id	sid	tid	token	lemma	pos
american_scientific_journal-3982	1	1	240	240	NUM
american_scientific_journal-3982	1	2	american	american	ADJ
american_scientific_journal-3982	1	3	scientific	scientific	ADJ
american_scientific_journal-3982	1	4	research	research	NOUN
american_scientific_journal-3982	1	5	journal	journal	NOUN
american_scientific_journal-3982	1	6	for	for	ADP
american_scientific_journal-3982	1	7	engineering	engineering	NOUN
american_scientific_journal-3982	1	8	,	,	PUNCT
american_scientific_journal-3982	1	9	technology	technology	NOUN
american_scientific_journal-3982	1	10	,	,	PUNCT
american_scientific_journal-3982	1	11	and	and	CCONJ
american_scientific_journal-3982	1	12	sciences	science	NOUN
american_scientific_journal-3982	1	13	(	(	PUNCT
american_scientific_journal-3982	1	14	asrjets	asrjet	NOUN
american_scientific_journal-3982	1	15	)	)	PUNCT
american_scientific_journal-3982	1	16	issn	issn	PROPN
american_scientific_journal-3982	1	17	(	(	PUNCT
american_scientific_journal-3982	1	18	print	print	NOUN
american_scientific_journal-3982	1	19	)	)	PUNCT
american_scientific_journal-3982	1	20	2313	2313	NUM
american_scientific_journal-3982	1	21	-	-	SYM
american_scientific_journal-3982	1	22	4410	4410	NUM
american_scientific_journal-3982	1	23	,	,	PUNCT
american_scientific_journal-3982	1	24	issn	issn	PROPN
american_scientific_journal-3982	1	25	(	(	PUNCT
american_scientific_journal-3982	1	26	online	online	ADJ
american_scientific_journal-3982	1	27	)	)	PUNCT
american_scientific_journal-3982	1	28	2313	2313	NUM
american_scientific_journal-3982	1	29	-	-	SYM
american_scientific_journal-3982	1	30	4402	4402	NUM
american_scientific_journal-3982	1	31	©	©	PROPN
american_scientific_journal-3982	1	32	global	global	ADJ
american_scientific_journal-3982	1	33	society	society	NOUN
american_scientific_journal-3982	1	34	of	of	ADP
american_scientific_journal-3982	1	35	scientific	scientific	ADJ
american_scientific_journal-3982	1	36	research	research	NOUN
american_scientific_journal-3982	1	37	and	and	CCONJ
american_scientific_journal-3982	1	38	researchers	researcher	NOUN
american_scientific_journal-3982	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-3982	1	40	about	about	ADP
american_scientific_journal-3982	1	41	the	the	DET
american_scientific_journal-3982	1	42	proof	proof	NOUN
american_scientific_journal-3982	1	43	of	of	ADP
american_scientific_journal-3982	1	44	the	the	DET
american_scientific_journal-3982	1	45	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	1	46	's	's	PART
american_scientific_journal-3982	1	47	rule	rule	NOUN
american_scientific_journal-3982	1	48	gulmaro	gulmaro	NOUN
american_scientific_journal-3982	1	49	corona	corona	NOUN
american_scientific_journal-3982	1	50	-	-	PUNCT
american_scientific_journal-3982	1	51	corona	corona	NOUN
american_scientific_journal-3982	1	52	*	*	PUNCT
american_scientific_journal-3982	1	53	universidad	universidad	PROPN
american_scientific_journal-3982	1	54	autónoma	autónoma	PROPN
american_scientific_journal-3982	1	55	metropolitana	metropolitana	PROPN
american_scientific_journal-3982	1	56	,	,	PUNCT
american_scientific_journal-3982	1	57	unidad	unidad	PROPN
american_scientific_journal-3982	1	58	azcapotzalco	azcapotzalco	NOUN
american_scientific_journal-3982	1	59	,	,	PUNCT
american_scientific_journal-3982	1	60	departamento	departamento	PROPN
american_scientific_journal-3982	1	61	de	de	PROPN
american_scientific_journal-3982	1	62	ciencias	ciencias	PROPN
american_scientific_journal-3982	1	63	básicas	básicas	PROPN
american_scientific_journal-3982	1	64	e	e	PROPN
american_scientific_journal-3982	1	65	ingeniería	ingeniería	PROPN
american_scientific_journal-3982	1	66	,	,	PUNCT
american_scientific_journal-3982	1	67	area	area	NOUN
american_scientific_journal-3982	1	68	de	de	X
american_scientific_journal-3982	1	69	análisis	análisis	PROPN
american_scientific_journal-3982	1	70	matemático	matemático	PROPN
american_scientific_journal-3982	1	71	y	y	PROPN
american_scientific_journal-3982	1	72	sus	sus	PROPN
american_scientific_journal-3982	1	73	aplicaciones	aplicaciones	PROPN
american_scientific_journal-3982	1	74	,	,	PUNCT
american_scientific_journal-3982	1	75	ave	ave	PROPN
american_scientific_journal-3982	1	76	.	.	PUNCT
american_scientific_journal-3982	2	1	san	san	PROPN
american_scientific_journal-3982	2	2	pablo	pablo	PROPN
american_scientific_journal-3982	2	3	180	180	NUM
american_scientific_journal-3982	2	4	,	,	PUNCT
american_scientific_journal-3982	2	5	colonia	colonia	PROPN
american_scientific_journal-3982	2	6	reynosa	reynosa	PROPN
american_scientific_journal-3982	2	7	tamaulipas	tamaulipas	PROPN
american_scientific_journal-3982	2	8	,	,	PUNCT
american_scientific_journal-3982	2	9	delegación	delegación	NOUN
american_scientific_journal-3982	2	10	azcapotzalco	azcapotzalco	NOUN
american_scientific_journal-3982	2	11	,	,	PUNCT
american_scientific_journal-3982	2	12	cdmx	cdmx	NOUN
american_scientific_journal-3982	2	13	,	,	PUNCT
american_scientific_journal-3982	2	14	c.p	c.p	PROPN
american_scientific_journal-3982	2	15	.	.	PROPN
american_scientific_journal-3982	2	16	02200	02200	NUM
american_scientific_journal-3982	2	17	,	,	PUNCT
american_scientific_journal-3982	2	18	méxico	méxico	PROPN
american_scientific_journal-3982	2	19	email	email	NOUN
american_scientific_journal-3982	2	20	:	:	PUNCT
american_scientific_journal-3982	2	21	ccg@correo.azc.uam.mx	ccg@correo.azc.uam.mx	ADJ
american_scientific_journal-3982	2	22	abstract	abstract	NOUN
american_scientific_journal-3982	2	23	the	the	DET
american_scientific_journal-3982	2	24	recent	recent	ADJ
american_scientific_journal-3982	2	25	proofs	proof	NOUN
american_scientific_journal-3982	2	26	of	of	ADP
american_scientific_journal-3982	2	27	l’hopital	l’hopital	PROPN
american_scientific_journal-3982	2	28	’s	’s	PART
american_scientific_journal-3982	2	29	rule	rule	NOUN
american_scientific_journal-3982	2	30	require	require	VERB
american_scientific_journal-3982	2	31	the	the	DET
american_scientific_journal-3982	2	32	continuity	continuity	NOUN
american_scientific_journal-3982	2	33	of	of	ADP
american_scientific_journal-3982	2	34	the	the	DET
american_scientific_journal-3982	2	35	derivatives	derivative	NOUN
american_scientific_journal-3982	2	36	of	of	ADP
american_scientific_journal-3982	2	37	the	the	DET
american_scientific_journal-3982	2	38	functions	function	NOUN
american_scientific_journal-3982	2	39	in	in	ADP
american_scientific_journal-3982	2	40	an	an	DET
american_scientific_journal-3982	2	41	interval	interval	NOUN
american_scientific_journal-3982	2	42	.	.	PUNCT
american_scientific_journal-3982	3	1	in	in	ADP
american_scientific_journal-3982	3	2	this	this	DET
american_scientific_journal-3982	3	3	work	work	NOUN
american_scientific_journal-3982	3	4	,	,	PUNCT
american_scientific_journal-3982	3	5	a	a	DET
american_scientific_journal-3982	3	6	proof	proof	NOUN
american_scientific_journal-3982	3	7	is	be	AUX
american_scientific_journal-3982	3	8	given	give	VERB
american_scientific_journal-3982	3	9	so	so	SCONJ
american_scientific_journal-3982	3	10	that	that	SCONJ
american_scientific_journal-3982	3	11	it	it	PRON
american_scientific_journal-3982	3	12	does	do	AUX
american_scientific_journal-3982	3	13	not	not	PART
american_scientific_journal-3982	3	14	require	require	VERB
american_scientific_journal-3982	3	15	the	the	DET
american_scientific_journal-3982	3	16	existence	existence	NOUN
american_scientific_journal-3982	3	17	of	of	ADP
american_scientific_journal-3982	3	18	the	the	DET
american_scientific_journal-3982	3	19	derivatives	derivative	NOUN
american_scientific_journal-3982	3	20	of	of	ADP
american_scientific_journal-3982	3	21	the	the	DET
american_scientific_journal-3982	3	22	functions	function	NOUN
american_scientific_journal-3982	3	23	in	in	ADP
american_scientific_journal-3982	3	24	any	any	DET
american_scientific_journal-3982	3	25	other	other	ADJ
american_scientific_journal-3982	3	26	number	number	NOUN
american_scientific_journal-3982	3	27	than	than	ADP
american_scientific_journal-3982	3	28	the	the	DET
american_scientific_journal-3982	3	29	number	number	NOUN
american_scientific_journal-3982	3	30	where	where	SCONJ
american_scientific_journal-3982	3	31	the	the	DET
american_scientific_journal-3982	3	32	limit	limit	NOUN
american_scientific_journal-3982	3	33	of	of	ADP
american_scientific_journal-3982	3	34	its	its	PRON
american_scientific_journal-3982	3	35	ratio	ratio	NOUN
american_scientific_journal-3982	3	36	is	be	AUX
american_scientific_journal-3982	3	37	calculated	calculate	VERB
american_scientific_journal-3982	3	38	,	,	PUNCT
american_scientific_journal-3982	3	39	more	more	ADV
american_scientific_journal-3982	3	40	precisely	precisely	ADV
american_scientific_journal-3982	3	41	the	the	DET
american_scientific_journal-3982	3	42	l’hopital	l’hopital	ADJ
american_scientific_journal-3982	3	43	rule	rule	NOUN
american_scientific_journal-3982	3	44	extends	extend	VERB
american_scientific_journal-3982	3	45	to	to	ADP
american_scientific_journal-3982	3	46	locally	locally	ADV
american_scientific_journal-3982	3	47	defined	define	VERB
american_scientific_journal-3982	3	48	and	and	CCONJ
american_scientific_journal-3982	3	49	derivable	derivable	ADJ
american_scientific_journal-3982	3	50	functions	function	NOUN
american_scientific_journal-3982	3	51	in	in	ADP
american_scientific_journal-3982	3	52	the	the	DET
american_scientific_journal-3982	3	53	number	number	NOUN
american_scientific_journal-3982	3	54	where	where	SCONJ
american_scientific_journal-3982	3	55	the	the	DET
american_scientific_journal-3982	3	56	limit	limit	NOUN
american_scientific_journal-3982	3	57	of	of	ADP
american_scientific_journal-3982	3	58	the	the	DET
american_scientific_journal-3982	3	59	ratio	ratio	NOUN
american_scientific_journal-3982	3	60	of	of	ADP
american_scientific_journal-3982	3	61	the	the	DET
american_scientific_journal-3982	3	62	functions	function	NOUN
american_scientific_journal-3982	3	63	is	be	AUX
american_scientific_journal-3982	3	64	calculated	calculate	VERB
american_scientific_journal-3982	3	65	.	.	PUNCT
american_scientific_journal-3982	4	1	keywords	keyword	NOUN
american_scientific_journal-3982	4	2	:	:	PUNCT
american_scientific_journal-3982	4	3	locally	locally	ADV
american_scientific_journal-3982	4	4	defined	define	VERB
american_scientific_journal-3982	4	5	;	;	PUNCT
american_scientific_journal-3982	4	6	l’hopital	l’hopital	PROPN
american_scientific_journal-3982	4	7	’s	’s	PART
american_scientific_journal-3982	4	8	rule	rule	NOUN
american_scientific_journal-3982	4	9	;	;	PUNCT
american_scientific_journal-3982	4	10	limit	limit	NOUN
american_scientific_journal-3982	4	11	.	.	PUNCT
american_scientific_journal-3982	5	1	1	1	X
american_scientific_journal-3982	5	2	.	.	X
american_scientific_journal-3982	5	3	introduction	introduction	NOUN
american_scientific_journal-3982	5	4	the	the	DET
american_scientific_journal-3982	5	5	present	present	ADJ
american_scientific_journal-3982	5	6	l’hopital	l’hopital	ADJ
american_scientific_journal-3982	5	7	rule	rule	NOUN
american_scientific_journal-3982	5	8	proof	proof	NOUN
american_scientific_journal-3982	5	9	is	be	AUX
american_scientific_journal-3982	5	10	based	base	VERB
american_scientific_journal-3982	5	11	on	on	ADP
american_scientific_journal-3982	5	12	the	the	DET
american_scientific_journal-3982	5	13	algebra	algebra	NOUN
american_scientific_journal-3982	5	14	of	of	ADP
american_scientific_journal-3982	5	15	limits	limit	NOUN
american_scientific_journal-3982	5	16	of	of	ADP
american_scientific_journal-3982	5	17	locally	locally	ADV
american_scientific_journal-3982	5	18	defined	define	VERB
american_scientific_journal-3982	5	19	functions	function	NOUN
american_scientific_journal-3982	5	20	in	in	ADP
american_scientific_journal-3982	5	21	the	the	DET
american_scientific_journal-3982	5	22	number	number	NOUN
american_scientific_journal-3982	5	23	where	where	SCONJ
american_scientific_journal-3982	5	24	the	the	DET
american_scientific_journal-3982	5	25	limit	limit	NOUN
american_scientific_journal-3982	5	26	is	be	AUX
american_scientific_journal-3982	5	27	calculated	calculate	VERB
american_scientific_journal-3982	5	28	,	,	PUNCT
american_scientific_journal-3982	5	29	as	as	SCONJ
american_scientific_journal-3982	5	30	it	it	PRON
american_scientific_journal-3982	5	31	is	be	AUX
american_scientific_journal-3982	5	32	done	do	VERB
american_scientific_journal-3982	5	33	for	for	ADP
american_scientific_journal-3982	5	34	the	the	DET
american_scientific_journal-3982	5	35	proofs	proof	NOUN
american_scientific_journal-3982	5	36	of	of	ADP
american_scientific_journal-3982	5	37	the	the	DET
american_scientific_journal-3982	5	38	derivation	derivation	NOUN
american_scientific_journal-3982	5	39	rules	rule	NOUN
american_scientific_journal-3982	5	40	where	where	SCONJ
american_scientific_journal-3982	5	41	the	the	DET
american_scientific_journal-3982	5	42	functions	function	NOUN
american_scientific_journal-3982	5	43	involved	involve	VERB
american_scientific_journal-3982	5	44	need	need	VERB
american_scientific_journal-3982	5	45	to	to	PART
american_scientific_journal-3982	5	46	be	be	AUX
american_scientific_journal-3982	5	47	defined	define	VERB
american_scientific_journal-3982	5	48	locally	locally	ADV
american_scientific_journal-3982	5	49	and	and	CCONJ
american_scientific_journal-3982	5	50	derivable	derivable	ADJ
american_scientific_journal-3982	5	51	only	only	ADV
american_scientific_journal-3982	5	52	in	in	ADP
american_scientific_journal-3982	5	53	the	the	DET
american_scientific_journal-3982	5	54	number	number	NOUN
american_scientific_journal-3982	5	55	where	where	SCONJ
american_scientific_journal-3982	5	56	the	the	DET
american_scientific_journal-3982	5	57	limit	limit	NOUN
american_scientific_journal-3982	5	58	is	be	AUX
american_scientific_journal-3982	5	59	calculated	calculate	VERB
american_scientific_journal-3982	5	60	.	.	PUNCT
american_scientific_journal-3982	6	1	consequently	consequently	ADV
american_scientific_journal-3982	6	2	,	,	PUNCT
american_scientific_journal-3982	6	3	this	this	DET
american_scientific_journal-3982	6	4	proof	proof	NOUN
american_scientific_journal-3982	6	5	extends	extend	VERB
american_scientific_journal-3982	6	6	the	the	DET
american_scientific_journal-3982	6	7	l’hopital	l’hopital	ADJ
american_scientific_journal-3982	6	8	rule	rule	NOUN
american_scientific_journal-3982	6	9	to	to	ADP
american_scientific_journal-3982	6	10	locally	locally	ADV
american_scientific_journal-3982	6	11	defined	define	VERB
american_scientific_journal-3982	6	12	and	and	CCONJ
american_scientific_journal-3982	6	13	derivable	derivable	ADJ
american_scientific_journal-3982	6	14	functions	function	NOUN
american_scientific_journal-3982	6	15	only	only	ADV
american_scientific_journal-3982	6	16	in	in	ADP
american_scientific_journal-3982	6	17	the	the	DET
american_scientific_journal-3982	6	18	number	number	NOUN
american_scientific_journal-3982	6	19	where	where	SCONJ
american_scientific_journal-3982	6	20	the	the	DET
american_scientific_journal-3982	6	21	limit	limit	NOUN
american_scientific_journal-3982	6	22	of	of	ADP
american_scientific_journal-3982	6	23	the	the	DET
american_scientific_journal-3982	6	24	ratio	ratio	NOUN
american_scientific_journal-3982	6	25	of	of	ADP
american_scientific_journal-3982	6	26	the	the	DET
american_scientific_journal-3982	6	27	same	same	ADJ
american_scientific_journal-3982	6	28	is	be	AUX
american_scientific_journal-3982	6	29	calculated.the	calculated.the	DET
american_scientific_journal-3982	6	30	ratio	ratio	NOUN
american_scientific_journal-3982	6	31	for	for	ADP
american_scientific_journal-3982	6	32	the	the	DET
american_scientific_journal-3982	6	33	differences	difference	NOUN
american_scientific_journal-3982	6	34	of	of	ADP
american_scientific_journal-3982	6	35	the	the	DET
american_scientific_journal-3982	6	36	given	give	VERB
american_scientific_journal-3982	6	37	functions	function	NOUN
american_scientific_journal-3982	6	38	will	will	AUX
american_scientific_journal-3982	6	39	be	be	AUX
american_scientific_journal-3982	6	40	considered	consider	VERB
american_scientific_journal-3982	6	41	,	,	PUNCT
american_scientific_journal-3982	6	42	which	which	PRON
american_scientific_journal-3982	6	43	will	will	AUX
american_scientific_journal-3982	6	44	be	be	AUX
american_scientific_journal-3982	6	45	expressed	express	VERB
american_scientific_journal-3982	6	46	as	as	ADP
american_scientific_journal-3982	6	47	a	a	DET
american_scientific_journal-3982	6	48	ratio	ratio	NOUN
american_scientific_journal-3982	6	49	of	of	ADP
american_scientific_journal-3982	6	50	derivation	derivation	NOUN
american_scientific_journal-3982	6	51	quotients	quotient	NOUN
american_scientific_journal-3982	6	52	of	of	ADP
american_scientific_journal-3982	6	53	each	each	PRON
american_scientific_journal-3982	6	54	of	of	ADP
american_scientific_journal-3982	6	55	the	the	DET
american_scientific_journal-3982	6	56	two	two	NUM
american_scientific_journal-3982	6	57	functions	function	NOUN
american_scientific_journal-3982	6	58	,	,	PUNCT
american_scientific_journal-3982	6	59	which	which	PRON
american_scientific_journal-3982	6	60	by	by	ADP
american_scientific_journal-3982	6	61	their	their	PRON
american_scientific_journal-3982	6	62	definition	definition	NOUN
american_scientific_journal-3982	6	63	tend	tend	VERB
american_scientific_journal-3982	6	64	to	to	ADP
american_scientific_journal-3982	6	65	the	the	DET
american_scientific_journal-3982	6	66	derivatives	derivative	NOUN
american_scientific_journal-3982	6	67	of	of	ADP
american_scientific_journal-3982	6	68	the	the	DET
american_scientific_journal-3982	6	69	functions	function	NOUN
american_scientific_journal-3982	6	70	,	,	PUNCT
american_scientific_journal-3982	6	71	respectively.the	respectively.the	DET
american_scientific_journal-3982	6	72	derivation	derivation	NOUN
american_scientific_journal-3982	6	73	quotient	quotient	NOUN
american_scientific_journal-3982	6	74	of	of	ADP
american_scientific_journal-3982	6	75	a	a	DET
american_scientific_journal-3982	6	76	given	give	VERB
american_scientific_journal-3982	6	77	function	function	NOUN
american_scientific_journal-3982	6	78	is	be	AUX
american_scientific_journal-3982	6	79	the	the	DET
american_scientific_journal-3982	6	80	one	one	NOUN
american_scientific_journal-3982	6	81	that	that	PRON
american_scientific_journal-3982	6	82	is	be	AUX
american_scientific_journal-3982	6	83	used	use	VERB
american_scientific_journal-3982	6	84	to	to	PART
american_scientific_journal-3982	6	85	calculate	calculate	VERB
american_scientific_journal-3982	6	86	the	the	DET
american_scientific_journal-3982	6	87	derivative	derivative	NOUN
american_scientific_journal-3982	6	88	of	of	ADP
american_scientific_journal-3982	6	89	it	it	PRON
american_scientific_journal-3982	6	90	.	.	PUNCT
american_scientific_journal-3982	7	1	this	this	DET
american_scientific_journal-3982	7	2	quotient	quotient	NOUN
american_scientific_journal-3982	7	3	is	be	AUX
american_scientific_journal-3982	7	4	locally	locally	ADV
american_scientific_journal-3982	7	5	defined	define	VERB
american_scientific_journal-3982	7	6	and	and	CCONJ
