1	[	[	X
ajst-25566	181	2	5	5	NUM
ajst-25566	181	3	]	]	X
ajst-25566	181	4	goldberg	goldberg	PROPN
ajst-25566	181	5	,	,	PUNCT
ajst-25566	181	6	d.	d.	PROPN
ajst-25566	181	7	e.	e.	PROPN
ajst-25566	181	8	(	(	PUNCT
ajst-25566	181	9	1989	1989	NUM
ajst-25566	181	10	)	)	PUNCT
ajst-25566	181	11	.	.	PUNCT
ajst-25566	182	1	genetic	genetic	ADJ
ajst-25566	182	2	algorithms	algorithm	NOUN
ajst-25566	182	3	in	in	ADP
ajst-25566	182	4	search	search	NOUN
ajst-25566	182	5	,	,	PUNCT
ajst-25566	182	6	optimization	optimization	NOUN
ajst-25566	182	7	,	,	PUNCT
ajst-25566	182	8	and	and	CCONJ
ajst-25566	182	9	machine	machine	NOUN
ajst-25566	182	10	learning	learning	NOUN
ajst-25566	182	11	.	.	PUNCT
ajst-25566	183	1	addison	addison	PROPN
ajst-25566	183	2	-	-	PUNCT
ajst-25566	183	3	wesley	wesley	PROPN
ajst-25566	183	4	.	.	PUNCT
ajst-25566	184	1	[	[	X
ajst-25566	184	2	6	6	NUM
ajst-25566	184	3	]	]	X
ajst-25566	184	4	smith	smith	PROPN
ajst-25566	184	5	,	,	PUNCT
ajst-25566	184	6	t.	t.	PROPN
ajst-25566	184	7	j.	j.	PROPN
ajst-25566	184	8	,	,	PUNCT
ajst-25566	184	9	et	et	PROPN
ajst-25566	184	10	al	al	PROPN
ajst-25566	184	11	.	.	PUNCT
ajst-25566	184	12	(	(	PUNCT
ajst-25566	184	13	2015	2015	NUM
ajst-25566	184	14	)	)	PUNCT
ajst-25566	184	15	.	.	PUNCT
ajst-25566	185	1	data	datum	NOUN
ajst-25566	185	2	analysis	analysis	NOUN
ajst-25566	185	3	in	in	ADP
ajst-25566	185	4	medical	medical	ADJ
ajst-25566	185	5	research	research	NOUN
ajst-25566	185	6	.	.	PUNCT
ajst-25566	186	1	oxford	oxford	PROPN
ajst-25566	186	2	university	university	PROPN
ajst-25566	186	3	press	press	NOUN
ajst-25566	186	4	.	.	PUNCT
ajst-25566	187	1	[	[	X
ajst-25566	187	2	7	7	NUM
ajst-25566	187	3	]	]	SYM
ajst-25566	187	4	jones	jones	PROPN
ajst-25566	187	5	,	,	PUNCT
ajst-25566	187	6	a.	a.	NOUN
ajst-25566	187	7	m.	m.	NOUN
ajst-25566	187	8	,	,	PUNCT
ajst-25566	187	9	et	et	PROPN
ajst-25566	187	10	al	al	PROPN
ajst-25566	187	11	.	.	PUNCT
ajst-25566	188	1	(	(	PUNCT
ajst-25566	188	2	2018	2018	NUM
ajst-25566	188	3	)	)	PUNCT
ajst-25566	188	4	.	.	PUNCT
ajst-25566	189	1	application	application	NOUN
ajst-25566	189	2	of	of	ADP
ajst-25566	189	3	function	function	NOUN
ajst-25566	189	4	difference	difference	NOUN
ajst-25566	189	5	in	in	ADP
ajst-25566	189	6	environmental	environmental	ADJ
ajst-25566	189	7	pollutant	pollutant	ADJ
ajst-25566	189	8	concentration	concentration	NOUN
ajst-25566	189	9	analysis	analysis	NOUN
ajst-25566	189	10	.	.	PUNCT
ajst-25566	190	1	environmental	environmental	ADJ
ajst-25566	190	2	science	science	PROPN
ajst-25566	190	3	&	&	CCONJ
ajst-25566	190	4	technology	technology	NOUN
ajst-25566	190	5	.	.	PUNCT