american_scientific_journal-3982	7	7	always	always	ADV
american_scientific_journal-3982	7	8	different	different	ADJ
american_scientific_journal-3982	7	9	from	from	ADP
american_scientific_journal-3982	7	10	zero	zero	NUM
american_scientific_journal-3982	7	11	when	when	SCONJ
american_scientific_journal-3982	7	12	the	the	DET
american_scientific_journal-3982	7	13	derivative	derivative	NOUN
american_scientific_journal-3982	7	14	is	be	AUX
american_scientific_journal-3982	7	15	different	different	ADJ
american_scientific_journal-3982	7	16	from	from	ADP
american_scientific_journal-3982	7	17	zero	zero	NUM
american_scientific_journal-3982	7	18	in	in	ADP
american_scientific_journal-3982	7	19	the	the	DET
american_scientific_journal-3982	7	20	number	number	NOUN
american_scientific_journal-3982	7	21	where	where	SCONJ
american_scientific_journal-3982	7	22	the	the	DET
american_scientific_journal-3982	7	23	limit	limit	NOUN
american_scientific_journal-3982	7	24	is	be	AUX
american_scientific_journal-3982	7	25	calculated	calculate	VERB
american_scientific_journal-3982	7	26	,	,	PUNCT
american_scientific_journal-3982	7	27	so	so	SCONJ
american_scientific_journal-3982	7	28	that	that	SCONJ
american_scientific_journal-3982	7	29	the	the	DET
american_scientific_journal-3982	7	30	ratio	ratio	NOUN
american_scientific_journal-3982	7	31	of	of	ADP
american_scientific_journal-3982	7	32	the	the	DET
american_scientific_journal-3982	7	33	differences	difference	NOUN
american_scientific_journal-3982	7	34	of	of	ADP
american_scientific_journal-3982	7	35	the	the	DET
american_scientific_journal-3982	7	36	functions	function	NOUN
american_scientific_journal-3982	7	37	(	(	PUNCT
american_scientific_journal-3982	7	38	e.g.	e.g.	ADV
american_scientific_journal-3982	7	39	[	[	X
american_scientific_journal-3982	7	40	4	4	NUM
american_scientific_journal-3982	7	41	]	]	NUM
american_scientific_journal-3982	7	42	)	)	PUNCT
american_scientific_journal-3982	7	43	,	,	PUNCT
american_scientific_journal-3982	7	44	can	can	AUX
american_scientific_journal-3982	7	45	be	be	AUX
american_scientific_journal-3982	7	46	expressed	express	VERB
american_scientific_journal-3982	7	47	as	as	ADP
american_scientific_journal-3982	7	48	a	a	DET
american_scientific_journal-3982	7	49	ratio	ratio	NOUN
american_scientific_journal-3982	7	50	of	of	ADP
american_scientific_journal-3982	7	51	derivation	derivation	NOUN
american_scientific_journal-3982	7	52	quotients	quotient	NOUN
american_scientific_journal-3982	7	53	.	.	PUNCT
american_scientific_journal-3982	8	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-3982	9	1	*	*	PUNCT
american_scientific_journal-3982	9	2	corresponding	correspond	VERB
american_scientific_journal-3982	9	3	author	author	NOUN
american_scientific_journal-3982	9	4	.	.	PUNCT
american_scientific_journal-3982	10	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-3982	10	2	american	american	PROPN
american_scientific_journal-3982	10	3	scientific	scientific	PROPN
american_scientific_journal-3982	10	4	research	research	NOUN
american_scientific_journal-3982	10	5	journal	journal	NOUN
american_scientific_journal-3982	10	6	for	for	ADP
american_scientific_journal-3982	10	7	engineering	engineering	NOUN
american_scientific_journal-3982	10	8	,	,	PUNCT
american_scientific_journal-3982	10	9	technology	technology	NOUN
american_scientific_journal-3982	10	10	,	,	PUNCT
american_scientific_journal-3982	10	11	and	and	CCONJ
american_scientific_journal-3982	10	12	sciences	science	NOUN
american_scientific_journal-3982	10	13	(	(	PUNCT
american_scientific_journal-3982	10	14	asrjets	asrjet	NOUN
american_scientific_journal-3982	10	15	)	)	PUNCT
american_scientific_journal-3982	10	16	(	(	PUNCT
american_scientific_journal-3982	10	17	2018	2018	NUM
american_scientific_journal-3982	10	18	)	)	PUNCT
american_scientific_journal-3982	10	19	volume	volume	NOUN
american_scientific_journal-3982	10	20	41	41	NUM
american_scientific_journal-3982	10	21	,	,	PUNCT
american_scientific_journal-3982	10	22	no	no	DET
american_scientific_journal-3982	10	23	1	1	NUM
american_scientific_journal-3982	10	24	,	,	PUNCT
american_scientific_journal-3982	10	25	pp	pp	ADV
american_scientific_journal-3982	10	26	240	240	NUM
american_scientific_journal-3982	10	27	-	-	SYM
american_scientific_journal-3982	10	28	245	245	NUM
american_scientific_journal-3982	10	29	241	241	NUM
american_scientific_journal-3982	10	30	2	2	NUM
american_scientific_journal-3982	10	31	.	.	PUNCT
american_scientific_journal-3982	11	1	definitions	definition	NOUN
american_scientific_journal-3982	11	2	y	y	PROPN
american_scientific_journal-3982	11	3	results	result	VERB
american_scientific_journal-3982	11	4	on	on	ADP
american_scientific_journal-3982	11	5	continuity	continuity	NOUN
american_scientific_journal-3982	11	6	and	and	CCONJ
american_scientific_journal-3982	11	7	derivation	derivation	NOUN
american_scientific_journal-3982	11	8	of	of	ADP
american_scientific_journal-3982	11	9	locally	locally	ADV
american_scientific_journal-3982	11	10	defined	define	VERB
american_scientific_journal-3982	11	11	functions	function	NOUN
american_scientific_journal-3982	11	12	for	for	ADP
american_scientific_journal-3982	11	13	our	our	PRON
american_scientific_journal-3982	11	14	purposes	purpose	NOUN
american_scientific_journal-3982	11	15	it	it	PRON
american_scientific_journal-3982	11	16	will	will	AUX
american_scientific_journal-3982	11	17	be	be	AUX
american_scientific_journal-3982	11	18	necessary	necessary	ADJ
american_scientific_journal-3982	11	19	to	to	PART
american_scientific_journal-3982	11	20	define	define	VERB
american_scientific_journal-3982	11	21	what	what	PRON
american_scientific_journal-3982	11	22	means	mean	VERB
american_scientific_journal-3982	11	23	locally	locally	ADV
american_scientific_journal-3982	11	24	defined	define	VERB
american_scientific_journal-3982	11	25	functions	function	NOUN
american_scientific_journal-3982	11	26	in	in	ADP
american_scientific_journal-3982	11	27	a	a	DET
american_scientific_journal-3982	11	28	given	give	VERB
american_scientific_journal-3982	11	29	number	number	NOUN
american_scientific_journal-3982	11	30	and	and	CCONJ
american_scientific_journal-3982	11	31	their	their	PRON
american_scientific_journal-3982	11	32	derivation	derivation	NOUN
american_scientific_journal-3982	11	33	quotients	quotient	NOUN
american_scientific_journal-3982	11	34	,	,	PUNCT
american_scientific_journal-3982	11	35	for	for	ADP
american_scientific_journal-3982	11	36	which	which	PRON
american_scientific_journal-3982	11	37	it	it	PRON
american_scientific_journal-3982	11	38	is	be	AUX
american_scientific_journal-3982	11	39	necessary	necessary	ADJ
american_scientific_journal-3982	11	40	to	to	PART
american_scientific_journal-3982	11	41	introduce	introduce	VERB
american_scientific_journal-3982	11	42	some	some	DET
american_scientific_journal-3982	11	43	basic	basic	ADJ
american_scientific_journal-3982	11	44	auxiliary	auxiliary	ADJ
american_scientific_journal-3982	11	45	concepts	concept	NOUN
american_scientific_journal-3982	11	46	and	and	CCONJ
american_scientific_journal-3982	11	47	results	result	NOUN
american_scientific_journal-3982	11	48	.	.	PUNCT
american_scientific_journal-3982	12	1	definition	definition	NOUN
american_scientific_journal-3982	12	2	1	1	NUM
american_scientific_journal-3982	12	3	.	.	PUNCT
american_scientific_journal-3982	13	1	given	give	VERB
american_scientific_journal-3982	13	2	a	a	DET
american_scientific_journal-3982	13	3	number	number	NOUN
american_scientific_journal-3982	13	4	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	13	5	=	=	SYM
american_scientific_journal-3982	13	6	0	0	NUM
american_scientific_journal-3982	13	7	in	in	ADP
american_scientific_journal-3982	13	8	te	te	ADP
american_scientific_journal-3982	13	9	interval	interval	NOUN
american_scientific_journal-3982	13	10	(	(	PUNCT
american_scientific_journal-3982	13	11	−∞	−∞	NOUN
american_scientific_journal-3982	13	12	,	,	PUNCT
american_scientific_journal-3982	13	13	+	+	NOUN
american_scientific_journal-3982	13	14	∞	∞	NOUN
american_scientific_journal-3982	13	15	)	)	PUNCT
american_scientific_journal-3982	13	16	,	,	PUNCT
american_scientific_journal-3982	13	17	𝑠𝑠𝑠𝑠𝑠𝑠(𝑎𝑎	𝑠𝑠𝑠𝑠𝑠𝑠(𝑎𝑎	NOUN
american_scientific_journal-3982	13	18	)	)	PUNCT
american_scientific_journal-3982	13	19	=	=	VERB
american_scientific_journal-3982	13	20	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-3982	13	21	|𝑎𝑎|	|𝑎𝑎|	PROPN
american_scientific_journal-3982	13	22	.	.	PUNCT
american_scientific_journal-3982	14	1	for	for	ADP
american_scientific_journal-3982	14	2	our	our	PRON
american_scientific_journal-3982	14	3	purposes	purpose	NOUN
american_scientific_journal-3982	14	4	we	we	PRON
american_scientific_journal-3982	14	5	define	define	VERB
american_scientific_journal-3982	14	6	te	te	ADP
american_scientific_journal-3982	14	7	norm	norm	NOUN
american_scientific_journal-3982	14	8	of	of	ADP
american_scientific_journal-3982	14	9	a	a	DET
american_scientific_journal-3982	14	10	couple	couple	NOUN
american_scientific_journal-3982	14	11	of	of	ADP
american_scientific_journal-3982	14	12	numbers	number	NOUN
american_scientific_journal-3982	14	13	.	.	PUNCT
american_scientific_journal-3982	15	1	definition	definition	NOUN
american_scientific_journal-3982	15	2	2	2	NUM
american_scientific_journal-3982	15	3	.	.	PUNCT
american_scientific_journal-3982	16	1	given	give	VERB
american_scientific_journal-3982	16	2	a	a	DET
american_scientific_journal-3982	16	3	pair	pair	NOUN
american_scientific_journal-3982	16	4	of	of	ADP
american_scientific_journal-3982	16	5	numbers	number	NOUN
american_scientific_journal-3982	16	6	(	(	PUNCT
american_scientific_journal-3982	16	7	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	16	8	,	,	PUNCT
american_scientific_journal-3982	16	9	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-3982	16	10	)	)	PUNCT
american_scientific_journal-3982	16	11	,	,	PUNCT
american_scientific_journal-3982	16	12	denote	denote	VERB
american_scientific_journal-3982	16	13	𝑎𝑎2	𝑎𝑎2	X
american_scientific_journal-3982	17	1	+	+	CCONJ
american_scientific_journal-3982	17	2	𝑏𝑏2	𝑏𝑏2	NOUN
american_scientific_journal-3982	17	3	by	by	ADP
american_scientific_journal-3982	17	4	‖𝑎𝑎	‖𝑎𝑎	PROPN
american_scientific_journal-3982	17	5	,	,	PUNCT
american_scientific_journal-3982	17	6	𝑏𝑏‖2	𝑏𝑏‖2	PROPN
american_scientific_journal-3982	17	7	=	=	SYM
american_scientific_journal-3982	17	8	𝑎𝑎2	𝑎𝑎2	X
american_scientific_journal-3982	17	9	+	+	CCONJ
american_scientific_journal-3982	17	10	𝑏𝑏2	𝑏𝑏2	PROPN
american_scientific_journal-3982	17	11	.	.	PROPN
american_scientific_journal-3982	17	12	remark	remark	PROPN
american_scientific_journal-3982	18	1	3	3	NUM
american_scientific_journal-3982	18	2	.	.	X
american_scientific_journal-3982	18	3	𝑠𝑠𝑠𝑠𝑠𝑠(𝑏𝑏	𝑠𝑠𝑠𝑠𝑠𝑠(𝑏𝑏	VERB
american_scientific_journal-3982	18	4	)	)	PUNCT
american_scientific_journal-3982	19	1	−	−	PROPN
american_scientific_journal-3982	19	2	𝑠𝑠𝑠𝑠𝑠𝑠(𝑎𝑎	𝑠𝑠𝑠𝑠𝑠𝑠(𝑎𝑎	NOUN
american_scientific_journal-3982	19	3	)	)	PUNCT
american_scientific_journal-3982	19	4	=	=	SYM
american_scientific_journal-3982	19	5	�	�	PROPN
american_scientific_journal-3982	19	6	0	0	NUM
american_scientific_journal-3982	19	7	,	,	PUNCT
american_scientific_journal-3982	19	8	𝑠𝑠𝑠𝑠	𝑠𝑠𝑠𝑠	NOUN
american_scientific_journal-3982	19	9	𝑠𝑠𝑠𝑠𝑠𝑠(𝑏𝑏	𝑠𝑠𝑠𝑠𝑠𝑠(𝑏𝑏	NOUN
american_scientific_journal-3982	19	10	)	)	PUNCT
american_scientific_journal-3982	19	11	=	=	SYM
american_scientific_journal-3982	19	12	𝑠𝑠𝑠𝑠𝑠𝑠(𝑎𝑎	𝑠𝑠𝑠𝑠𝑠𝑠(𝑎𝑎	NOUN
american_scientific_journal-3982	19	13	)	)	PUNCT
american_scientific_journal-3982	19	14	±2	±2	NOUN
american_scientific_journal-3982	19	15	,	,	PUNCT
american_scientific_journal-3982	19	16	𝑠𝑠𝑠𝑠	𝑠𝑠𝑠𝑠	NOUN
american_scientific_journal-3982	19	17	𝑠𝑠𝑠𝑠𝑠𝑠(𝑏𝑏	𝑠𝑠𝑠𝑠𝑠𝑠(𝑏𝑏	NOUN
american_scientific_journal-3982	19	18	)	)	PUNCT
american_scientific_journal-3982	19	19	=	=	SYM
american_scientific_journal-3982	19	20	𝑠𝑠𝑠𝑠𝑠𝑠(𝑎𝑎	𝑠𝑠𝑠𝑠𝑠𝑠(𝑎𝑎	NOUN
american_scientific_journal-3982	19	21	)	)	PUNCT
american_scientific_journal-3982	19	22	and	and	CCONJ
american_scientific_journal-3982	19	23	for	for	ADP
american_scientific_journal-3982	19	24	any	any	DET
american_scientific_journal-3982	19	25	pair	pair	NOUN
american_scientific_journal-3982	19	26	of	of	ADP
american_scientific_journal-3982	19	27	numbers	number	NOUN
american_scientific_journal-3982	19	28	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	19	29	,	,	PUNCT
american_scientific_journal-3982	19	30	𝑏𝑏	𝑏𝑏	NUM
american_scientific_journal-3982	19	31	:	:	PUNCT
american_scientific_journal-3982	19	32	|𝑎𝑎|	|𝑎𝑎|	PROPN
american_scientific_journal-3982	19	33	,	,	PUNCT
american_scientific_journal-3982	19	34	|𝑏𝑏|	|𝑏𝑏|	VERB
american_scientific_journal-3982	19	35	≤	≤	PUNCT
american_scientific_journal-3982	19	36	‖𝑎𝑎	‖𝑎𝑎	PROPN
american_scientific_journal-3982	19	37	,	,	PUNCT
american_scientific_journal-3982	19	38	𝑏𝑏‖.	𝑏𝑏‖.	NOUN
american_scientific_journal-3982	19	39	proposition	proposition	NOUN
american_scientific_journal-3982	19	40	4	4	NUM
american_scientific_journal-3982	19	41	.	.	PUNCT
american_scientific_journal-3982	19	42	assume	assume	VERB
american_scientific_journal-3982	20	1	that	that	SCONJ
american_scientific_journal-3982	20	2	|𝑎𝑎	|𝑎𝑎	ADV
american_scientific_journal-3982	20	3	−	−	PROPN
american_scientific_journal-3982	20	4	𝑏𝑏|	𝑏𝑏|	NOUN
american_scientific_journal-3982	20	5	<	<	X
american_scientific_journal-3982	21	1	𝜀𝜀	𝜀𝜀	INTJ
american_scientific_journal-3982	21	2	<	<	X
american_scientific_journal-3982	21	3	|𝑎𝑎|	|𝑎𝑎|	PROPN
american_scientific_journal-3982	21	4	then	then	ADV
american_scientific_journal-3982	21	5	𝑠𝑠𝑠𝑠𝑠𝑠(𝑎𝑎	𝑠𝑠𝑠𝑠𝑠𝑠(𝑎𝑎	NOUN
american_scientific_journal-3982	21	6	)	)	PUNCT
american_scientific_journal-3982	21	7	=	=	SYM
american_scientific_journal-3982	21	8	𝑠𝑠𝑠𝑠𝑠𝑠(𝑏𝑏	𝑠𝑠𝑠𝑠𝑠𝑠(𝑏𝑏	NOUN
american_scientific_journal-3982	21	9	)	)	PUNCT
american_scientific_journal-3982	21	10	proof	proof	NOUN
american_scientific_journal-3982	21	11	.	.	PUNCT
american_scientific_journal-3982	22	1	sgn(𝑎𝑎	sgn(𝑎𝑎	NOUN
american_scientific_journal-3982	22	2	)	)	PUNCT
american_scientific_journal-3982	22	3	−	−	PROPN
american_scientific_journal-3982	22	4	sgn(𝑏𝑏	sgn(𝑏𝑏	NOUN
american_scientific_journal-3982	22	5	)	)	PUNCT
american_scientific_journal-3982	22	6	=	=	VERB
american_scientific_journal-3982	22	7	𝑎𝑎	𝑎𝑎	VERB
american_scientific_journal-3982	22	8	|𝑎𝑎|	|𝑎𝑎|	PROPN
american_scientific_journal-3982	22	9	−	−	PROPN
american_scientific_journal-3982	22	10	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-3982	22	11	|𝑏𝑏|	|𝑏𝑏|	NOUN
american_scientific_journal-3982	22	12	=	=	SYM
american_scientific_journal-3982	22	13	|𝑏𝑏|𝑎𝑎−|𝑎𝑎|𝑏𝑏	|𝑏𝑏|𝑎𝑎−|𝑎𝑎|𝑏𝑏	PROPN
american_scientific_journal-3982	22	14	|𝑎𝑎||𝑏𝑏|	|𝑎𝑎||𝑏𝑏|	NOUN
american_scientific_journal-3982	22	15	=	=	SYM
american_scientific_journal-3982	22	16	|𝑏𝑏|(𝑎𝑎−𝑏𝑏)+(|𝑏𝑏|−|𝑎𝑎|)𝑏𝑏	|𝑏𝑏|(𝑎𝑎−𝑏𝑏)+(|𝑏𝑏|−|𝑎𝑎|)𝑏𝑏	ADJ
american_scientific_journal-3982	22	17	|𝑎𝑎||𝑏𝑏|	|𝑎𝑎||𝑏𝑏|	NOUN
american_scientific_journal-3982	22	18	then	then	ADV
american_scientific_journal-3982	22	19	|sgn(𝑎𝑎	|sgn(𝑎𝑎	PROPN
american_scientific_journal-3982	22	20	)	)	PUNCT
american_scientific_journal-3982	22	21	−	−	ADP
american_scientific_journal-3982	22	22	sgn(𝑏𝑏)|	sgn(𝑏𝑏)|	NOUN
american_scientific_journal-3982	22	23	≤	≤	NOUN
american_scientific_journal-3982	22	24	|𝑏𝑏||𝑎𝑎−𝑏𝑏|+	|𝑏𝑏||𝑎𝑎−𝑏𝑏|+	SYM
american_scientific_journal-3982	22	25	�	�	NOUN
american_scientific_journal-3982	22	26	|𝑏𝑏|−|𝑎𝑎|	|𝑏𝑏|−|𝑎𝑎|	VERB
american_scientific_journal-3982	22	27	�	�	PROPN
american_scientific_journal-3982	22	28	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-3982	22	29	|𝑎𝑎||𝑏𝑏|	|𝑎𝑎||𝑏𝑏|	NOUN
american_scientific_journal-3982	22	30	≤	≤	NUM
american_scientific_journal-3982	22	31	|𝑏𝑏|	|𝑏𝑏|	NOUN
american_scientific_journal-3982	22	32	|𝑎𝑎||𝑏𝑏|	|𝑎𝑎||𝑏𝑏|	NOUN
american_scientific_journal-3982	22	33	|𝑎𝑎	|𝑎𝑎	ADP
american_scientific_journal-3982	22	34	−	−	PROPN
american_scientific_journal-3982	22	35	𝑏𝑏|	𝑏𝑏|	PROPN
american_scientific_journal-3982	22	36	≤	≤	PROPN
american_scientific_journal-3982	22	37	|𝑎𝑎−𝑏𝑏|	|𝑎𝑎−𝑏𝑏|	NOUN
american_scientific_journal-3982	22	38	|𝑎𝑎|	|𝑎𝑎|	PROPN
american_scientific_journal-3982	22	39	<	<	X
american_scientific_journal-3982	22	40	|𝑎𝑎−𝑏𝑏|	|𝑎𝑎−𝑏𝑏|	NOUN
american_scientific_journal-3982	22	41	𝜀𝜀	𝜀𝜀	NOUN
american_scientific_journal-3982	22	42	<	<	X
american_scientific_journal-3982	22	43	1	1	NUM
american_scientific_journal-3982	22	44	.	.	PUNCT
american_scientific_journal-3982	22	45	because	because	SCONJ
american_scientific_journal-3982	22	46	of	of	ADP
american_scientific_journal-3982	22	47	the	the	DET
american_scientific_journal-3982	22	48	observation	observation	NOUN
american_scientific_journal-3982	22	49	3	3	NUM
american_scientific_journal-3982	22	50	,	,	PUNCT
american_scientific_journal-3982	22	51	we	we	PRON
american_scientific_journal-3982	22	52	have	have	VERB
american_scientific_journal-3982	22	53	sgn(𝑎𝑎	sgn(𝑎𝑎	NOUN
american_scientific_journal-3982	22	54	)	)	PUNCT
american_scientific_journal-3982	22	55	=	=	SYM
american_scientific_journal-3982	22	56	sgn(𝑏𝑏	sgn(𝑏𝑏	NOUN
american_scientific_journal-3982	22	57	)	)	PUNCT
american_scientific_journal-3982	22	58	.	.	PUNCT
american_scientific_journal-3982	23	1	proposition	proposition	NOUN
american_scientific_journal-3982	23	2	5	5	NUM
american_scientific_journal-3982	23	3	.	.	PUNCT
american_scientific_journal-3982	24	1	assuming	assume	VERB
american_scientific_journal-3982	24	2	that	that	SCONJ
american_scientific_journal-3982	24	3	𝜀𝜀	𝜀𝜀	INTJ
american_scientific_journal-3982	24	4	<	<	X
american_scientific_journal-3982	24	5	|𝑎𝑎|	|𝑎𝑎|	PROPN
american_scientific_journal-3982	24	6	,	,	PUNCT
american_scientific_journal-3982	24	7	|𝑏𝑏	|𝑏𝑏	NUM
american_scientific_journal-3982	24	8	−	−	PROPN
american_scientific_journal-3982	24	9	𝑎𝑎|	𝑎𝑎|	NOUN
american_scientific_journal-3982	24	10	<	<	X
american_scientific_journal-3982	24	11	𝜀𝜀	𝜀𝜀	INTJ
american_scientific_journal-3982	24	12	sí	sí	PROPN
american_scientific_journal-3982	24	13	y	y	PROPN
american_scientific_journal-3982	24	14	sí	sí	PROPN
american_scientific_journal-3982	24	15	y	y	PROPN
american_scientific_journal-3982	24	16	solo	solo	NOUN
american_scientific_journal-3982	24	17	si	si	PROPN
american_scientific_journal-3982	24	18	0	0	PUNCT
american_scientific_journal-3982	24	19	<	<	X
american_scientific_journal-3982	24	20	|𝑎𝑎|	|𝑎𝑎|	PROPN
american_scientific_journal-3982	24	21	−	−	NOUN
american_scientific_journal-3982	24	22	𝜀𝜀	𝜀𝜀	INTJ
american_scientific_journal-3982	24	23	<	<	X
american_scientific_journal-3982	24	24	𝑏𝑏	𝑏𝑏	X
american_scientific_journal-3982	24	25	<	<	X
american_scientific_journal-3982	24	26	|𝑎𝑎|	|𝑎𝑎|	PROPN
american_scientific_journal-3982	24	27	+	+	CCONJ
american_scientific_journal-3982	24	28	𝜀𝜀.	𝜀𝜀.	NOUN
american_scientific_journal-3982	24	29	proof	proof	NOUN
american_scientific_journal-3982	24	30	.	.	PUNCT
american_scientific_journal-3982	25	1	:	:	PUNCT
american_scientific_journal-3982	25	2	0	0	NUM
american_scientific_journal-3982	25	3	<	<	X
american_scientific_journal-3982	25	4	𝜀𝜀2	𝜀𝜀2	X
american_scientific_journal-3982	25	5	−	−	PROPN
american_scientific_journal-3982	25	6	(	(	PUNCT
american_scientific_journal-3982	25	7	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-3982	25	8	−	−	PROPN
american_scientific_journal-3982	25	9	𝑎𝑎)2	𝑎𝑎)2	PROPN
american_scientific_journal-3982	25	10	=	=	PUNCT
american_scientific_journal-3982	25	11	𝜀𝜀2	𝜀𝜀2	NOUN
american_scientific_journal-3982	25	12	−	−	PROPN
american_scientific_journal-3982	25	13	𝑏𝑏2	𝑏𝑏2	NOUN
american_scientific_journal-3982	25	14	−	−	PROPN
american_scientific_journal-3982	25	15	𝑎𝑎2	𝑎𝑎2	X
american_scientific_journal-3982	25	16	+	+	CCONJ
american_scientific_journal-3982	26	1	2𝑎𝑎𝑏𝑏	2𝑎𝑎𝑏𝑏	NUM
american_scientific_journal-3982	26	2	,	,	PUNCT
american_scientific_journal-3982	26	3	that	that	PRON
american_scientific_journal-3982	26	4	is	be	AUX
american_scientific_journal-3982	26	5	to	to	PART
american_scientific_journal-3982	26	6	say	say	VERB
american_scientific_journal-3982	26	7	‖𝑎𝑎	‖𝑎𝑎	PROPN
american_scientific_journal-3982	26	8	,	,	PUNCT
american_scientific_journal-3982	26	9	𝑏𝑏‖2	𝑏𝑏‖2	PROPN
american_scientific_journal-3982	26	10	−	−	PROPN
american_scientific_journal-3982	27	1	𝜀𝜀2	𝜀𝜀2	NOUN
american_scientific_journal-3982	27	2	<	<	X
american_scientific_journal-3982	27	3	2𝑎𝑎𝑏𝑏	2𝑎𝑎𝑏𝑏	NUM
american_scientific_journal-3982	27	4	then	then	ADV
american_scientific_journal-3982	27	5	by	by	ADP
american_scientific_journal-3982	27	6	the	the	DET
american_scientific_journal-3982	27	7	assumption	assumption	NOUN
american_scientific_journal-3982	27	8	about	about	ADP
american_scientific_journal-3982	27	9	the	the	DET
american_scientific_journal-3982	27	10	norm	norm	NOUN
american_scientific_journal-3982	27	11	and	and	CCONJ
american_scientific_journal-3982	27	12	the	the	DET
american_scientific_journal-3982	27	13	observation	observation	NOUN
american_scientific_journal-3982	27	14	3	3	NUM
american_scientific_journal-3982	27	15	,	,	PUNCT
american_scientific_journal-3982	27	16	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-3982	27	17	>	>	X
american_scientific_journal-3982	27	18	0	0	NUM
american_scientific_journal-3982	27	19	,	,	PUNCT
american_scientific_journal-3982	27	20	if	if	SCONJ
american_scientific_journal-3982	27	21	and	and	CCONJ
american_scientific_journal-3982	27	22	only	only	ADV
american_scientific_journal-3982	27	23	if	if	SCONJ
american_scientific_journal-3982	27	24	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-3982	27	25	=	=	SYM
american_scientific_journal-3982	27	26	|𝑎𝑎𝑏𝑏|	|𝑎𝑎𝑏𝑏|	NUM
american_scientific_journal-3982	27	27	=	=	SYM
american_scientific_journal-3982	27	28	|𝑎𝑎||𝑏𝑏|	|𝑎𝑎||𝑏𝑏|	NOUN
american_scientific_journal-3982	27	29	if	if	SCONJ
american_scientific_journal-3982	27	30	and	and	CCONJ
american_scientific_journal-3982	27	31	only	only	ADV
american_scientific_journal-3982	27	32	if	if	SCONJ
american_scientific_journal-3982	27	33	0	0	NUM
american_scientific_journal-3982	27	34	<	<	X
american_scientific_journal-3982	27	35	𝜀𝜀2	𝜀𝜀2	X
american_scientific_journal-3982	27	36	−	−	PROPN
american_scientific_journal-3982	27	37	𝑏𝑏2	𝑏𝑏2	NOUN
american_scientific_journal-3982	27	38	−	−	PROPN
american_scientific_journal-3982	27	39	𝑎𝑎2	𝑎𝑎2	VERB
american_scientific_journal-3982	28	1	+	+	CCONJ
american_scientific_journal-3982	28	2	2𝑎𝑎𝑏𝑏	2𝑎𝑎𝑏𝑏	NUM
american_scientific_journal-3982	28	3	=	=	SYM
american_scientific_journal-3982	28	4	𝜀𝜀2	𝜀𝜀2	X
american_scientific_journal-3982	28	5	−	−	NOUN
american_scientific_journal-3982	28	6	|𝑏𝑏|2	|𝑏𝑏|2	PUNCT
american_scientific_journal-3982	28	7	−	−	PROPN
american_scientific_journal-3982	28	8	|𝑎𝑎|2	|𝑎𝑎|2	PUNCT
american_scientific_journal-3982	29	1	+	+	PUNCT
american_scientific_journal-3982	29	2	2|𝑎𝑎||𝑏𝑏|	2|𝑎𝑎||𝑏𝑏|	NUM
american_scientific_journal-3982	29	3	=	=	SYM
american_scientific_journal-3982	29	4	𝜀𝜀2	𝜀𝜀2	NOUN
american_scientific_journal-3982	29	5	−	−	PROPN
american_scientific_journal-3982	29	6	(	(	PUNCT
american_scientific_journal-3982	29	7	|𝑏𝑏|	|𝑏𝑏|	VERB
american_scientific_journal-3982	29	8	−	−	PROPN
american_scientific_journal-3982	29	9	|𝑎𝑎|)2	|𝑎𝑎|)2	NOUN
american_scientific_journal-3982	29	10	if	if	SCONJ
american_scientific_journal-3982	29	11	and	and	CCONJ
american_scientific_journal-3982	29	12	only	only	ADV
american_scientific_journal-3982	29	13	if	if	SCONJ
american_scientific_journal-3982	29	14	�	�	NOUN
american_scientific_journal-3982	29	15	|𝑏𝑏|	|𝑏𝑏|	NOUN
american_scientific_journal-3982	29	16	−	−	PROPN
american_scientific_journal-3982	29	17	|𝑎𝑎|	|𝑎𝑎|	PROPN
american_scientific_journal-3982	29	18	�	�	PROPN
american_scientific_journal-3982	29	19	<	<	X
american_scientific_journal-3982	29	20	𝜀𝜀	𝜀𝜀	INTJ
american_scientific_journal-3982	29	21	if	if	SCONJ
american_scientific_journal-3982	29	22	and	and	CCONJ
american_scientific_journal-3982	29	23	only	only	ADV
american_scientific_journal-3982	29	24	if	if	SCONJ
american_scientific_journal-3982	29	25	−𝜀𝜀	−𝜀𝜀	PROPN
american_scientific_journal-3982	29	26	+	+	X
american_scientific_journal-3982	29	27	|𝑎𝑎|	|𝑎𝑎|	X
american_scientific_journal-3982	29	28	<	<	X
american_scientific_journal-3982	29	29	𝑏𝑏	𝑏𝑏	NOUN
american_scientific_journal-3982	29	30	<	<	X
american_scientific_journal-3982	29	31	𝜀𝜀	𝜀𝜀	PRON
american_scientific_journal-3982	29	32	+	+	X
american_scientific_journal-3982	29	33	|𝑎𝑎|	|𝑎𝑎|	NOUN
american_scientific_journal-3982	29	34	.	.	PUNCT
american_scientific_journal-3982	30	1	reciprocally	reciprocally	ADV
american_scientific_journal-3982	30	2	,	,	PUNCT
american_scientific_journal-3982	30	3	if	if	SCONJ
american_scientific_journal-3982	30	4	0	0	NUM
american_scientific_journal-3982	30	5	<	<	X
american_scientific_journal-3982	30	6	|𝑎𝑎|	|𝑎𝑎|	PROPN
american_scientific_journal-3982	31	1	−	−	NOUN
american_scientific_journal-3982	31	2	𝜀𝜀	𝜀𝜀	INTJ
american_scientific_journal-3982	31	3	<	<	X
american_scientific_journal-3982	31	4	𝑏𝑏	𝑏𝑏	X
american_scientific_journal-3982	31	5	<	<	X
american_scientific_journal-3982	31	6	|𝑎𝑎|	|𝑎𝑎|	PROPN
american_scientific_journal-3982	32	1	+	+	CCONJ
american_scientific_journal-3982	32	2	𝜀𝜀	𝜀𝜀	INTJ
american_scientific_journal-3982	32	3	by	by	ADP
american_scientific_journal-3982	32	4	te	te	ADP
american_scientific_journal-3982	32	5	supposition	supposition	NOUN
american_scientific_journal-3982	32	6	and	and	CCONJ
american_scientific_journal-3982	32	7	the	the	DET
american_scientific_journal-3982	32	8	preceding	precede	VERB
american_scientific_journal-3982	32	9	proposition	proposition	NOUN
american_scientific_journal-3982	32	10	sgn(𝑎𝑎	sgn(𝑎𝑎	NOUN
american_scientific_journal-3982	32	11	)	)	PUNCT
american_scientific_journal-3982	32	12	=	=	SYM
american_scientific_journal-3982	32	13	sgn(𝑏𝑏	sgn(𝑏𝑏	NOUN
american_scientific_journal-3982	32	14	)	)	PUNCT
american_scientific_journal-3982	33	1	if	if	SCONJ
american_scientific_journal-3982	33	2	and	and	CCONJ
american_scientific_journal-3982	33	3	only	only	ADV
american_scientific_journal-3982	33	4	if	if	SCONJ
american_scientific_journal-3982	33	5	𝑎𝑎𝑏𝑏	𝑎𝑎𝑏𝑏	NOUN
american_scientific_journal-3982	33	6	=	=	PUNCT
american_scientific_journal-3982	33	7	|𝑎𝑎𝑏𝑏|	|𝑎𝑎𝑏𝑏|	X
american_scientific_journal-3982	33	8	if	if	SCONJ
american_scientific_journal-3982	33	9	and	and	CCONJ
american_scientific_journal-3982	33	10	only	only	ADV
american_scientific_journal-3982	33	11	if	if	SCONJ
american_scientific_journal-3982	33	12	|𝑎𝑎	|𝑎𝑎	NUM
american_scientific_journal-3982	33	13	−	−	PROPN
american_scientific_journal-3982	33	14	𝑏𝑏|	𝑏𝑏|	NOUN
american_scientific_journal-3982	33	15	<	<	X
american_scientific_journal-3982	33	16	𝜀𝜀.	𝜀𝜀.	X
american_scientific_journal-3982	33	17	we	we	PRON
american_scientific_journal-3982	33	18	will	will	AUX
american_scientific_journal-3982	33	19	consider	consider	VERB
american_scientific_journal-3982	33	20	functions	function	NOUN
american_scientific_journal-3982	33	21	defined	define	VERB
american_scientific_journal-3982	33	22	in	in	ADP
american_scientific_journal-3982	33	23	te	te	ADP
american_scientific_journal-3982	33	24	subsets	subset	NOUN
american_scientific_journal-3982	33	25	of	of	ADP
american_scientific_journal-3982	33	26	the	the	DET
american_scientific_journal-3982	33	27	interval	interval	NOUN
american_scientific_journal-3982	33	28	(	(	PUNCT
american_scientific_journal-3982	33	29	−∞	−∞	NOUN
american_scientific_journal-3982	33	30	,	,	PUNCT
american_scientific_journal-3982	33	31	+	+	NOUN
american_scientific_journal-3982	33	32	∞	∞	NOUN
american_scientific_journal-3982	33	33	)	)	PUNCT
american_scientific_journal-3982	33	34	and	and	CCONJ
american_scientific_journal-3982	33	35	with	with	ADP
american_scientific_journal-3982	33	36	the	the	DET
american_scientific_journal-3982	33	37	range	range	NOUN
american_scientific_journal-3982	33	38	in	in	ADP
american_scientific_journal-3982	33	39	the	the	DET
american_scientific_journal-3982	33	40	same	same	ADJ
american_scientific_journal-3982	33	41	interval	interval	NOUN
american_scientific_journal-3982	33	42	.	.	PUNCT
american_scientific_journal-3982	34	1	definition	definition	NOUN
american_scientific_journal-3982	34	2	6	6	NUM
american_scientific_journal-3982	34	3	.	.	PUNCT
american_scientific_journal-3982	35	1	a	a	DET
american_scientific_journal-3982	35	2	number	number	NOUN
american_scientific_journal-3982	35	3	in	in	ADP
american_scientific_journal-3982	35	4	the	the	DET
american_scientific_journal-3982	35	5	domain	domain	NOUN
american_scientific_journal-3982	35	6	of	of	ADP
american_scientific_journal-3982	35	7	a	a	DET
american_scientific_journal-3982	35	8	function	function	NOUN
american_scientific_journal-3982	35	9	is	be	AUX
american_scientific_journal-3982	35	10	said	say	VERB
american_scientific_journal-3982	35	11	to	to	PART
american_scientific_journal-3982	35	12	be	be	AUX
american_scientific_journal-3982	35	13	a	a	DET
american_scientific_journal-3982	35	14	pre	pre	NOUN
american_scientific_journal-3982	35	15	-	-	NOUN
american_scientific_journal-3982	35	16	image	image	NOUN
american_scientific_journal-3982	35	17	or	or	CCONJ
american_scientific_journal-3982	35	18	simply	simply	ADV
american_scientific_journal-3982	35	19	a	a	DET
american_scientific_journal-3982	35	20	number	number	NOUN
american_scientific_journal-3982	35	21	of	of	ADP
american_scientific_journal-3982	35	22	the	the	DET
american_scientific_journal-3982	35	23	given	give	VERB
american_scientific_journal-3982	35	24	function	function	NOUN
american_scientific_journal-3982	35	25	.	.	PUNCT
american_scientific_journal-3982	36	1	definition	definition	NOUN
american_scientific_journal-3982	36	2	7	7	NUM
american_scientific_journal-3982	36	3	.	.	PUNCT
american_scientific_journal-3982	37	1	a	a	DET
american_scientific_journal-3982	37	2	number	number	NOUN
american_scientific_journal-3982	37	3	in	in	ADP
american_scientific_journal-3982	37	4	the	the	DET
american_scientific_journal-3982	37	5	range	range	NOUN
american_scientific_journal-3982	37	6	of	of	ADP
american_scientific_journal-3982	37	7	a	a	DET
american_scientific_journal-3982	37	8	function	function	NOUN
american_scientific_journal-3982	37	9	is	be	AUX
american_scientific_journal-3982	37	10	called	call	VERB
american_scientific_journal-3982	37	11	a	a	DET
american_scientific_journal-3982	37	12	value	value	NOUN
american_scientific_journal-3982	37	13	of	of	ADP
american_scientific_journal-3982	37	14	the	the	DET
american_scientific_journal-3982	37	15	given	give	VERB
american_scientific_journal-3982	37	16	function	function	NOUN
american_scientific_journal-3982	37	17	.	.	PUNCT
american_scientific_journal-3982	38	1	definition	definition	NOUN
american_scientific_journal-3982	38	2	8	8	NUM
american_scientific_journal-3982	38	3	.	.	PUNCT
american_scientific_journal-3982	39	1	it	it	PRON
american_scientific_journal-3982	39	2	is	be	AUX
american_scientific_journal-3982	39	3	said	say	VERB
american_scientific_journal-3982	39	4	that	that	SCONJ
american_scientific_journal-3982	39	5	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	39	6	=	=	PUNCT
american_scientific_journal-3982	39	7	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	39	8	is	be	AUX
american_scientific_journal-3982	39	9	close	close	ADJ
american_scientific_journal-3982	39	10	to	to	ADP
american_scientific_journal-3982	39	11	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	39	12	if	if	SCONJ
american_scientific_journal-3982	39	13	and	and	CCONJ
american_scientific_journal-3982	40	1	only	only	ADV
american_scientific_journal-3982	40	2	if	if	SCONJ
american_scientific_journal-3982	40	3	|𝑥𝑥	|𝑥𝑥	PROPN
american_scientific_journal-3982	40	4	−	−	PROPN
american_scientific_journal-3982	40	5	𝑎𝑎|	𝑎𝑎|	PROPN
american_scientific_journal-3982	40	6	<	<	X
american_scientific_journal-3982	40	7	𝛿𝛿	𝛿𝛿	PROPN
american_scientific_journal-3982	40	8	for	for	ADP
american_scientific_journal-3982	40	9	some	some	DET
american_scientific_journal-3982	40	10	𝛿𝛿	𝛿𝛿	NOUN
american_scientific_journal-3982	40	11	=	=	SYM
american_scientific_journal-3982	40	12	𝛿𝛿(𝑎𝑎	𝛿𝛿(𝑎𝑎	PROPN
american_scientific_journal-3982	40	13	)	)	PUNCT
american_scientific_journal-3982	40	14	.	.	PUNCT
american_scientific_journal-3982	41	1	the	the	DET
american_scientific_journal-3982	41	2	functions	function	NOUN
american_scientific_journal-3982	41	3	considered	consider	VERB
american_scientific_journal-3982	41	4	here	here	ADV
american_scientific_journal-3982	41	5	do	do	AUX
american_scientific_journal-3982	41	6	not	not	PART
american_scientific_journal-3982	41	7	need	need	VERB
american_scientific_journal-3982	41	8	to	to	PART
american_scientific_journal-3982	41	9	be	be	AUX
american_scientific_journal-3982	41	10	defined	define	VERB
american_scientific_journal-3982	41	11	globally	globally	ADV
american_scientific_journal-3982	41	12	.	.	PUNCT
american_scientific_journal-3982	42	1	american	american	ADJ
american_scientific_journal-3982	42	2	scientific	scientific	ADJ
american_scientific_journal-3982	42	3	research	research	PROPN
american_scientific_journal-3982	42	4	journal	journal	NOUN
american_scientific_journal-3982	42	5	for	for	ADP
american_scientific_journal-3982	42	6	engineering	engineering	NOUN
american_scientific_journal-3982	42	7	,	,	PUNCT
american_scientific_journal-3982	42	8	technology	technology	NOUN
american_scientific_journal-3982	42	9	,	,	PUNCT
american_scientific_journal-3982	42	10	and	and	CCONJ
american_scientific_journal-3982	42	11	sciences	science	NOUN
american_scientific_journal-3982	42	12	(	(	PUNCT
american_scientific_journal-3982	42	13	asrjets	asrjet	NOUN
american_scientific_journal-3982	42	14	)	)	PUNCT
american_scientific_journal-3982	42	15	(	(	PUNCT
american_scientific_journal-3982	42	16	2018	2018	NUM
american_scientific_journal-3982	42	17	)	)	PUNCT
american_scientific_journal-3982	42	18	volume	volume	NOUN
american_scientific_journal-3982	42	19	41	41	NUM
american_scientific_journal-3982	42	20	,	,	PUNCT
american_scientific_journal-3982	42	21	no	no	DET
american_scientific_journal-3982	42	22	1	1	NUM
american_scientific_journal-3982	42	23	,	,	PUNCT
american_scientific_journal-3982	42	24	pp	pp	ADV
american_scientific_journal-3982	42	25	240	240	NUM
american_scientific_journal-3982	42	26	-	-	SYM
american_scientific_journal-3982	42	27	245	245	NUM
american_scientific_journal-3982	42	28	242	242	NUM
american_scientific_journal-3982	42	29	definition	definition	NOUN
american_scientific_journal-3982	42	30	9	9	NUM
american_scientific_journal-3982	42	31	.	.	PUNCT
american_scientific_journal-3982	43	1	a	a	DET
american_scientific_journal-3982	43	2	function	function	NOUN
american_scientific_journal-3982	43	3	is	be	AUX
american_scientific_journal-3982	43	4	said	say	VERB
american_scientific_journal-3982	43	5	to	to	PART
american_scientific_journal-3982	43	6	be	be	AUX
american_scientific_journal-3982	43	7	locally	locally	ADV
american_scientific_journal-3982	43	8	defined	define	VERB
american_scientific_journal-3982	43	9	in	in	ADP
american_scientific_journal-3982	43	10	a	a	DET
american_scientific_journal-3982	43	11	given	give	VERB
american_scientific_journal-3982	43	12	number	number	NOUN
american_scientific_journal-3982	43	13	if	if	SCONJ
american_scientific_journal-3982	43	14	it	it	PRON
american_scientific_journal-3982	43	15	is	be	AUX
american_scientific_journal-3982	43	16	defined	define	VERB
american_scientific_journal-3982	43	17	for	for	ADP
american_scientific_journal-3982	43	18	all	all	DET
american_scientific_journal-3982	43	19	pre	pre	NOUN
american_scientific_journal-3982	43	20	-	-	NOUN
american_scientific_journal-3982	43	21	images	image	NOUN
american_scientific_journal-3982	43	22	(	(	PUNCT
american_scientific_journal-3982	43	23	numbers	number	NOUN
american_scientific_journal-3982	43	24	of	of	ADP
american_scientific_journal-3982	43	25	the	the	DET
american_scientific_journal-3982	43	26	function	function	NOUN
american_scientific_journal-3982	43	27	)	)	PUNCT
american_scientific_journal-3982	43	28	close	close	ADV
american_scientific_journal-3982	43	29	to	to	ADP
american_scientific_journal-3982	43	30	the	the	DET
american_scientific_journal-3982	43	31	number	number	NOUN
american_scientific_journal-3982	43	32	𝑎𝑎.	𝑎𝑎.	PROPN
american_scientific_journal-3982	43	33	example	example	NOUN
american_scientific_journal-3982	43	34	10	10	NUM
american_scientific_journal-3982	43	35	.	.	PUNCT
american_scientific_journal-3982	44	1	the	the	DET
american_scientific_journal-3982	44	2	function	function	NOUN
american_scientific_journal-3982	44	3	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	44	4	↦	↦	PROPN
american_scientific_journal-3982	44	5	𝑠𝑠𝑠𝑠𝑠𝑠(𝑥𝑥	𝑠𝑠𝑠𝑠𝑠𝑠(𝑥𝑥	PROPN
american_scientific_journal-3982	44	6	)	)	PUNCT
american_scientific_journal-3982	44	7	is	be	AUX
american_scientific_journal-3982	44	8	locally	locally	ADV
american_scientific_journal-3982	44	9	defined	define	VERB
american_scientific_journal-3982	44	10	at	at	ADP
american_scientific_journal-3982	44	11	0	0	NUM
american_scientific_journal-3982	44	12	,	,	PUNCT
american_scientific_journal-3982	44	13	since	since	SCONJ
american_scientific_journal-3982	44	14	it	it	PRON
american_scientific_journal-3982	44	15	is	be	AUX
american_scientific_journal-3982	44	16	defined	define	VERB
american_scientific_journal-3982	44	17	for	for	ADP
american_scientific_journal-3982	44	18	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	44	19	=	=	NOUN
american_scientific_journal-3982	44	20	0	0	NUM
american_scientific_journal-3982	44	21	and	and	CCONJ
american_scientific_journal-3982	44	22	close	close	ADJ
american_scientific_journal-3982	44	23	to	to	ADP
american_scientific_journal-3982	44	24	0	0	NUM
american_scientific_journal-3982	44	25	.	.	PUNCT
american_scientific_journal-3982	45	1	definition	definition	NOUN
american_scientific_journal-3982	45	2	11	11	NUM
american_scientific_journal-3982	45	3	.	.	PUNCT
american_scientific_journal-3982	46	1	let	let	VERB
american_scientific_journal-3982	46	2	𝑠𝑠	𝑠𝑠	ADV
american_scientific_journal-3982	46	3	be	be	AUX
american_scientific_journal-3982	46	4	defined	define	VERB
american_scientific_journal-3982	46	5	locally	locally	ADV
american_scientific_journal-3982	46	6	in	in	ADP
american_scientific_journal-3982	46	7	a	a	DET
american_scientific_journal-3982	46	8	number	number	NOUN
american_scientific_journal-3982	46	9	𝑎𝑎.	𝑎𝑎.	NOUN
american_scientific_journal-3982	46	10	it	it	PRON
american_scientific_journal-3982	46	11	is	be	AUX
american_scientific_journal-3982	46	12	said	say	VERB
american_scientific_journal-3982	46	13	that	that	SCONJ
american_scientific_journal-3982	46	14	the	the	DET
american_scientific_journal-3982	46	15	limit	limit	NOUN
american_scientific_journal-3982	46	16	of	of	ADP
american_scientific_journal-3982	46	17	such	such	ADJ
american_scientific_journal-3982	46	18	function	function	NOUN
american_scientific_journal-3982	46	19	exists	exist	VERB
american_scientific_journal-3982	46	20	in	in	ADP
american_scientific_journal-3982	46	21	the	the	DET
american_scientific_journal-3982	46	22	given	give	VERB
american_scientific_journal-3982	46	23	number	number	NOUN
american_scientific_journal-3982	46	24	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	46	25	when	when	SCONJ
american_scientific_journal-3982	46	26	there	there	PRON
american_scientific_journal-3982	46	27	is	be	VERB
american_scientific_journal-3982	46	28	a	a	DET
american_scientific_journal-3982	46	29	number	number	NOUN
american_scientific_journal-3982	46	30	𝑙𝑙	𝑙𝑙	ADP
american_scientific_journal-3982	46	31	such	such	ADJ
american_scientific_journal-3982	46	32	that	that	PRON
american_scientific_journal-3982	46	33	for	for	ADP
american_scientific_journal-3982	46	34	any	any	DET
american_scientific_journal-3982	46	35	positive	positive	ADJ
american_scientific_journal-3982	46	36	number	number	NOUN
american_scientific_journal-3982	47	1	𝜀𝜀	𝜀𝜀	INTJ
american_scientific_journal-3982	47	2	there	there	ADV
american_scientific_journal-3982	47	3	exists	exist	VERB
american_scientific_journal-3982	47	4	𝛿𝛿	𝛿𝛿	NOUN
american_scientific_journal-3982	47	5	such	such	ADJ
american_scientific_journal-3982	47	6	that	that	DET
american_scientific_journal-3982	47	7	|𝑠𝑠(𝑥𝑥	|𝑠𝑠(𝑥𝑥	NOUN
american_scientific_journal-3982	47	8	)	)	PUNCT
american_scientific_journal-3982	47	9	−	−	PROPN
american_scientific_journal-3982	48	1	𝑙𝑙|	𝑙𝑙|	NOUN
american_scientific_journal-3982	48	2	<	<	X
american_scientific_journal-3982	48	3	𝜀𝜀	𝜀𝜀	INTJ
american_scientific_journal-3982	48	4	provided	provide	VERB
american_scientific_journal-3982	48	5	that	that	SCONJ
american_scientific_journal-3982	48	6	|𝑥𝑥	|𝑥𝑥	NOUN
american_scientific_journal-3982	48	7	−	−	PROPN
american_scientific_journal-3982	48	8	𝑎𝑎|	𝑎𝑎|	PROPN
american_scientific_journal-3982	48	9	<	<	X
american_scientific_journal-3982	48	10	𝛿𝛿	𝛿𝛿	PROPN
american_scientific_journal-3982	48	11	:	:	PUNCT
american_scientific_journal-3982	48	12	the	the	DET
american_scientific_journal-3982	48	13	values	value	NOUN
american_scientific_journal-3982	48	14	of	of	ADP
american_scientific_journal-3982	48	15	𝑠𝑠	𝑠𝑠	ADV
american_scientific_journal-3982	48	16	are	be	AUX
american_scientific_journal-3982	48	17	arbitrarily	arbitrarily	ADV
american_scientific_journal-3982	48	18	close	close	ADJ
american_scientific_journal-3982	48	19	to	to	PART
american_scientific_journal-3982	48	20	𝑙𝑙	𝑙𝑙	VERB
american_scientific_journal-3982	48	21	for	for	ADP
american_scientific_journal-3982	48	22	all	all	DET
american_scientific_journal-3982	48	23	the	the	DET
american_scientific_journal-3982	48	24	numbers	number	NOUN
american_scientific_journal-3982	48	25	of	of	ADP
american_scientific_journal-3982	48	26	the	the	DET
american_scientific_journal-3982	48	27	function	function	NOUN
american_scientific_journal-3982	48	28	sufficiently	sufficiently	ADV
american_scientific_journal-3982	48	29	close	close	ADJ
american_scientific_journal-3982	48	30	to	to	ADP
american_scientific_journal-3982	48	31	𝑎𝑎.	𝑎𝑎.	NOUN
american_scientific_journal-3982	48	32	remark	remark	NOUN
american_scientific_journal-3982	48	33	12	12	NUM
american_scientific_journal-3982	48	34	.	.	PUNCT
american_scientific_journal-3982	49	1	if	if	SCONJ
american_scientific_journal-3982	49	2	𝑙𝑙𝑠𝑠𝑙𝑙	𝑙𝑙𝑠𝑠𝑙𝑙	PROPN
american_scientific_journal-3982	49	3	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PRON
american_scientific_journal-3982	49	4	𝑓𝑓(𝑥𝑥	𝑓𝑓(𝑥𝑥	PROPN
american_scientific_journal-3982	49	5	)	)	PUNCT
american_scientific_journal-3982	49	6	exists	exist	VERB
american_scientific_journal-3982	49	7	,	,	PUNCT
american_scientific_journal-3982	49	8	then	then	ADV
american_scientific_journal-3982	49	9	𝑓𝑓(𝑥𝑥	𝑓𝑓(𝑥𝑥	PROPN
american_scientific_journal-3982	49	10	)	)	PUNCT
american_scientific_journal-3982	50	1	=	=	PROPN
american_scientific_journal-3982	50	2	�	�	PROPN
american_scientific_journal-3982	50	3	𝑓𝑓(𝑥𝑥	𝑓𝑓(𝑥𝑥	PROPN
american_scientific_journal-3982	50	4	)	)	PUNCT
american_scientific_journal-3982	50	5	,	,	PUNCT
american_scientific_journal-3982	50	6	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	50	7	=	=	PUNCT
american_scientific_journal-3982	50	8	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	50	9	𝑙𝑙𝑠𝑠𝑙𝑙	𝑙𝑙𝑠𝑠𝑙𝑙	PROPN
american_scientific_journal-3982	50	10	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	NOUN
american_scientific_journal-3982	50	11	𝑓𝑓(𝑥𝑥	𝑓𝑓(𝑥𝑥	PROPN
american_scientific_journal-3982	50	12	)	)	PUNCT
american_scientific_journal-3982	50	13	,	,	PUNCT
american_scientific_journal-3982	50	14	𝑥𝑥	𝑥𝑥	SCONJ
american_scientific_journal-3982	50	15	=	=	SYM
american_scientific_journal-3982	50	16	𝑎𝑎.	𝑎𝑎.	PROPN
american_scientific_journal-3982	50	17	is	be	AUX
american_scientific_journal-3982	50	18	continuous	continuous	ADJ
american_scientific_journal-3982	50	19	at	at	ADP
american_scientific_journal-3982	50	20	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	50	21	in	in	ADP
american_scientific_journal-3982	50	22	which	which	DET
american_scientific_journal-3982	50	23	case	case	NOUN
american_scientific_journal-3982	50	24	it	it	PRON
american_scientific_journal-3982	50	25	is	be	AUX
american_scientific_journal-3982	50	26	asserted	assert	VERB
american_scientific_journal-3982	50	27	that	that	SCONJ
american_scientific_journal-3982	50	28	𝑓𝑓	𝑓𝑓	NOUN
american_scientific_journal-3982	50	29	is	be	AUX
american_scientific_journal-3982	50	30	continuously	continuously	ADV
american_scientific_journal-3982	50	31	extended	extend	VERB
american_scientific_journal-3982	50	32	to	to	ADP
american_scientific_journal-3982	50	33	𝑎𝑎.	𝑎𝑎.	NOUN
american_scientific_journal-3982	50	34	definition	definition	NOUN
american_scientific_journal-3982	50	35	13.the	13.the	DET
american_scientific_journal-3982	50	36	derivation	derivation	NOUN
american_scientific_journal-3982	50	37	quotient	quotient	NOUN
american_scientific_journal-3982	50	38	of	of	ADP
american_scientific_journal-3982	50	39	a	a	DET
american_scientific_journal-3982	50	40	function	function	NOUN
american_scientific_journal-3982	50	41	𝑓𝑓	𝑓𝑓	ADP
american_scientific_journal-3982	50	42	locally	locally	ADV
american_scientific_journal-3982	50	43	defined	define	VERB
american_scientific_journal-3982	50	44	at	at	ADP
american_scientific_journal-3982	50	45	the	the	DET
american_scientific_journal-3982	50	46	number	number	NOUN
american_scientific_journal-3982	50	47	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	50	48	is	be	AUX
american_scientific_journal-3982	50	49	the	the	DET
american_scientific_journal-3982	50	50	ratio	ratio	NOUN
american_scientific_journal-3982	50	51	of	of	ADP
american_scientific_journal-3982	50	52	differences	difference	NOUN
american_scientific_journal-3982	50	53	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	50	54	)	)	PUNCT
american_scientific_journal-3982	50	55	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	X
american_scientific_journal-3982	50	56	.	.	PUNCT
american_scientific_journal-3982	51	1	proposition	proposition	NOUN
american_scientific_journal-3982	51	2	14	14	NUM
american_scientific_journal-3982	51	3	.	.	PUNCT
american_scientific_journal-3982	52	1	there	there	PRON
american_scientific_journal-3982	52	2	exists	exist	VERB
american_scientific_journal-3982	52	3	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	PROPN
american_scientific_journal-3982	52	4	)	)	PUNCT
american_scientific_journal-3982	52	5	and	and	CCONJ
american_scientific_journal-3982	52	6	it	it	PRON
american_scientific_journal-3982	52	7	is	be	AUX
american_scientific_journal-3982	52	8	not	not	PART
american_scientific_journal-3982	52	9	null	null	ADJ
american_scientific_journal-3982	52	10	if	if	SCONJ
american_scientific_journal-3982	52	11	and	and	CCONJ
american_scientific_journal-3982	52	12	only	only	ADV
american_scientific_journal-3982	52	13	if	if	SCONJ
american_scientific_journal-3982	52	14	there	there	PRON
american_scientific_journal-3982	52	15	exists	exist	VERB
american_scientific_journal-3982	52	16	�	�	PROPN
american_scientific_journal-3982	52	17	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	52	18	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	52	19	)	)	PUNCT
american_scientific_journal-3982	52	20	�	�	PROPN
american_scientific_journal-3982	52	21	(	(	PUNCT
american_scientific_journal-3982	52	22	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	52	23	)	)	PUNCT
american_scientific_journal-3982	52	24	and	and	CCONJ
american_scientific_journal-3982	52	25	it	it	PRON
american_scientific_journal-3982	52	26	is	be	AUX
american_scientific_journal-3982	52	27	null	null	ADJ
american_scientific_journal-3982	52	28	.	.	PUNCT
american_scientific_journal-3982	53	1	proof	proof	NOUN
american_scientific_journal-3982	53	2	.	.	PUNCT
american_scientific_journal-3982	54	1	by	by	ADP
american_scientific_journal-3982	54	2	the	the	DET
american_scientific_journal-3982	54	3	definition	definition	NOUN
american_scientific_journal-3982	54	4	of	of	ADP
american_scientific_journal-3982	54	5	derivative	derivative	NOUN
american_scientific_journal-3982	54	6	:	:	PUNCT
american_scientific_journal-3982	54	7	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	NUM
american_scientific_journal-3982	54	8	)	)	PUNCT
american_scientific_journal-3982	54	9	=	=	SYM
american_scientific_journal-3982	54	10	lim	lim	PROPN
american_scientific_journal-3982	54	11	𝑥𝑥↦𝑎𝑎	𝑥𝑥↦𝑎𝑎	PROPN
american_scientific_journal-3982	54	12	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	54	13	)	)	PUNCT
american_scientific_journal-3982	54	14	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	54	15	and	and	CCONJ
american_scientific_journal-3982	54	16	by	by	ADP
american_scientific_journal-3982	54	17	the	the	DET
american_scientific_journal-3982	54	18	definition	definition	NOUN
american_scientific_journal-3982	54	19	of	of	ADP
american_scientific_journal-3982	54	20	limit	limit	NOUN
american_scientific_journal-3982	54	21	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	54	22	↦	↦	PROPN
american_scientific_journal-3982	54	23	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	54	24	)	)	PUNCT
american_scientific_journal-3982	54	25	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	PROPN
american_scientific_journal-3982	55	1	it	it	PRON
american_scientific_journal-3982	55	2	is	be	AUX
american_scientific_journal-3982	55	3	locally	locally	ADV
american_scientific_journal-3982	55	4	defined	define	VERB
american_scientific_journal-3982	55	5	at	at	ADP
american_scientific_journal-3982	55	6	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	55	7	and	and	CCONJ
american_scientific_journal-3982	55	8	�	�	NOUN
american_scientific_journal-3982	55	9	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	55	10	)	)	PUNCT
american_scientific_journal-3982	55	11	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	55	12	−	−	ADP
american_scientific_journal-3982	55	13	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	NUM
american_scientific_journal-3982	55	14	)	)	PUNCT
american_scientific_journal-3982	55	15	�	�	PROPN
american_scientific_journal-3982	55	16	<	<	X
american_scientific_journal-3982	55	17	𝜀𝜀	𝜀𝜀	INTJ
american_scientific_journal-3982	55	18	for	for	ADP
american_scientific_journal-3982	55	19	any	any	PRON
american_scientific_journal-3982	55	20	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	55	21	sufficiently	sufficiently	ADV
american_scientific_journal-3982	55	22	close	close	ADJ
american_scientific_journal-3982	55	23	to	to	ADP
american_scientific_journal-3982	55	24	𝑎𝑎.	𝑎𝑎.	NOUN
american_scientific_journal-3982	55	25	by	by	ADP
american_scientific_journal-3982	55	26	proposition	proposition	NOUN
american_scientific_journal-3982	55	27	6	6	NUM
american_scientific_journal-3982	55	28	we	we	PRON
american_scientific_journal-3982	55	29	have	have	VERB
american_scientific_journal-3982	55	30	that	that	SCONJ
american_scientific_journal-3982	55	31	if	if	SCONJ
american_scientific_journal-3982	55	32	𝜀𝜀	𝜀𝜀	PRON
american_scientific_journal-3982	55	33	<	<	X
american_scientific_journal-3982	55	34	|𝑠𝑠′(𝑎𝑎)|	|𝑠𝑠′(𝑎𝑎)|	PROPN
american_scientific_journal-3982	55	35	,	,	PUNCT
american_scientific_journal-3982	55	36	then	then	ADV
american_scientific_journal-3982	55	37	0	0	NUM
american_scientific_journal-3982	55	38	<	<	X
american_scientific_journal-3982	55	39	|𝑠𝑠′(𝑎𝑎)|	|𝑠𝑠′(𝑎𝑎)|	ADV
american_scientific_journal-3982	55	40	−	−	ADP
american_scientific_journal-3982	55	41	𝜀𝜀	𝜀𝜀	INTJ
american_scientific_journal-3982	55	42	<	<	X
american_scientific_journal-3982	55	43	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	55	44	)	)	PUNCT
american_scientific_journal-3982	55	45	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	55	46	for	for	ADP
american_scientific_journal-3982	55	47	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	55	48	sufficiently	sufficiently	ADV
american_scientific_journal-3982	55	49	close	close	ADJ
american_scientific_journal-3982	55	50	to	to	ADP
american_scientific_journal-3982	55	51	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	55	52	.	.	PUNCT
american_scientific_journal-3982	56	1	consequently	consequently	ADV
american_scientific_journal-3982	56	2	,	,	PUNCT
american_scientific_journal-3982	56	3	the	the	DET
american_scientific_journal-3982	56	4	quotient	quotient	NOUN
american_scientific_journal-3982	56	5	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	56	6	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	56	7	)	)	PUNCT
american_scientific_journal-3982	56	8	is	be	AUX
american_scientific_journal-3982	56	9	defined	define	VERB
american_scientific_journal-3982	56	10	for	for	ADP
american_scientific_journal-3982	56	11	esta	esta	NOUN
american_scientific_journal-3982	56	12	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	56	13	sufficiently	sufficiently	ADV
american_scientific_journal-3982	56	14	close	close	ADJ
american_scientific_journal-3982	56	15	to	to	ADP
american_scientific_journal-3982	56	16	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	56	17	.	.	PUNCT
american_scientific_journal-3982	57	1	by	by	ADP
american_scientific_journal-3982	57	2	the	the	DET
american_scientific_journal-3982	57	3	definition	definition	NOUN
american_scientific_journal-3982	57	4	of	of	ADP
american_scientific_journal-3982	57	5	derivative	derivative	NOUN
american_scientific_journal-3982	57	6	:	:	PUNCT
american_scientific_journal-3982	57	7	�	�	PROPN
american_scientific_journal-3982	57	8	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	57	9	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	57	10	)	)	PUNCT
american_scientific_journal-3982	57	11	�	�	PROPN
american_scientific_journal-3982	57	12	=	=	SYM
american_scientific_journal-3982	57	13	lim	lim	PROPN
american_scientific_journal-3982	57	14	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PRON
american_scientific_journal-3982	57	15	�	�	PROPN
american_scientific_journal-3982	57	16	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	ADV
american_scientific_journal-3982	57	17	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎)−lim𝑥𝑥→𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎)−lim𝑥𝑥→𝑎𝑎	X
american_scientific_journal-3982	57	18	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	X
american_scientific_journal-3982	57	19	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	57	20	)	)	PUNCT
american_scientific_journal-3982	57	21	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	PROPN
american_scientific_journal-3982	57	22	�	�	PROPN
american_scientific_journal-3982	57	23	=	=	SYM
american_scientific_journal-3982	57	24	lim	lim	PROPN
american_scientific_journal-3982	57	25	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PRON
american_scientific_journal-3982	57	26	�	�	PROPN
american_scientific_journal-3982	57	27	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	PART
american_scientific_journal-3982	57	28	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎)−lim𝑥𝑥→𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎)−lim𝑥𝑥→𝑎𝑎	X
american_scientific_journal-3982	57	29	1	1	NUM
american_scientific_journal-3982	57	30	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	57	31	)	)	PUNCT
american_scientific_journal-3982	57	32	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	57	33	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	X
american_scientific_journal-3982	57	34	�	�	PROPN
american_scientific_journal-3982	57	35	=	=	SYM
american_scientific_journal-3982	57	36	lim	lim	PROPN
american_scientific_journal-3982	57	37	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	57	38	⎝	⎝	PROPN
american_scientific_journal-3982	57	39	⎜⎜	⎜⎜	NOUN
american_scientific_journal-3982	57	40	⎛	⎛	NOUN
american_scientific_journal-3982	57	41	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	57	42	−	−	PROPN
american_scientific_journal-3982	57	43	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	57	44	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	NOUN
american_scientific_journal-3982	57	45	)	)	PUNCT
american_scientific_journal-3982	57	46	−	−	PROPN
american_scientific_journal-3982	57	47	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	57	48	)	)	PUNCT
american_scientific_journal-3982	57	49	−	−	PROPN
american_scientific_journal-3982	57	50	1	1	NUM
american_scientific_journal-3982	57	51	lim	lim	PROPN
american_scientific_journal-3982	57	52	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	57	53	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	PROPN
american_scientific_journal-3982	57	54	)	)	PUNCT
american_scientific_journal-3982	57	55	−	−	PROPN
american_scientific_journal-3982	58	1	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	58	2	)	)	PUNCT
american_scientific_journal-3982	58	3	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	58	4	−	−	NOUN
american_scientific_journal-3982	58	5	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	58	6	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	58	7	−	−	NOUN
american_scientific_journal-3982	58	8	𝑎𝑎	𝑎𝑎	ADJ
american_scientific_journal-3982	58	9	⎠	⎠	NOUN
american_scientific_journal-3982	58	10	⎟⎟	⎟⎟	NOUN
american_scientific_journal-3982	58	11	⎞	⎞	NOUN
american_scientific_journal-3982	58	12	=	=	SYM
american_scientific_journal-3982	58	13	lim	lim	PROPN
american_scientific_journal-3982	58	14	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PRON
american_scientific_journal-3982	58	15	�	�	PROPN
american_scientific_journal-3982	58	16	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	58	17	−	−	PROPN
american_scientific_journal-3982	58	18	𝑎𝑎	𝑎𝑎	ADJ
american_scientific_journal-3982	58	19	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	NOUN
american_scientific_journal-3982	58	20	)	)	PUNCT
american_scientific_journal-3982	59	1	−	−	PROPN
american_scientific_journal-3982	60	1	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	60	2	)	)	PUNCT
american_scientific_journal-3982	60	3	−	−	PROPN
american_scientific_journal-3982	60	4	1	1	NUM
american_scientific_journal-3982	60	5	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	NOUN
american_scientific_journal-3982	60	6	)	)	PUNCT
american_scientific_journal-3982	60	7	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	60	8	−	−	PROPN
american_scientific_journal-3982	60	9	𝑎𝑎	𝑎𝑎	PUNCT
american_scientific_journal-3982	60	10	�	�	PROPN
american_scientific_journal-3982	60	11	=	=	SYM
american_scientific_journal-3982	60	12	lim	lim	PROPN
american_scientific_journal-3982	60	13	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	60	14	⎝	⎝	NUM
american_scientific_journal-3982	60	15	⎜	⎜	PROPN
american_scientific_journal-3982	60	16	⎛	⎛	NOUN
american_scientific_journal-3982	60	17	(	(	PUNCT
american_scientific_journal-3982	60	18	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	60	19	−	−	PROPN
american_scientific_journal-3982	60	20	𝑎𝑎)𝑠𝑠′(𝑎𝑎	𝑎𝑎)𝑠𝑠′(𝑎𝑎	NOUN
american_scientific_journal-3982	60	21	)	)	PUNCT
american_scientific_journal-3982	60	22	−	−	PROPN
american_scientific_journal-3982	60	23	�	�	PROPN
american_scientific_journal-3982	60	24	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	PROPN
american_scientific_journal-3982	60	25	)	)	PUNCT
american_scientific_journal-3982	60	26	−	−	PROPN
american_scientific_journal-3982	60	27	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	60	28	)	)	PUNCT
american_scientific_journal-3982	60	29	�	�	PROPN
american_scientific_journal-3982	60	30	�	�	PROPN
american_scientific_journal-3982	60	31	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	PROPN
american_scientific_journal-3982	60	32	)	)	PUNCT
american_scientific_journal-3982	60	33	−	−	PROPN
american_scientific_journal-3982	60	34	𝑠𝑠(𝑎𝑎)	𝑠𝑠(𝑎𝑎)	PROPN
american_scientific_journal-3982	60	35	�	�	PROPN
american_scientific_journal-3982	60	36	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	PROPN
american_scientific_journal-3982	60	37	)	)	PUNCT
american_scientific_journal-3982	60	38	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	60	39	−	−	NOUN
american_scientific_journal-3982	60	40	𝑎𝑎	𝑎𝑎	ADJ
american_scientific_journal-3982	60	41	⎠	⎠	NOUN
american_scientific_journal-3982	60	42	⎟	⎟	X
american_scientific_journal-3982	60	43	⎞	⎞	PROPN
american_scientific_journal-3982	61	1	=	=	VERB
american_scientific_journal-3982	61	2	lim	lim	PROPN
american_scientific_journal-3982	61	3	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	61	4	⎝	⎝	PUNCT
american_scientific_journal-3982	61	5	⎜	⎜	PROPN
american_scientific_journal-3982	61	6	⎛	⎛	NOUN
american_scientific_journal-3982	61	7	(	(	PUNCT
american_scientific_journal-3982	61	8	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	61	9	−	−	PROPN
american_scientific_journal-3982	61	10	𝑎𝑎)𝑠𝑠′(𝑎𝑎	𝑎𝑎)𝑠𝑠′(𝑎𝑎	NOUN
american_scientific_journal-3982	61	11	)	)	PUNCT
american_scientific_journal-3982	61	12	−	−	PROPN
american_scientific_journal-3982	61	13	�	�	PROPN
american_scientific_journal-3982	61	14	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	PROPN
american_scientific_journal-3982	61	15	)	)	PUNCT
american_scientific_journal-3982	61	16	−	−	PROPN
american_scientific_journal-3982	61	17	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	61	18	)	)	PUNCT
american_scientific_journal-3982	61	19	�	�	PROPN
american_scientific_journal-3982	61	20	�	�	PROPN
american_scientific_journal-3982	61	21	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	PROPN
american_scientific_journal-3982	61	22	)	)	PUNCT
american_scientific_journal-3982	61	23	−	−	PROPN
american_scientific_journal-3982	62	1	𝑠𝑠(𝑎𝑎)	𝑠𝑠(𝑎𝑎)	PROPN
american_scientific_journal-3982	62	2	�	�	PROPN
american_scientific_journal-3982	62	3	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	PROPN
american_scientific_journal-3982	62	4	)	)	PUNCT
american_scientific_journal-3982	62	5	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	62	6	−	−	NOUN
american_scientific_journal-3982	62	7	𝑎𝑎	𝑎𝑎	ADJ
american_scientific_journal-3982	62	8	⎠	⎠	NOUN
american_scientific_journal-3982	62	9	⎟	⎟	X
american_scientific_journal-3982	62	10	⎞	⎞	PROPN
american_scientific_journal-3982	63	1	=	=	VERB
american_scientific_journal-3982	63	2	lim	lim	PROPN
american_scientific_journal-3982	63	3	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	63	4	⎝	⎝	PUNCT
american_scientific_journal-3982	63	5	⎜	⎜	PROPN
american_scientific_journal-3982	63	6	⎛	⎛	NOUN
american_scientific_journal-3982	63	7	(	(	PUNCT
american_scientific_journal-3982	63	8	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	63	9	−	−	NOUN
american_scientific_journal-3982	63	10	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	63	11	)	)	PUNCT
american_scientific_journal-3982	63	12	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	PROPN
american_scientific_journal-3982	63	13	)	)	PUNCT
american_scientific_journal-3982	63	14	−	−	PROPN
american_scientific_journal-3982	63	15	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	NOUN
american_scientific_journal-3982	63	16	)	)	PUNCT
american_scientific_journal-3982	63	17	−	−	PROPN
american_scientific_journal-3982	64	1	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	64	2	)	)	PUNCT
american_scientific_journal-3982	64	3	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	64	4	−	−	PROPN
american_scientific_journal-3982	64	5	𝑎𝑎	𝑎𝑎	ADJ
american_scientific_journal-3982	64	6	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	NOUN
american_scientific_journal-3982	64	7	)	)	PUNCT
american_scientific_journal-3982	64	8	−	−	PROPN
american_scientific_journal-3982	64	9	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	64	10	)	)	PUNCT
american_scientific_journal-3982	64	11	(	(	PUNCT
american_scientific_journal-3982	64	12	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	64	13	−	−	NOUN
american_scientific_journal-3982	64	14	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	64	15	)	)	PUNCT
american_scientific_journal-3982	64	16	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	NOUN
american_scientific_journal-3982	64	17	)	)	PUNCT
american_scientific_journal-3982	64	18	⎠	⎠	NOUN
american_scientific_journal-3982	65	1	⎟	⎟	X
american_scientific_journal-3982	65	2	⎞	⎞	VERB
american_scientific_journal-3982	65	3	=	=	VERB
american_scientific_journal-3982	65	4	lim	lim	PROPN
american_scientific_journal-3982	65	5	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	65	6	⎝	⎝	PUNCT
american_scientific_journal-3982	65	7	⎜	⎜	PROPN
american_scientific_journal-3982	65	8	⎛	⎛	NOUN
american_scientific_journal-3982	65	9	(	(	PUNCT
american_scientific_journal-3982	65	10	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	65	11	−	−	NOUN
american_scientific_journal-3982	65	12	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	65	13	)	)	PUNCT
american_scientific_journal-3982	65	14	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	PROPN
american_scientific_journal-3982	65	15	)	)	PUNCT
american_scientific_journal-3982	65	16	−	−	PROPN
american_scientific_journal-3982	65	17	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	NOUN
american_scientific_journal-3982	65	18	)	)	PUNCT
american_scientific_journal-3982	65	19	−	−	PROPN
american_scientific_journal-3982	65	20	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	65	21	)	)	PUNCT
american_scientific_journal-3982	65	22	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	65	23	−	−	PROPN
american_scientific_journal-3982	65	24	𝑎𝑎	𝑎𝑎	ADJ
american_scientific_journal-3982	65	25	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	NOUN
american_scientific_journal-3982	65	26	)	)	PUNCT
american_scientific_journal-3982	65	27	−	−	PROPN
american_scientific_journal-3982	65	28	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	65	29	)	)	PUNCT
american_scientific_journal-3982	65	30	(	(	PUNCT
american_scientific_journal-3982	65	31	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	65	32	−	−	NOUN
american_scientific_journal-3982	65	33	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	65	34	)	)	PUNCT
american_scientific_journal-3982	65	35	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	NOUN
american_scientific_journal-3982	65	36	)	)	PUNCT
american_scientific_journal-3982	65	37	⎠	⎠	NOUN
american_scientific_journal-3982	65	38	⎟	⎟	X
american_scientific_journal-3982	65	39	⎞	⎞	VERB
american_scientific_journal-3982	65	40	=	=	VERB
american_scientific_journal-3982	65	41	lim	lim	PROPN
american_scientific_journal-3982	65	42	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	X
american_scientific_journal-3982	65	43	(	(	PUNCT
american_scientific_journal-3982	65	44	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	65	45	−	−	PROPN
american_scientific_journal-3982	65	46	𝑎𝑎)lim	𝑎𝑎)lim	X
american_scientific_journal-3982	65	47	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	X
american_scientific_journal-3982	65	48	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	NUM
american_scientific_journal-3982	65	49	)	)	PUNCT
american_scientific_journal-3982	65	50	−	−	PROPN
american_scientific_journal-3982	65	51	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	NOUN
american_scientific_journal-3982	65	52	)	)	PUNCT
american_scientific_journal-3982	65	53	−	−	PROPN
american_scientific_journal-3982	65	54	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	65	55	)	)	PUNCT
american_scientific_journal-3982	65	56	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	65	57	−	−	PROPN
american_scientific_journal-3982	65	58	𝑎𝑎	𝑎𝑎	ADJ
american_scientific_journal-3982	65	59	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	NOUN
american_scientific_journal-3982	65	60	)	)	PUNCT
american_scientific_journal-3982	65	61	−	−	PROPN
american_scientific_journal-3982	66	1	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	66	2	)	)	PUNCT
american_scientific_journal-3982	66	3	(	(	PUNCT
american_scientific_journal-3982	66	4	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	66	5	−	−	NOUN
american_scientific_journal-3982	66	6	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	66	7	)	)	PUNCT
american_scientific_journal-3982	66	8	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	PROPN
american_scientific_journal-3982	66	9	)	)	PUNCT
american_scientific_journal-3982	66	10	=	=	SYM
american_scientific_journal-3982	66	11	0	0	NUM
american_scientific_journal-3982	66	12	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	NUM
american_scientific_journal-3982	66	13	)	)	PUNCT
american_scientific_journal-3982	66	14	−	−	PROPN
american_scientific_journal-3982	66	15	lim	lim	PROPN
american_scientific_journal-3982	66	16	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	66	17	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	PROPN
american_scientific_journal-3982	66	18	)	)	PUNCT
american_scientific_journal-3982	66	19	−	−	PROPN
american_scientific_journal-3982	66	20	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	66	21	)	)	PUNCT
american_scientific_journal-3982	66	22	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	66	23	−	−	PROPN
american_scientific_journal-3982	66	24	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	66	25	�	�	PROPN
american_scientific_journal-3982	66	26	lim	lim	PROPN
american_scientific_journal-3982	66	27	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	66	28	𝑠𝑠(𝑥𝑥	𝑠𝑠(𝑥𝑥	PROPN
american_scientific_journal-3982	66	29	)	)	PUNCT
american_scientific_journal-3982	66	30	−	−	PROPN
american_scientific_journal-3982	67	1	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	67	2	)	)	PUNCT
american_scientific_journal-3982	67	3	(	(	PUNCT
american_scientific_journal-3982	67	4	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	67	5	−	−	NOUN
american_scientific_journal-3982	67	6	𝑎𝑎	𝑎𝑎	PROPN
american_scientific_journal-3982	67	7	)	)	PUNCT
american_scientific_journal-3982	67	8	�	�	PROPN
american_scientific_journal-3982	67	9	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	PROPN
american_scientific_journal-3982	67	10	)	)	PUNCT
american_scientific_journal-3982	67	11	=	=	SYM
american_scientific_journal-3982	67	12	0	0	NUM
american_scientific_journal-3982	67	13	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	NUM
american_scientific_journal-3982	67	14	)	)	PUNCT
american_scientific_journal-3982	67	15	−	−	PROPN
american_scientific_journal-3982	67	16	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	PROPN
american_scientific_journal-3982	67	17	)	)	PUNCT
american_scientific_journal-3982	67	18	𝑠𝑠′(𝑎𝑎)𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎)𝑠𝑠′(𝑎𝑎	PROPN
american_scientific_journal-3982	67	19	)	)	PUNCT
american_scientific_journal-3982	67	20	=	=	SYM
american_scientific_journal-3982	67	21	0(0	0(0	NUM
american_scientific_journal-3982	67	22	)	)	PUNCT
american_scientific_journal-3982	68	1	=	=	SYM
american_scientific_journal-3982	68	2	0	0	NUM
american_scientific_journal-3982	68	3	american	american	ADJ
american_scientific_journal-3982	68	4	scientific	scientific	ADJ
american_scientific_journal-3982	68	5	research	research	NOUN
american_scientific_journal-3982	68	6	journal	journal	NOUN
american_scientific_journal-3982	68	7	for	for	ADP
american_scientific_journal-3982	68	8	engineering	engineering	NOUN
american_scientific_journal-3982	68	9	,	,	PUNCT
american_scientific_journal-3982	68	10	technology	technology	NOUN
american_scientific_journal-3982	68	11	,	,	PUNCT
american_scientific_journal-3982	68	12	and	and	CCONJ
american_scientific_journal-3982	68	13	sciences	science	NOUN
american_scientific_journal-3982	68	14	(	(	PUNCT
american_scientific_journal-3982	68	15	asrjets	asrjet	NOUN
american_scientific_journal-3982	68	16	)	)	PUNCT
american_scientific_journal-3982	68	17	(	(	PUNCT
american_scientific_journal-3982	68	18	2018	2018	NUM
american_scientific_journal-3982	68	19	)	)	PUNCT
american_scientific_journal-3982	68	20	volume	volume	NOUN
american_scientific_journal-3982	68	21	41	41	NUM
american_scientific_journal-3982	68	22	,	,	PUNCT
american_scientific_journal-3982	68	23	no	no	DET
american_scientific_journal-3982	68	24	1	1	NUM
american_scientific_journal-3982	68	25	,	,	PUNCT
american_scientific_journal-3982	68	26	pp	pp	ADV
american_scientific_journal-3982	68	27	240	240	NUM
american_scientific_journal-3982	68	28	-	-	SYM
american_scientific_journal-3982	68	29	245	245	NUM
american_scientific_journal-3982	68	30	243	243	NUM
american_scientific_journal-3982	68	31	reciprocally	reciprocally	ADV
american_scientific_journal-3982	68	32	,	,	PUNCT
american_scientific_journal-3982	68	33	by	by	ADP
american_scientific_journal-3982	68	34	te	te	ADP
american_scientific_journal-3982	68	35	definition	definition	NOUN
american_scientific_journal-3982	68	36	of	of	ADP
american_scientific_journal-3982	68	37	�	�	PROPN
american_scientific_journal-3982	68	38	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	68	39	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	68	40	)	)	PUNCT
american_scientific_journal-3982	68	41	�	�	PROPN
american_scientific_journal-3982	68	42	(	(	PUNCT
american_scientific_journal-3982	68	43	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	68	44	)	)	PUNCT
american_scientific_journal-3982	68	45	and	and	CCONJ
american_scientific_journal-3982	68	46	the	the	DET
american_scientific_journal-3982	68	47	definition	definition	NOUN
american_scientific_journal-3982	68	48	of	of	ADP
american_scientific_journal-3982	68	49	limit	limit	NOUN
american_scientific_journal-3982	68	50	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	68	51	→	→	SYM
american_scientific_journal-3982	68	52	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	ADJ
american_scientific_journal-3982	68	53	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎)−	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎)−	ADJ
american_scientific_journal-3982	68	54	1	1	NUM
american_scientific_journal-3982	68	55	lim𝑥𝑥→𝑎𝑎	lim𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	68	56	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	68	57	)	)	PUNCT
american_scientific_journal-3982	68	58	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	68	59	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	X
american_scientific_journal-3982	69	1	it	it	PRON
american_scientific_journal-3982	69	2	is	be	AUX
american_scientific_journal-3982	69	3	definied	definie	VERB
american_scientific_journal-3982	69	4	and	and	CCONJ
american_scientific_journal-3982	69	5	�	�	PROPN
american_scientific_journal-3982	69	6	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	ADV
american_scientific_journal-3982	69	7	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎)−lim𝑥𝑥→𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎)−lim𝑥𝑥→𝑎𝑎	X
american_scientific_journal-3982	69	8	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	X
american_scientific_journal-3982	69	9	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	69	10	)	)	PUNCT
american_scientific_journal-3982	69	11	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	PROPN
american_scientific_journal-3982	69	12	�	�	PROPN
american_scientific_journal-3982	69	13	<	<	X
american_scientific_journal-3982	69	14	𝜀𝜀	𝜀𝜀	INTJ
american_scientific_journal-3982	69	15	for	for	ADP
american_scientific_journal-3982	69	16	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	69	17	sufficiently	sufficiently	ADV
american_scientific_journal-3982	69	18	close	close	ADJ
american_scientific_journal-3982	69	19	to	to	ADP
american_scientific_journal-3982	69	20	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	69	21	if	if	SCONJ
american_scientific_journal-3982	69	22	and	and	CCONJ
american_scientific_journal-3982	69	23	only	only	ADV
american_scientific_journal-3982	69	24	if	if	SCONJ
american_scientific_journal-3982	69	25	there	there	PRON
american_scientific_journal-3982	69	26	existslim	existslim	VERB
american_scientific_journal-3982	69	27	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	NOUN
american_scientific_journal-3982	69	28	1	1	NUM
american_scientific_journal-3982	69	29	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	69	30	)	)	PUNCT
american_scientific_journal-3982	69	31	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	70	1	=	=	SYM
american_scientific_journal-3982	70	2	1	1	NUM
american_scientific_journal-3982	70	3	lim	lim	PROPN
american_scientific_journal-3982	70	4	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	70	5	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	70	6	)	)	PUNCT
american_scientific_journal-3982	70	7	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	PUNCT
american_scientific_journal-3982	71	1	if	if	SCONJ
american_scientific_journal-3982	71	2	and	and	CCONJ
american_scientific_journal-3982	71	3	only	only	ADV
american_scientific_journal-3982	71	4	if	if	SCONJ
american_scientific_journal-3982	71	5	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	NUM
american_scientific_journal-3982	71	6	)	)	PUNCT
american_scientific_journal-3982	71	7	there	there	PRON
american_scientific_journal-3982	71	8	exists	exist	VERB
american_scientific_journal-3982	71	9	and	and	CCONJ
american_scientific_journal-3982	71	10	its	its	PRON
american_scientific_journal-3982	71	11	value	value	NOUN
american_scientific_journal-3982	71	12	is	be	AUX
american_scientific_journal-3982	71	13	not	not	PART
american_scientific_journal-3982	71	14	null	null	ADJ
american_scientific_journal-3982	71	15	.	.	PUNCT
american_scientific_journal-3982	72	1	3	3	X
american_scientific_journal-3982	72	2	.	.	X
american_scientific_journal-3982	72	3	main	main	ADJ
american_scientific_journal-3982	72	4	results	result	NOUN
american_scientific_journal-3982	72	5	the	the	DET
american_scientific_journal-3982	72	6	derivation	derivation	NOUN
american_scientific_journal-3982	72	7	quotients	quotient	NOUN
american_scientific_journal-3982	72	8	are	be	AUX
american_scientific_journal-3982	72	9	the	the	DET
american_scientific_journal-3982	72	10	main	main	ADJ
american_scientific_journal-3982	72	11	ingredient	ingredient	NOUN
american_scientific_journal-3982	72	12	for	for	ADP
american_scientific_journal-3982	72	13	the	the	DET
american_scientific_journal-3982	72	14	demonstration	demonstration	NOUN
american_scientific_journal-3982	72	15	of	of	ADP
american_scientific_journal-3982	72	16	the	the	DET
american_scientific_journal-3982	72	17	l’hopital	l’hopital	ADJ
american_scientific_journal-3982	72	18	rule	rule	NOUN
american_scientific_journal-3982	72	19	presented	present	VERB
american_scientific_journal-3982	72	20	here	here	ADV
american_scientific_journal-3982	72	21	.	.	PUNCT
american_scientific_journal-3982	73	1	theorem	theorem	VERB
american_scientific_journal-3982	73	2	15	15	NUM
american_scientific_journal-3982	73	3	.	.	PUNCT
american_scientific_journal-3982	74	1	if	if	SCONJ
american_scientific_journal-3982	74	2	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	NOUN
american_scientific_journal-3982	74	3	)	)	PUNCT
american_scientific_journal-3982	74	4	exists	exist	VERB
american_scientific_journal-3982	74	5	and	and	CCONJ
american_scientific_journal-3982	74	6	it	it	PRON
american_scientific_journal-3982	74	7	is	be	AUX
american_scientific_journal-3982	74	8	not	not	PART
american_scientific_journal-3982	74	9	null	null	ADJ
american_scientific_journal-3982	74	10	,	,	PUNCT
american_scientific_journal-3982	74	11	then	then	ADV
american_scientific_journal-3982	74	12	𝑙𝑙𝑠𝑠𝑙𝑙	𝑙𝑙𝑠𝑠𝑙𝑙	PROPN
american_scientific_journal-3982	74	13	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	SYM
american_scientific_journal-3982	74	14	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	74	15	)	)	PUNCT
american_scientific_journal-3982	74	16	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	74	17	)	)	PUNCT
american_scientific_journal-3982	74	18	exists	exist	VERB
american_scientific_journal-3982	74	19	if	if	SCONJ
american_scientific_journal-3982	74	20	and	and	CCONJ
american_scientific_journal-3982	74	21	only	only	ADV
american_scientific_journal-3982	74	22	if	if	SCONJ
american_scientific_journal-3982	74	23	𝑓𝑓′(𝑎𝑎	𝑓𝑓′(𝑎𝑎	NOUN
american_scientific_journal-3982	74	24	)	)	PUNCT
american_scientific_journal-3982	74	25	exists	exist	VERB
american_scientific_journal-3982	74	26	.	.	PUNCT
american_scientific_journal-3982	75	1	in	in	ADP
american_scientific_journal-3982	75	2	this	this	DET
american_scientific_journal-3982	75	3	case	case	NOUN
american_scientific_journal-3982	75	4	𝑙𝑙𝑠𝑠𝑙𝑙	𝑙𝑙𝑠𝑠𝑙𝑙	NOUN
american_scientific_journal-3982	75	5	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	NOUN
american_scientific_journal-3982	75	6	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	75	7	)	)	PUNCT
american_scientific_journal-3982	75	8	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	75	9	)	)	PUNCT
american_scientific_journal-3982	75	10	=	=	SYM
american_scientific_journal-3982	75	11	𝑓𝑓′	𝑓𝑓′	NOUN
american_scientific_journal-3982	75	12	𝑔𝑔′	𝑔𝑔′	NOUN
american_scientific_journal-3982	75	13	(	(	PUNCT
american_scientific_journal-3982	75	14	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	75	15	)	)	PUNCT
american_scientific_journal-3982	75	16	.	.	PUNCT
american_scientific_journal-3982	76	1	proof	proof	NOUN
american_scientific_journal-3982	76	2	.	.	PUNCT
american_scientific_journal-3982	77	1	by	by	ADP
american_scientific_journal-3982	77	2	the	the	DET
american_scientific_journal-3982	77	3	definition	definition	NOUN
american_scientific_journal-3982	77	4	of	of	ADP
american_scientific_journal-3982	77	5	derivative	derivative	ADJ
american_scientific_journal-3982	77	6	and	and	CCONJ
american_scientific_journal-3982	77	7	limit	limit	NOUN
american_scientific_journal-3982	77	8	,	,	PUNCT
american_scientific_journal-3982	77	9	proposition	proposition	NOUN
american_scientific_journal-3982	77	10	13	13	NUM
american_scientific_journal-3982	77	11	implies	imply	VERB
american_scientific_journal-3982	77	12	that	that	SCONJ
american_scientific_journal-3982	77	13	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	77	14	→	→	SYM
american_scientific_journal-3982	77	15	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	77	16	)	)	PUNCT
american_scientific_journal-3982	77	17	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	77	18	=	=	SYM
american_scientific_journal-3982	77	19	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	77	20	)	)	PUNCT
american_scientific_journal-3982	77	21	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	PROPN
american_scientific_journal-3982	77	22	�	�	PROPN
american_scientific_journal-3982	77	23	𝑓𝑓(𝑥𝑥	𝑓𝑓(𝑥𝑥	PROPN
american_scientific_journal-3982	77	24	)	)	PUNCT
american_scientific_journal-3982	77	25	−	−	PROPN
american_scientific_journal-3982	77	26	𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	77	27	)	)	PUNCT
american_scientific_journal-3982	77	28	�	�	PROPN
american_scientific_journal-3982	77	29	1	1	NUM
american_scientific_journal-3982	77	30	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	77	31	)	)	PUNCT
american_scientific_journal-3982	77	32	=	=	SYM
american_scientific_journal-3982	77	33	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	77	34	)	)	PUNCT
american_scientific_journal-3982	77	35	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	77	36	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	77	37	)	)	PUNCT
american_scientific_journal-3982	77	38	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	77	39	)	)	PUNCT
american_scientific_journal-3982	77	40	it	it	PRON
american_scientific_journal-3982	77	41	is	be	AUX
american_scientific_journal-3982	77	42	defined	define	VERB
american_scientific_journal-3982	77	43	for	for	ADP
american_scientific_journal-3982	77	44	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	77	45	close	close	ADV
american_scientific_journal-3982	77	46	to	to	ADP
american_scientific_journal-3982	77	47	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	77	48	as	as	ADP
american_scientific_journal-3982	77	49	the	the	DET
american_scientific_journal-3982	77	50	product	product	NOUN
american_scientific_journal-3982	77	51	of	of	ADP
american_scientific_journal-3982	77	52	the	the	DET
american_scientific_journal-3982	77	53	functions	function	NOUN
american_scientific_journal-3982	77	54	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	77	55	→	→	SYM
american_scientific_journal-3982	77	56	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	77	57	)	)	PUNCT
american_scientific_journal-3982	77	58	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	77	59	,	,	PUNCT
american_scientific_journal-3982	77	60	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	77	61	)	)	PUNCT
american_scientific_journal-3982	77	62	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	77	63	)	)	PUNCT
american_scientific_journal-3982	77	64	,	,	PUNCT
american_scientific_journal-3982	77	65	since	since	SCONJ
american_scientific_journal-3982	77	66	by	by	ADP
american_scientific_journal-3982	77	67	hypotesis	hypotesis	NOUN
american_scientific_journal-3982	77	68	there	there	PRON
american_scientific_journal-3982	77	69	is	be	VERB
american_scientific_journal-3982	77	70	a	a	DET
american_scientific_journal-3982	77	71	derivative	derivative	NOUN
american_scientific_journal-3982	77	72	of	of	ADP
american_scientific_journal-3982	77	73	𝑠𝑠	𝑠𝑠	PRON
american_scientific_journal-3982	77	74	and	and	CCONJ
american_scientific_journal-3982	77	75	the	the	DET
american_scientific_journal-3982	77	76	limit	limit	NOUN
american_scientific_journal-3982	77	77	of	of	ADP
american_scientific_journal-3982	77	78	the	the	DET
american_scientific_journal-3982	77	79	quotient	quotient	NOUN
american_scientific_journal-3982	77	80	of	of	ADP
american_scientific_journal-3982	77	81	the	the	DET
american_scientific_journal-3982	77	82	differences	difference	NOUN
american_scientific_journal-3982	77	83	in	in	ADP
american_scientific_journal-3982	77	84	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	77	85	of	of	ADP
american_scientific_journal-3982	77	86	the	the	DET
american_scientific_journal-3982	77	87	functions	function	NOUN
american_scientific_journal-3982	77	88	𝑓𝑓	𝑓𝑓	ADP
american_scientific_journal-3982	77	89	y	y	PRON
american_scientific_journal-3982	77	90	𝑠𝑠	𝑠𝑠	ADV
american_scientific_journal-3982	77	91	in	in	ADP
american_scientific_journal-3982	77	92	𝑎𝑎.	𝑎𝑎.	NOUN
american_scientific_journal-3982	77	93	by	by	ADP
american_scientific_journal-3982	77	94	the	the	DET
american_scientific_journal-3982	77	95	algebra	algebra	NOUN
american_scientific_journal-3982	77	96	of	of	ADP
american_scientific_journal-3982	77	97	limits	limit	NOUN
american_scientific_journal-3982	77	98	lim	lim	PROPN
american_scientific_journal-3982	77	99	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	77	100	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	77	101	)	)	PUNCT
american_scientific_journal-3982	77	102	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	78	1	=	=	SYM
american_scientific_journal-3982	78	2	lim	lim	PROPN
american_scientific_journal-3982	78	3	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	78	4	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	78	5	)	)	PUNCT
american_scientific_journal-3982	78	6	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	PROPN
american_scientific_journal-3982	78	7	lim	lim	PROPN
american_scientific_journal-3982	78	8	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	78	9	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	78	10	)	)	PUNCT
american_scientific_journal-3982	78	11	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	78	12	)	)	PUNCT
american_scientific_journal-3982	78	13	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	NOUN
american_scientific_journal-3982	78	14	,	,	PUNCT
american_scientific_journal-3982	78	15	that	that	ADV
american_scientific_journal-3982	78	16	is	is	ADV
american_scientific_journal-3982	78	17	,	,	PUNCT
american_scientific_journal-3982	78	18	there	there	PRON
american_scientific_journal-3982	78	19	is	be	VERB
american_scientific_journal-3982	78	20	a	a	DET
american_scientific_journal-3982	78	21	derivative	derivative	NOUN
american_scientific_journal-3982	78	22	of	of	ADP
american_scientific_journal-3982	78	23	𝑓𝑓	𝑓𝑓	NOUN
american_scientific_journal-3982	78	24	in	in	ADP
american_scientific_journal-3982	78	25	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	78	26	and	and	CCONJ
american_scientific_journal-3982	78	27	consequently	consequently	ADV
american_scientific_journal-3982	78	28	𝑓𝑓′(𝑎𝑎	𝑓𝑓′(𝑎𝑎	X
american_scientific_journal-3982	78	29	)	)	PUNCT
american_scientific_journal-3982	78	30	=	=	SYM
american_scientific_journal-3982	78	31	𝑠𝑠′(𝑎𝑎)lim	𝑠𝑠′(𝑎𝑎)lim	PROPN
american_scientific_journal-3982	78	32	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	NOUN
american_scientific_journal-3982	78	33	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	78	34	)	)	PUNCT
american_scientific_journal-3982	78	35	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	78	36	)	)	PUNCT
american_scientific_journal-3982	78	37	and	and	CCONJ
american_scientific_journal-3982	78	38	in	in	ADP
american_scientific_journal-3982	78	39	this	this	DET
american_scientific_journal-3982	78	40	case	case	NOUN
american_scientific_journal-3982	78	41	𝑓𝑓′(𝑎𝑎	𝑓𝑓′(𝑎𝑎	X
american_scientific_journal-3982	78	42	)	)	PUNCT
american_scientific_journal-3982	78	43	𝑔𝑔′(𝑎𝑎	𝑔𝑔′(𝑎𝑎	NOUN
american_scientific_journal-3982	78	44	)	)	PUNCT
american_scientific_journal-3982	78	45	=	=	SYM
american_scientific_journal-3982	78	46	lim	lim	PROPN
american_scientific_journal-3982	78	47	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	78	48	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	78	49	)	)	PUNCT
american_scientific_journal-3982	78	50	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	78	51	)	)	PUNCT
american_scientific_journal-3982	78	52	.	.	PUNCT
american_scientific_journal-3982	79	1	recíprocally	recíprocally	ADV
american_scientific_journal-3982	79	2	,	,	PUNCT
american_scientific_journal-3982	79	3	the	the	DET
american_scientific_journal-3982	79	4	functions	function	NOUN
american_scientific_journal-3982	79	5	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	79	6	→	→	SYM
american_scientific_journal-3982	79	7	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	79	8	)	)	PUNCT
american_scientific_journal-3982	79	9	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	79	10	,	,	PUNCT
american_scientific_journal-3982	79	11	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	79	12	)	)	PUNCT
american_scientific_journal-3982	79	13	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	ADV
american_scientific_journal-3982	79	14	are	be	AUX
american_scientific_journal-3982	79	15	defined	define	VERB
american_scientific_journal-3982	79	16	for	for	ADP
american_scientific_journal-3982	79	17	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	79	18	sufficiently	sufficiently	ADV
american_scientific_journal-3982	79	19	close	close	ADJ
american_scientific_journal-3982	79	20	to	to	ADP
american_scientific_journal-3982	79	21	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	79	22	by	by	ADP
american_scientific_journal-3982	79	23	proposition	proposition	NOUN
american_scientific_journal-3982	79	24	13	13	NUM
american_scientific_journal-3982	79	25	and	and	CCONJ
american_scientific_journal-3982	79	26	the	the	DET
american_scientific_journal-3982	79	27	definition	definition	NOUN
american_scientific_journal-3982	79	28	of	of	ADP
american_scientific_journal-3982	79	29	derivative	derivative	NOUN
american_scientific_journal-3982	79	30	and	and	CCONJ
american_scientific_journal-3982	79	31	in	in	ADP
american_scientific_journal-3982	79	32	this	this	DET
american_scientific_journal-3982	79	33	case	case	NOUN
american_scientific_journal-3982	79	34	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	79	35	)	)	PUNCT
american_scientific_journal-3982	79	36	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	79	37	)	)	PUNCT
american_scientific_journal-3982	79	38	=	=	SYM
american_scientific_journal-3982	79	39	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	79	40	)	)	PUNCT
american_scientific_journal-3982	79	41	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	79	42	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	X
american_scientific_journal-3982	79	43	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	79	44	)	)	PUNCT
american_scientific_journal-3982	79	45	=	=	SYM
american_scientific_journal-3982	79	46	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	79	47	)	)	PUNCT
american_scientific_journal-3982	79	48	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	79	49	1	1	NUM
american_scientific_journal-3982	79	50	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	79	51	)	)	PUNCT
american_scientific_journal-3982	79	52	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	79	53	=	=	SYM
american_scientific_journal-3982	79	54	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	79	55	)	)	PUNCT
american_scientific_journal-3982	79	56	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	79	57	1	1	NUM
american_scientific_journal-3982	79	58	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	79	59	)	)	PUNCT
american_scientific_journal-3982	79	60	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	79	61	=	=	SYM
american_scientific_journal-3982	79	62	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	79	63	)	)	PUNCT
american_scientific_journal-3982	79	64	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	79	65	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	79	66	)	)	PUNCT
american_scientific_journal-3982	79	67	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	79	68	,	,	PUNCT
american_scientific_journal-3982	79	69	then	then	ADV
american_scientific_journal-3982	79	70	by	by	ADP
american_scientific_journal-3982	79	71	the	the	DET
american_scientific_journal-3982	79	72	algebra	algebra	NOUN
american_scientific_journal-3982	79	73	of	of	ADP
american_scientific_journal-3982	79	74	limits	limit	NOUN
american_scientific_journal-3982	79	75	,	,	PUNCT
american_scientific_journal-3982	79	76	we	we	PRON
american_scientific_journal-3982	79	77	have	have	VERB
american_scientific_journal-3982	79	78	lim	lim	PROPN
american_scientific_journal-3982	79	79	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	79	80	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	79	81	)	)	PUNCT
american_scientific_journal-3982	79	82	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	79	83	)	)	PUNCT
american_scientific_journal-3982	80	1	=	=	PROPN
american_scientific_journal-3982	80	2	lim	lim	PROPN
american_scientific_journal-3982	80	3	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	80	4	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	80	5	)	)	PUNCT
american_scientific_journal-3982	80	6	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	80	7	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	80	8	)	)	PUNCT
american_scientific_journal-3982	80	9	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	81	1	=	=	SYM
american_scientific_journal-3982	81	2	lim	lim	PROPN
american_scientific_journal-3982	81	3	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	81	4	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑥𝑥)−𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	81	5	)	)	PUNCT
american_scientific_journal-3982	81	6	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	PROPN
american_scientific_journal-3982	81	7	lim	lim	PROPN
american_scientific_journal-3982	81	8	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PROPN
american_scientific_journal-3982	81	9	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	𝑔𝑔(𝑥𝑥)−𝑔𝑔(𝑎𝑎	PROPN
american_scientific_journal-3982	81	10	)	)	PUNCT
american_scientific_journal-3982	81	11	𝑥𝑥−𝑎𝑎	𝑥𝑥−𝑎𝑎	NOUN
american_scientific_journal-3982	81	12	=	=	SYM
american_scientific_journal-3982	81	13	𝑓𝑓′	𝑓𝑓′	NOUN
american_scientific_journal-3982	81	14	𝑔𝑔′	𝑔𝑔′	NOUN
american_scientific_journal-3982	81	15	(	(	PUNCT
american_scientific_journal-3982	81	16	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	81	17	)	)	PUNCT
american_scientific_journal-3982	81	18	.	.	PUNCT
american_scientific_journal-3982	82	1	corollary	corollary	ADJ
american_scientific_journal-3982	82	2	16	16	NUM
american_scientific_journal-3982	82	3	.	.	PUNCT
american_scientific_journal-3982	83	1	if	if	SCONJ
american_scientific_journal-3982	83	2	𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	83	3	)	)	PUNCT
american_scientific_journal-3982	83	4	=	=	SYM
american_scientific_journal-3982	83	5	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	83	6	)	)	PUNCT
american_scientific_journal-3982	83	7	=	=	SYM
american_scientific_journal-3982	83	8	0	0	NUM
american_scientific_journal-3982	83	9	and	and	CCONJ
american_scientific_journal-3982	83	10	also	also	ADV
american_scientific_journal-3982	83	11	𝑠𝑠′(𝑎𝑎	𝑠𝑠′(𝑎𝑎	PROPN
american_scientific_journal-3982	83	12	)	)	PUNCT
american_scientific_journal-3982	83	13	exists	exist	VERB
american_scientific_journal-3982	83	14	and	and	CCONJ
american_scientific_journal-3982	83	15	is	be	AUX
american_scientific_journal-3982	83	16	not	not	PART
american_scientific_journal-3982	83	17	null	null	ADJ
american_scientific_journal-3982	83	18	,	,	PUNCT
american_scientific_journal-3982	83	19	then	then	ADV
american_scientific_journal-3982	83	20	𝑙𝑙𝑠𝑠𝑙𝑙	𝑙𝑙𝑠𝑠𝑙𝑙	PROPN
american_scientific_journal-3982	83	21	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	NUM
american_scientific_journal-3982	83	22	𝑓𝑓(𝑥𝑥	𝑓𝑓(𝑥𝑥	PROPN
american_scientific_journal-3982	83	23	)	)	PUNCT
american_scientific_journal-3982	83	24	𝑔𝑔(𝑥𝑥	𝑔𝑔(𝑥𝑥	PROPN
american_scientific_journal-3982	83	25	)	)	PUNCT
american_scientific_journal-3982	83	26	exists	exist	VERB
american_scientific_journal-3982	83	27	if	if	SCONJ
american_scientific_journal-3982	83	28	and	and	CCONJ
american_scientific_journal-3982	83	29	only	only	ADV
american_scientific_journal-3982	83	30	if	if	SCONJ
american_scientific_journal-3982	83	31	𝑓𝑓′(𝑎𝑎	𝑓𝑓′(𝑎𝑎	NOUN
american_scientific_journal-3982	83	32	)	)	PUNCT
american_scientific_journal-3982	83	33	exists	exist	VERB
american_scientific_journal-3982	83	34	.	.	PUNCT
american_scientific_journal-3982	84	1	in	in	ADP
american_scientific_journal-3982	84	2	this	this	DET
american_scientific_journal-3982	84	3	case	case	NOUN
american_scientific_journal-3982	84	4	𝑙𝑙𝑠𝑠𝑙𝑙	𝑙𝑙𝑠𝑠𝑙𝑙	NOUN
american_scientific_journal-3982	84	5	𝑥𝑥→𝑎𝑎	𝑥𝑥→𝑎𝑎	PRON
american_scientific_journal-3982	84	6	𝑓𝑓	𝑓𝑓	ADP
american_scientific_journal-3982	84	7	𝑔𝑔	𝑔𝑔	INTJ
american_scientific_journal-3982	84	8	(	(	PUNCT
american_scientific_journal-3982	84	9	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	84	10	)	)	PUNCT
american_scientific_journal-3982	84	11	=	=	SYM
american_scientific_journal-3982	84	12	𝑓𝑓′	𝑓𝑓′	NOUN
american_scientific_journal-3982	84	13	𝑔𝑔′	𝑔𝑔′	NOUN
american_scientific_journal-3982	84	14	(	(	PUNCT
american_scientific_journal-3982	84	15	𝑎𝑎	𝑎𝑎	NOUN
american_scientific_journal-3982	84	16	)	)	PUNCT
american_scientific_journal-3982	84	17	proof	proof	NOUN
american_scientific_journal-3982	84	18	.	.	PUNCT
american_scientific_journal-3982	85	1	replacing	replace	VERB
american_scientific_journal-3982	85	2	the	the	DET
american_scientific_journal-3982	85	3	present	present	ADJ
american_scientific_journal-3982	85	4	hypothesis	hypothesis	NOUN
american_scientific_journal-3982	85	5	,	,	PUNCT
american_scientific_journal-3982	85	6	that	that	ADV
american_scientific_journal-3982	85	7	is	is	AUX
american_scientific_journal-3982	85	8	,	,	PUNCT
american_scientific_journal-3982	85	9	𝑓𝑓(𝑎𝑎	𝑓𝑓(𝑎𝑎	PROPN
american_scientific_journal-3982	85	10	)	)	PUNCT
american_scientific_journal-3982	85	11	=	=	SYM
american_scientific_journal-3982	85	12	𝑠𝑠(𝑎𝑎	𝑠𝑠(𝑎𝑎	PROPN
american_scientific_journal-3982	85	13	)	)	PUNCT
american_scientific_journal-3982	85	14	=	=	SYM
american_scientific_journal-3982	85	15	0	0	NUM
american_scientific_journal-3982	85	16	,	,	PUNCT
american_scientific_journal-3982	85	17	in	in	ADP
american_scientific_journal-3982	85	18	theorem	theorem	NOUN
american_scientific_journal-3982	85	19	15	15	NUM
american_scientific_journal-3982	85	20	,	,	PUNCT
american_scientific_journal-3982	85	21	we	we	PRON
american_scientific_journal-3982	85	22	have	have	VERB
american_scientific_journal-3982	85	23	the	the	DET
american_scientific_journal-3982	85	24	result	result	NOUN
american_scientific_journal-3982	85	25	of	of	ADP
american_scientific_journal-3982	85	26	the	the	DET
american_scientific_journal-3982	85	27	present	present	ADJ
american_scientific_journal-3982	85	28	corollary	corollary	NOUN
american_scientific_journal-3982	85	29	.	.	PUNCT
american_scientific_journal-3982	86	1	4	4	X
american_scientific_journal-3982	86	2	.	.	X
american_scientific_journal-3982	86	3	discussion	discussion	NOUN
american_scientific_journal-3982	86	4	several	several	ADJ
american_scientific_journal-3982	86	5	authors	author	NOUN
american_scientific_journal-3982	86	6	such	such	ADJ
american_scientific_journal-3982	86	7	as	as	ADP
american_scientific_journal-3982	86	8	[	[	X
american_scientific_journal-3982	86	9	1	1	NUM
american_scientific_journal-3982	86	10	;	;	PUNCT
american_scientific_journal-3982	86	11	25	25	NUM
american_scientific_journal-3982	86	12	]	]	PUNCT
american_scientific_journal-3982	86	13	require	require	VERB
american_scientific_journal-3982	86	14	the	the	DET
american_scientific_journal-3982	86	15	assumption	assumption	NOUN
american_scientific_journal-3982	86	16	of	of	ADP
american_scientific_journal-3982	86	17	the	the	DET
american_scientific_journal-3982	86	18	continuity	continuity	NOUN
american_scientific_journal-3982	86	19	of	of	ADP
american_scientific_journal-3982	86	20	the	the	DET
american_scientific_journal-3982	86	21	derivatives	derivative	NOUN
american_scientific_journal-3982	86	22	while	while	SCONJ
american_scientific_journal-3982	86	23	in	in	ADP
american_scientific_journal-3982	86	24	this	this	DET
american_scientific_journal-3982	86	25	work	work	NOUN
american_scientific_journal-3982	86	26	,	,	PUNCT
american_scientific_journal-3982	86	27	such	such	ADJ
american_scientific_journal-3982	86	28	assumption	assumption	NOUN
american_scientific_journal-3982	86	29	is	be	AUX
american_scientific_journal-3982	86	30	not	not	PART
american_scientific_journal-3982	86	31	necessary	necessary	ADJ
american_scientific_journal-3982	86	32	,	,	PUNCT
american_scientific_journal-3982	86	33	causing	cause	VERB
american_scientific_journal-3982	86	34	the	the	DET
american_scientific_journal-3982	86	35	spectrum	spectrum	NOUN
american_scientific_journal-3982	86	36	of	of	ADP
american_scientific_journal-3982	86	37	application	application	NOUN
american_scientific_journal-3982	86	38	of	of	ADP
american_scientific_journal-3982	86	39	this	this	DET
american_scientific_journal-3982	86	40	rule	rule	NOUN
american_scientific_journal-3982	86	41	to	to	PART
american_scientific_journal-3982	86	42	be	be	AUX
american_scientific_journal-3982	86	43	extended	extend	VERB
american_scientific_journal-3982	86	44	.	.	PUNCT
american_scientific_journal-3982	87	1	american	american	ADJ
american_scientific_journal-3982	87	2	scientific	scientific	ADJ
american_scientific_journal-3982	87	3	research	research	PROPN
american_scientific_journal-3982	87	4	journal	journal	NOUN
american_scientific_journal-3982	87	5	for	for	ADP
american_scientific_journal-3982	87	6	engineering	engineering	NOUN
american_scientific_journal-3982	87	7	,	,	PUNCT
american_scientific_journal-3982	87	8	technology	technology	NOUN
american_scientific_journal-3982	87	9	,	,	PUNCT
american_scientific_journal-3982	87	10	and	and	CCONJ
american_scientific_journal-3982	87	11	sciences	science	NOUN
american_scientific_journal-3982	87	12	(	(	PUNCT
american_scientific_journal-3982	87	13	asrjets	asrjet	NOUN
american_scientific_journal-3982	87	14	)	)	PUNCT
american_scientific_journal-3982	87	15	(	(	PUNCT
american_scientific_journal-3982	87	16	2018	2018	NUM
american_scientific_journal-3982	87	17	)	)	PUNCT
american_scientific_journal-3982	87	18	volume	volume	NOUN
american_scientific_journal-3982	87	19	41	41	NUM
american_scientific_journal-3982	87	20	,	,	PUNCT
american_scientific_journal-3982	87	21	no	no	DET
american_scientific_journal-3982	87	22	1	1	NUM
american_scientific_journal-3982	87	23	,	,	PUNCT
american_scientific_journal-3982	87	24	pp	pp	ADV
american_scientific_journal-3982	87	25	240	240	NUM
american_scientific_journal-3982	87	26	-	-	SYM
american_scientific_journal-3982	87	27	245	245	NUM
american_scientific_journal-3982	87	28	244	244	NUM
american_scientific_journal-3982	87	29	5	5	NUM
american_scientific_journal-3982	87	30	.	.	PUNCT
american_scientific_journal-3982	88	1	conclusions	conclusion	NOUN
american_scientific_journal-3982	88	2	it	it	PRON
american_scientific_journal-3982	88	3	is	be	AUX
american_scientific_journal-3982	88	4	well	well	ADV
american_scientific_journal-3982	88	5	known	know	VERB
american_scientific_journal-3982	88	6	that	that	SCONJ
american_scientific_journal-3982	88	7	the	the	DET
american_scientific_journal-3982	88	8	l’hopital	l’hopital	ADJ
american_scientific_journal-3982	88	9	rule	rule	NOUN
american_scientific_journal-3982	88	10	proof	proof	NOUN
american_scientific_journal-3982	88	11	depends	depend	VERB
american_scientific_journal-3982	88	12	directly	directly	ADV
american_scientific_journal-3982	88	13	on	on	ADP
american_scientific_journal-3982	88	14	the	the	DET
american_scientific_journal-3982	88	15	roll	roll	NOUN
american_scientific_journal-3982	88	16	theorem	theorem	NOUN
american_scientific_journal-3982	88	17	or	or	CCONJ
american_scientific_journal-3982	88	18	the	the	DET
american_scientific_journal-3982	88	19	mean	mean	ADJ
american_scientific_journal-3982	88	20	value	value	NOUN
american_scientific_journal-3982	88	21	theorem	theorem	VERB
american_scientific_journal-3982	88	22	,	,	PUNCT
american_scientific_journal-3982	88	23	that	that	ADV
american_scientific_journal-3982	88	24	is	is	ADV
american_scientific_journal-3982	88	25	,	,	PUNCT
american_scientific_journal-3982	88	26	it	it	PRON
american_scientific_journal-3982	88	27	is	be	AUX
american_scientific_journal-3982	88	28	necessary	necessary	ADJ
american_scientific_journal-3982	88	29	to	to	PART
american_scientific_journal-3982	88	30	assume	assume	VERB
american_scientific_journal-3982	88	31	the	the	DET
american_scientific_journal-3982	88	32	global	global	ADJ
american_scientific_journal-3982	88	33	continuity	continuity	NOUN
american_scientific_journal-3982	88	34	of	of	ADP
american_scientific_journal-3982	88	35	the	the	DET
american_scientific_journal-3982	88	36	derivative	derivative	NOUN
american_scientific_journal-3982	88	37	(	(	PUNCT
american_scientific_journal-3982	88	38	even	even	ADV
american_scientific_journal-3982	88	39	where	where	SCONJ
american_scientific_journal-3982	88	40	the	the	DET
american_scientific_journal-3982	88	41	logic	logic	NOUN
american_scientific_journal-3982	88	42	of	of	ADP
american_scientific_journal-3982	88	43	the	the	DET
american_scientific_journal-3982	88	44	proof	proof	NOUN
american_scientific_journal-3982	88	45	of	of	ADP
american_scientific_journal-3982	88	46	the	the	DET
american_scientific_journal-3982	88	47	considered	consider	VERB
american_scientific_journal-3982	88	48	rule	rule	NOUN
american_scientific_journal-3982	88	49	(	(	PUNCT
american_scientific_journal-3982	88	50	see	see	VERB
american_scientific_journal-3982	88	51	for	for	ADP
american_scientific_journal-3982	88	52	example.[2	example.[2	NOUN
american_scientific_journal-3982	88	53	]	]	NUM
american_scientific_journal-3982	88	54	)	)	PUNCT
american_scientific_journal-3982	88	55	.	.	PUNCT
american_scientific_journal-3982	89	1	it	it	PRON
american_scientific_journal-3982	89	2	has	have	AUX
american_scientific_journal-3982	89	3	been	be	AUX
american_scientific_journal-3982	89	4	established	establish	VERB
american_scientific_journal-3982	89	5	,	,	PUNCT
american_scientific_journal-3982	89	6	the	the	DET
american_scientific_journal-3982	89	7	rule	rule	NOUN
american_scientific_journal-3982	89	8	of	of	ADP
american_scientific_journal-3982	89	9	l’höpital	l’höpital	NOUN
american_scientific_journal-3982	89	10	as	as	SCONJ
american_scientific_journal-3982	89	11	it	it	PRON
american_scientific_journal-3982	89	12	is	be	AUX
american_scientific_journal-3982	89	13	established	establish	VERB
american_scientific_journal-3982	89	14	the	the	DET
american_scientific_journal-3982	89	15	rules	rule	NOUN
american_scientific_journal-3982	89	16	of	of	ADP
american_scientific_journal-3982	89	17	derivation	derivation	NOUN
american_scientific_journal-3982	89	18	,	,	PUNCT
american_scientific_journal-3982	89	19	that	that	PRON
american_scientific_journal-3982	89	20	is	be	AUX
american_scientific_journal-3982	89	21	to	to	PART
american_scientific_journal-3982	89	22	say	say	VERB
american_scientific_journal-3982	89	23	the	the	DET
american_scientific_journal-3982	89	24	rule	rule	NOUN
american_scientific_journal-3982	89	25	of	of	ADP
american_scientific_journal-3982	89	26	h’ôpital	h’ôpital	ADJ
american_scientific_journal-3982	89	27	can	can	AUX
american_scientific_journal-3982	89	28	be	be	AUX
american_scientific_journal-3982	89	29	considered	consider	VERB
american_scientific_journal-3982	89	30	that	that	SCONJ
american_scientific_journal-3982	89	31	it	it	PRON
american_scientific_journal-3982	89	32	becomes	become	VERB
american_scientific_journal-3982	89	33	one	one	NUM
american_scientific_journal-3982	89	34	more	more	ADJ
american_scientific_journal-3982	89	35	rule	rule	NOUN
american_scientific_journal-3982	89	36	of	of	ADP
american_scientific_journal-3982	89	37	derivation	derivation	NOUN
american_scientific_journal-3982	89	38	.	.	PUNCT
american_scientific_journal-3982	90	1	the	the	DET
american_scientific_journal-3982	90	2	substitution	substitution	NOUN
american_scientific_journal-3982	90	3	of	of	ADP
american_scientific_journal-3982	90	4	the	the	DET
american_scientific_journal-3982	90	5	ratio	ratio	NOUN
american_scientific_journal-3982	90	6	of	of	ADP
american_scientific_journal-3982	90	7	the	the	DET
american_scientific_journal-3982	90	8	derivatives	derivative	NOUN
american_scientific_journal-3982	90	9	by	by	ADP
american_scientific_journal-3982	90	10	the	the	DET
american_scientific_journal-3982	90	11	limit	limit	NOUN
american_scientific_journal-3982	90	12	of	of	ADP
american_scientific_journal-3982	90	13	the	the	DET
american_scientific_journal-3982	90	14	ratio	ratio	NOUN
american_scientific_journal-3982	90	15	of	of	ADP
american_scientific_journal-3982	90	16	the	the	DET
american_scientific_journal-3982	90	17	derivatives	derivative	NOUN
american_scientific_journal-3982	90	18	to	to	ADP
american_scientific_journal-3982	90	19	the	the	DET
american_scientific_journal-3982	90	20	number	number	NOUN
american_scientific_journal-3982	90	21	where	where	SCONJ
american_scientific_journal-3982	90	22	the	the	DET
american_scientific_journal-3982	90	23	limit	limit	NOUN
american_scientific_journal-3982	90	24	will	will	AUX
american_scientific_journal-3982	90	25	be	be	AUX
american_scientific_journal-3982	90	26	calculated	calculate	VERB
american_scientific_journal-3982	90	27	,	,	PUNCT
american_scientific_journal-3982	90	28	actually	actually	ADV
american_scientific_journal-3982	90	29	requires	require	VERB
american_scientific_journal-3982	90	30	that	that	SCONJ
american_scientific_journal-3982	90	31	the	the	DET
american_scientific_journal-3982	90	32	derivative	derivative	NOUN
american_scientific_journal-3982	90	33	of	of	ADP
american_scientific_journal-3982	90	34	the	the	DET
american_scientific_journal-3982	90	35	functions	function	NOUN
american_scientific_journal-3982	90	36	is	be	AUX
american_scientific_journal-3982	90	37	defined	define	VERB
american_scientific_journal-3982	90	38	in	in	ADP
american_scientific_journal-3982	90	39	an	an	DET
american_scientific_journal-3982	90	40	interval	interval	NOUN
american_scientific_journal-3982	90	41	contained	contain	VERB
american_scientific_journal-3982	90	42	in	in	ADP
american_scientific_journal-3982	90	43	the	the	DET
american_scientific_journal-3982	90	44	domain	domain	NOUN
american_scientific_journal-3982	90	45	of	of	ADP
american_scientific_journal-3982	90	46	the	the	DET
american_scientific_journal-3982	90	47	functions	function	NOUN
american_scientific_journal-3982	90	48	besides	besides	AUX
american_scientific_journal-3982	90	49	require	require	VERB
american_scientific_journal-3982	90	50	that	that	SCONJ
american_scientific_journal-3982	90	51	it	it	PRON
american_scientific_journal-3982	90	52	be	be	AUX
american_scientific_journal-3982	90	53	extended	extend	VERB
american_scientific_journal-3982	90	54	continuously	continuously	ADV
american_scientific_journal-3982	90	55	to	to	ADP
american_scientific_journal-3982	90	56	the	the	DET
american_scientific_journal-3982	90	57	number	number	NOUN
american_scientific_journal-3982	90	58	where	where	SCONJ
american_scientific_journal-3982	90	59	the	the	DET
american_scientific_journal-3982	90	60	limit	limit	NOUN
american_scientific_journal-3982	90	61	is	be	AUX
american_scientific_journal-3982	90	62	calculated	calculate	VERB
american_scientific_journal-3982	90	63	.	.	PUNCT
american_scientific_journal-3982	91	1	in	in	ADP
american_scientific_journal-3982	91	2	general	general	ADJ
american_scientific_journal-3982	91	3	,	,	PUNCT
american_scientific_journal-3982	91	4	the	the	DET
american_scientific_journal-3982	91	5	condition	condition	NOUN
american_scientific_journal-3982	91	6	of	of	ADP
american_scientific_journal-3982	91	7	local	local	ADJ
american_scientific_journal-3982	91	8	continuity	continuity	NOUN
american_scientific_journal-3982	91	9	has	have	AUX
american_scientific_journal-3982	91	10	been	be	AUX
american_scientific_journal-3982	91	11	replaced	replace	VERB
american_scientific_journal-3982	91	12	by	by	ADP
american_scientific_journal-3982	91	13	a	a	DET
american_scientific_journal-3982	91	14	sophisticated	sophisticated	ADJ
american_scientific_journal-3982	91	15	global	global	ADJ
american_scientific_journal-3982	91	16	condition	condition	NOUN
american_scientific_journal-3982	91	17	in	in	ADP
american_scientific_journal-3982	91	18	intervals	interval	NOUN
american_scientific_journal-3982	91	19	of	of	ADP
american_scientific_journal-3982	91	20	the	the	DET
american_scientific_journal-3982	91	21	number	number	NOUN
american_scientific_journal-3982	91	22	line	line	NOUN
american_scientific_journal-3982	91	23	,	,	PUNCT
american_scientific_journal-3982	91	24	such	such	ADJ
american_scientific_journal-3982	91	25	as	as	ADP
american_scientific_journal-3982	91	26	the	the	DET
american_scientific_journal-3982	91	27	existence	existence	NOUN
american_scientific_journal-3982	91	28	of	of	ADP
american_scientific_journal-3982	91	29	the	the	DET
american_scientific_journal-3982	91	30	derivative	derivative	NOUN
american_scientific_journal-3982	91	31	in	in	ADP
american_scientific_journal-3982	91	32	some	some	DET
american_scientific_journal-3982	91	33	interval	interval	NOUN
american_scientific_journal-3982	91	34	[	[	X
american_scientific_journal-3982	91	35	2,18	2,18	X
american_scientific_journal-3982	91	36	]	]	X
american_scientific_journal-3982	91	37	increasing	increase	VERB
american_scientific_journal-3982	91	38	ratios	ratio	NOUN
american_scientific_journal-3982	91	39	of	of	ADP
american_scientific_journal-3982	91	40	functions	function	NOUN
american_scientific_journal-3982	92	1	[	[	X
american_scientific_journal-3982	92	2	1,3,16,23	1,3,16,23	NUM
american_scientific_journal-3982	92	3	]	]	PUNCT
american_scientific_journal-3982	92	4	,	,	PUNCT
american_scientific_journal-3982	92	5	quotients	quotient	NOUN
american_scientific_journal-3982	92	6	of	of	ADP
american_scientific_journal-3982	92	7	functions	function	NOUN
american_scientific_journal-3982	92	8	of	of	ADP
american_scientific_journal-3982	92	9	c1	c1	NOUN
american_scientific_journal-3982	92	10	[	[	X
american_scientific_journal-3982	92	11	3,15	3,15	NUM
american_scientific_journal-3982	92	12	]	]	X
american_scientific_journal-3982	92	13	,	,	PUNCT
american_scientific_journal-3982	92	14	ratios	ratio	NOUN
american_scientific_journal-3982	92	15	of	of	ADP
american_scientific_journal-3982	92	16	series	series	NOUN
american_scientific_journal-3982	92	17	of	of	ADP
american_scientific_journal-3982	92	18	numbers	number	NOUN
american_scientific_journal-3982	92	19	[	[	X
american_scientific_journal-3982	92	20	8,19,25	8,19,25	NUM
american_scientific_journal-3982	92	21	]	]	PUNCT
american_scientific_journal-3982	92	22	,	,	PUNCT
american_scientific_journal-3982	92	23	ratios	ratio	NOUN
american_scientific_journal-3982	92	24	of	of	ADP
american_scientific_journal-3982	92	25	functions	function	NOUN
american_scientific_journal-3982	92	26	of	of	ADP
american_scientific_journal-3982	92	27	darboux	darboux	NOUN
american_scientific_journal-3982	92	28	and	and	CCONJ
american_scientific_journal-3982	92	29	/	/	SYM
american_scientific_journal-3982	92	30	or	or	CCONJ
american_scientific_journal-3982	92	31	generalized	generalized	ADJ
american_scientific_journal-3982	92	32	derivation	derivation	NOUN
american_scientific_journal-3982	93	1	[	[	X
american_scientific_journal-3982	93	2	9,21,24	9,21,24	NUM
american_scientific_journal-3982	93	3	]	]	PUNCT
american_scientific_journal-3982	93	4	,	,	PUNCT
american_scientific_journal-3982	93	5	functions	function	VERB
american_scientific_journal-3982	93	6	absolutely	absolutely	ADV
american_scientific_journal-3982	93	7	continuous	continuous	ADJ
american_scientific_journal-3982	93	8	and	and	CCONJ
american_scientific_journal-3982	93	9	/	/	SYM
american_scientific_journal-3982	93	10	or	or	CCONJ
american_scientific_journal-3982	93	11	frechet	frechet	NOUN
american_scientific_journal-3982	93	12	differentiable	differentiable	ADJ
american_scientific_journal-3982	94	1	[	[	X
american_scientific_journal-3982	94	2	10,12	10,12	NUM
american_scientific_journal-3982	94	3	]	]	PUNCT
american_scientific_journal-3982	94	4	,	,	PUNCT
american_scientific_journal-3982	94	5	analytic	analytic	ADJ
american_scientific_journal-3982	94	6	function	function	NOUN
american_scientific_journal-3982	94	7	quotients	quotient	VERB
american_scientific_journal-3982	94	8	[	[	X
american_scientific_journal-3982	94	9	11,17,20	11,17,20	NUM
american_scientific_journal-3982	94	10	]	]	PUNCT
american_scientific_journal-3982	94	11	,	,	PUNCT
american_scientific_journal-3982	94	12	quotients	quotient	NOUN
american_scientific_journal-3982	94	13	of	of	ADP
american_scientific_journal-3982	94	14	integrable	integrable	ADJ
american_scientific_journal-3982	94	15	functions	function	NOUN
american_scientific_journal-3982	94	16	[	[	X
american_scientific_journal-3982	94	17	14,20,22	14,20,22	NUM
american_scientific_journal-3982	94	18	]	]	X
american_scientific_journal-3982	94	19	.	.	PUNCT
american_scientific_journal-3982	95	1	this	this	DET
american_scientific_journal-3982	95	2	demonstration	demonstration	NOUN
american_scientific_journal-3982	95	3	can	can	AUX
american_scientific_journal-3982	95	4	be	be	AUX
american_scientific_journal-3982	95	5	used	use	VERB
american_scientific_journal-3982	95	6	with	with	ADP
american_scientific_journal-3982	95	7	baccalaureate	baccalaureate	NOUN
american_scientific_journal-3982	95	8	students	student	NOUN
american_scientific_journal-3982	95	9	as	as	ADP
american_scientific_journal-3982	95	10	a	a	DET
american_scientific_journal-3982	95	11	rule	rule	NOUN
american_scientific_journal-3982	95	12	to	to	PART
american_scientific_journal-3982	95	13	calculate	calculate	VERB
american_scientific_journal-3982	95	14	limits	limit	NOUN
american_scientific_journal-3982	95	15	such	such	ADJ
american_scientific_journal-3982	95	16	as	as	ADP
american_scientific_journal-3982	95	17	lim	lim	PROPN
american_scientific_journal-3982	95	18	𝑥𝑥→0	𝑥𝑥→0	PROPN
american_scientific_journal-3982	95	19	exp	exp	PROPN
american_scientific_journal-3982	95	20	�	�	PROPN
american_scientific_journal-3982	95	21	−1𝑥𝑥	−1𝑥𝑥	PROPN
american_scientific_journal-3982	95	22	�	�	NOUN
american_scientific_journal-3982	95	23	sin𝑥𝑥	sin𝑥𝑥	PROPN
american_scientific_journal-3982	95	24	=	=	SYM
american_scientific_journal-3982	95	25	�	�	PROPN
american_scientific_journal-3982	95	26	exp−1𝑥𝑥	exp−1𝑥𝑥	PROPN
american_scientific_journal-3982	95	27	�	�	PROPN
american_scientific_journal-3982	95	28	(0	(0	NOUN
american_scientific_journal-3982	95	29	)	)	PUNCT
american_scientific_journal-3982	95	30	sin′0	sin′0	NOUN
american_scientific_journal-3982	95	31	=	=	SYM
american_scientific_journal-3982	95	32	0	0	NUM
american_scientific_journal-3982	95	33	cos0	cos0	NOUN
american_scientific_journal-3982	95	34	=	=	SYM
american_scientific_journal-3982	95	35	0	0	NUM
american_scientific_journal-3982	95	36	,	,	PUNCT
american_scientific_journal-3982	95	37	in	in	ADP
american_scientific_journal-3982	95	38	terms	term	NOUN
american_scientific_journal-3982	95	39	of	of	ADP
american_scientific_journal-3982	95	40	the	the	DET
american_scientific_journal-3982	95	41	calculation	calculation	NOUN
american_scientific_journal-3982	95	42	of	of	ADP
american_scientific_journal-3982	95	43	derivatives	derivative	NOUN
american_scientific_journal-3982	95	44	.	.	PUNCT
american_scientific_journal-3982	96	1	where	where	SCONJ
american_scientific_journal-3982	96	2	the	the	DET
american_scientific_journal-3982	96	3	derivative	derivative	ADJ
american_scientific_journal-3982	96	4	�	�	PROPN
american_scientific_journal-3982	96	5	exp	exp	NOUN
american_scientific_journal-3982	96	6	−	−	PROPN
american_scientific_journal-3982	96	7	1	1	NUM
american_scientific_journal-3982	96	8	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3982	96	9	�	�	PROPN
american_scientific_journal-3982	96	10	(	(	PUNCT
american_scientific_journal-3982	96	11	0	0	NUM
american_scientific_journal-3982	96	12	)	)	PUNCT
american_scientific_journal-3982	96	13	has	have	AUX
american_scientific_journal-3982	96	14	been	be	AUX
american_scientific_journal-3982	96	15	calculated	calculate	VERB
american_scientific_journal-3982	96	16	with	with	ADP
american_scientific_journal-3982	96	17	the	the	DET
american_scientific_journal-3982	96	18	definition	definition	NOUN
american_scientific_journal-3982	96	19	of	of	ADP
american_scientific_journal-3982	96	20	derivative	derivative	NOUN
american_scientific_journal-3982	96	21	.	.	PUNCT
american_scientific_journal-3982	97	1	references	reference	NOUN
american_scientific_journal-3982	97	2	[	[	X
american_scientific_journal-3982	97	3	1	1	NUM
american_scientific_journal-3982	97	4	]	]	PUNCT
american_scientific_journal-3982	97	5	r.	r.	PROPN
american_scientific_journal-3982	97	6	estrada	estrada	PROPN
american_scientific_journal-3982	97	7	&	&	CCONJ
american_scientific_journal-3982	97	8	m.	m.	PROPN
american_scientific_journal-3982	97	9	pavlovi	pavlovi	PROPN
american_scientific_journal-3982	97	10	.	.	PUNCT
american_scientific_journal-3982	98	1	“	"	PUNCT
american_scientific_journal-3982	98	2	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	98	3	’s	’s	PART
american_scientific_journal-3982	98	4	monotone	monotone	ADJ
american_scientific_journal-3982	98	5	rule	rule	NOUN
american_scientific_journal-3982	98	6	,	,	PUNCT
american_scientific_journal-3982	98	7	gromov	gromov	PROPN
american_scientific_journal-3982	98	8	’s	’s	PART
american_scientific_journal-3982	98	9	theorem	theorem	ADJ
american_scientific_journal-3982	98	10	,	,	PUNCT
american_scientific_journal-3982	98	11	and	and	CCONJ
american_scientific_journal-3982	98	12	operations	operation	NOUN
american_scientific_journal-3982	98	13	that	that	PRON
american_scientific_journal-3982	98	14	preserve	preserve	VERB
american_scientific_journal-3982	98	15	the	the	DET
american_scientific_journal-3982	98	16	monotonicity	monotonicity	NOUN
american_scientific_journal-3982	98	17	of	of	ADP
american_scientific_journal-3982	98	18	quotients	quotient	NOUN
american_scientific_journal-3982	98	19	”	"	PUNCT
american_scientific_journal-3982	98	20	,	,	PUNCT
american_scientific_journal-3982	98	21	publ	publ	NOUN
american_scientific_journal-3982	98	22	.	.	PUNCT
american_scientific_journal-3982	99	1	inst	inst	PROPN
american_scientific_journal-3982	99	2	.	.	PUNCT
american_scientific_journal-3982	99	3	math	math	NOUN
american_scientific_journal-3982	99	4	.	.	PUNCT
american_scientific_journal-3982	100	1	(	(	PUNCT
american_scientific_journal-3982	100	2	beograd	beograd	PROPN
american_scientific_journal-3982	100	3	)	)	PUNCT
american_scientific_journal-3982	100	4	(	(	PUNCT
american_scientific_journal-3982	100	5	n.s	n.s	PROPN
american_scientific_journal-3982	100	6	.	.	PROPN
american_scientific_journal-3982	100	7	)	)	PUNCT
american_scientific_journal-3982	100	8	,	,	PUNCT
american_scientific_journal-3982	100	9	101,11–24	101,11–24	NUM
american_scientific_journal-3982	100	10	,	,	PUNCT
american_scientific_journal-3982	100	11	2017	2017	NUM
american_scientific_journal-3982	100	12	.	.	PUNCT
american_scientific_journal-3982	101	1	[	[	X
american_scientific_journal-3982	101	2	2	2	X
american_scientific_journal-3982	101	3	]	]	PUNCT
american_scientific_journal-3982	101	4	h.	h.	PROPN
american_scientific_journal-3982	101	5	struve	struve	PROPN
american_scientific_journal-3982	101	6	&	&	CCONJ
american_scientific_journal-3982	101	7	i.	i.	PROPN
american_scientific_journal-3982	101	8	witzke	witzke	PROPN
american_scientific_journal-3982	101	9	,	,	PUNCT
american_scientific_journal-3982	101	10	“	"	PUNCT
american_scientific_journal-3982	101	11	die	die	VERB
american_scientific_journal-3982	101	12	regel	regel	PROPN
american_scientific_journal-3982	101	13	von	von	PROPN
american_scientific_journal-3982	101	14	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	101	15	”	"	PUNCT
american_scientific_journal-3982	101	16	,	,	PUNCT
american_scientific_journal-3982	101	17	elem	elem	NOUN
american_scientific_journal-3982	101	18	.	.	PUNCT
american_scientific_journal-3982	102	1	math	math	NOUN
american_scientific_journal-3982	102	2	.	.	PUNCT
american_scientific_journal-3982	103	1	,69	,69	PROPN
american_scientific_journal-3982	103	2	,	,	PUNCT
american_scientific_journal-3982	104	1	118–129	118–129	NUM
american_scientific_journal-3982	104	2	,	,	PUNCT
american_scientific_journal-3982	104	3	july	july	PROPN
american_scientific_journal-3982	104	4	2017	2017	NUM
american_scientific_journal-3982	105	1	[	[	X
american_scientific_journal-3982	105	2	3	3	X
american_scientific_journal-3982	105	3	]	]	PUNCT
american_scientific_journal-3982	105	4	s.	s.	PROPN
american_scientific_journal-3982	105	5	zlobec,”l’hôpital	zlobec,”l’hôpital	PROPN
american_scientific_journal-3982	105	6	’s	’s	PART
american_scientific_journal-3982	105	7	rule	rule	NOUN
american_scientific_journal-3982	105	8	without	without	ADP
american_scientific_journal-3982	105	9	derivatives	derivative	NOUN
american_scientific_journal-3982	105	10	”	"	PUNCT
american_scientific_journal-3982	105	11	.	.	PUNCT
american_scientific_journal-3982	106	1	math	math	NOUN
american_scientific_journal-3982	106	2	.	.	PUNCT
american_scientific_journal-3982	107	1	commun,67	commun,67	NOUN
american_scientific_journal-3982	107	2	,	,	PUNCT
american_scientific_journal-3982	107	3	665–672	665–672	NUM
american_scientific_journal-3982	107	4	,	,	PUNCT
american_scientific_journal-3982	107	5	2012	2012	NUM
american_scientific_journal-3982	107	6	[	[	X
american_scientific_journal-3982	107	7	4	4	NUM
american_scientific_journal-3982	107	8	]	]	X
american_scientific_journal-3982	107	9	n.	n.	PROPN
american_scientific_journal-3982	107	10	martins	martins	PROPN
american_scientific_journal-3982	107	11	&	&	CCONJ
american_scientific_journal-3982	107	12	d.	d.	PROPN
american_scientific_journal-3982	107	13	torres	torres	PROPN
american_scientific_journal-3982	107	14	,	,	PUNCT
american_scientific_journal-3982	107	15	“	"	PUNCT
american_scientific_journal-3982	107	16	l’hôpital	l’hôpital	ADJ
american_scientific_journal-3982	107	17	-	-	PUNCT
american_scientific_journal-3982	107	18	type	type	NOUN
american_scientific_journal-3982	107	19	rules	rule	NOUN
american_scientific_journal-3982	107	20	for	for	ADP
american_scientific_journal-3982	107	21	monotonicity	monotonicity	NOUN
american_scientific_journal-3982	107	22	with	with	ADP
american_scientific_journal-3982	107	23	application	application	NOUN
american_scientific_journal-3982	107	24	to	to	ADP
american_scientific_journal-3982	107	25	quantum	quantum	NOUN
american_scientific_journal-3982	107	26	calculus	calculus	NOUN
american_scientific_journal-3982	107	27	”	"	PUNCT
american_scientific_journal-3982	107	28	.	.	PUNCT
american_scientific_journal-3982	108	1	int	int	NOUN
american_scientific_journal-3982	108	2	.	.	PUNCT
american_scientific_journal-3982	109	1	j.	j.	PROPN
american_scientific_journal-3982	109	2	math	math	PROPN
american_scientific_journal-3982	109	3	.	.	PUNCT
american_scientific_journal-3982	110	1	comput	comput	NOUN
american_scientific_journal-3982	110	2	.	.	PUNCT
american_scientific_journal-3982	111	1	10	10	NUM
american_scientific_journal-3982	111	2	,	,	PUNCT
american_scientific_journal-3982	111	3	99–106	99–106	NUM
american_scientific_journal-3982	111	4	,	,	PUNCT
american_scientific_journal-3982	111	5	2011	2011	NUM
american_scientific_journal-3982	111	6	.	.	PUNCT
american_scientific_journal-3982	112	1	[	[	X
american_scientific_journal-3982	112	2	5	5	NUM
american_scientific_journal-3982	112	3	]	]	PUNCT
american_scientific_journal-3982	112	4	a.	a.	NOUN
american_scientific_journal-3982	112	5	v.	v.	PROPN
american_scientific_journal-3982	112	6	shishkina	shishkina	PROPN
american_scientific_journal-3982	112	7	.	.	PUNCT
american_scientific_journal-3982	113	1	“	"	PUNCT
american_scientific_journal-3982	113	2	on	on	ADP
american_scientific_journal-3982	113	3	the	the	DET
american_scientific_journal-3982	113	4	inversion	inversion	NOUN
american_scientific_journal-3982	113	5	of	of	ADP
american_scientific_journal-3982	113	6	the	the	DET
american_scientific_journal-3982	113	7	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	113	8	rule	rule	NOUN
american_scientific_journal-3982	113	9	for	for	ADP
american_scientific_journal-3982	113	10	functions	function	NOUN
american_scientific_journal-3982	113	11	holomorphic	holomorphic	ADJ
american_scientific_journal-3982	113	12	in	in	ADP
american_scientific_journal-3982	113	13	the	the	DET
american_scientific_journal-3982	113	14	ball	ball	NOUN
american_scientific_journal-3982	113	15	”	"	PUNCT
american_scientific_journal-3982	113	16	,	,	PUNCT
american_scientific_journal-3982	113	17	izv	izv	PROPN
american_scientific_journal-3982	113	18	.	.	PROPN
american_scientific_journal-3982	113	19	vyssh	vyssh	PROPN
american_scientific_journal-3982	113	20	.	.	PUNCT
american_scientific_journal-3982	113	21	uchebn	uchebn	NOUN
american_scientific_journal-3982	113	22	.	.	PUNCT
american_scientific_journal-3982	114	1	zaved	zave	VERB
american_scientific_journal-3982	114	2	.	.	PUNCT
american_scientific_journal-3982	115	1	mat	mat	NOUN
american_scientific_journal-3982	115	2	.	.	PROPN
american_scientific_journal-3982	115	3	,50	,50	NOUN
american_scientific_journal-3982	115	4	,	,	PUNCT
american_scientific_journal-3982	115	5	76–82,2006	76–82,2006	NUM
american_scientific_journal-3982	115	6	..	..	PUNCT
american_scientific_journal-3982	116	1	[	[	X
american_scientific_journal-3982	116	2	6	6	NUM
american_scientific_journal-3982	116	3	]	]	PUNCT
american_scientific_journal-3982	116	4	a.	a.	NOUN
american_scientific_journal-3982	116	5	v.	v.	PROPN
american_scientific_journal-3982	116	6	shishkina	shishkina	PROPN
american_scientific_journal-3982	116	7	.	.	PUNCT
american_scientific_journal-3982	117	1	“	"	PUNCT
american_scientific_journal-3982	117	2	on	on	ADP
american_scientific_journal-3982	117	3	the	the	DET
american_scientific_journal-3982	117	4	inversion	inversion	NOUN
american_scientific_journal-3982	117	5	of	of	ADP
american_scientific_journal-3982	117	6	the	the	DET
american_scientific_journal-3982	117	7	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	117	8	rule	rule	NOUN
american_scientific_journal-3982	117	9	for	for	ADP
american_scientific_journal-3982	117	10	analytic	analytic	ADJ
american_scientific_journal-3982	117	11	functions	function	NOUN
american_scientific_journal-3982	117	12	”	"	PUNCT
american_scientific_journal-3982	117	13	,	,	PUNCT
american_scientific_journal-3982	117	14	sibirsk	sibirsk	NOUN
american_scientific_journal-3982	117	15	.	.	PUNCT
american_scientific_journal-3982	118	1	mat	mat	NOUN
american_scientific_journal-3982	118	2	.	.	PUNCT
american_scientific_journal-3982	119	1	zh	zh	PROPN
american_scientific_journal-3982	119	2	.	.	PROPN
american_scientific_journal-3982	119	3	,	,	PUNCT
american_scientific_journal-3982	119	4	46	46	NUM
american_scientific_journal-3982	119	5	,	,	PUNCT
american_scientific_journal-3982	119	6	957–962	957–962	NUM
american_scientific_journal-3982	119	7	2005	2005	NUM
american_scientific_journal-3982	119	8	.	.	PUNCT
american_scientific_journal-3982	120	1	[	[	X
american_scientific_journal-3982	120	2	7	7	NUM
american_scientific_journal-3982	120	3	]	]	X
american_scientific_journal-3982	120	4	popa	popa	NOUN
american_scientific_journal-3982	120	5	,	,	PUNCT
american_scientific_journal-3982	120	6	dumitru	dumitru	PROPN
american_scientific_journal-3982	120	7	,	,	PUNCT
american_scientific_journal-3982	120	8	“	"	PUNCT
american_scientific_journal-3982	120	9	on	on	ADP
american_scientific_journal-3982	120	10	the	the	DET
american_scientific_journal-3982	120	11	vector	vector	NOUN
american_scientific_journal-3982	120	12	form	form	NOUN
american_scientific_journal-3982	120	13	of	of	ADP
american_scientific_journal-3982	120	14	the	the	DET
american_scientific_journal-3982	120	15	lagrange	lagrange	NOUN
american_scientific_journal-3982	120	16	formula	formula	NOUN
american_scientific_journal-3982	120	17	,	,	PUNCT
american_scientific_journal-3982	120	18	the	the	DET
american_scientific_journal-3982	120	19	darboux	darboux	ADJ
american_scientific_journal-3982	120	20	property	property	NOUN
american_scientific_journal-3982	120	21	and	and	CCONJ
american_scientific_journal-3982	120	22	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	120	23	’s	’s	PART
american_scientific_journal-3982	120	24	rule	rule	NOUN
american_scientific_journal-3982	120	25	”	"	PUNCT
american_scientific_journal-3982	120	26	,	,	PUNCT
american_scientific_journal-3982	120	27	real	real	ADJ
american_scientific_journal-3982	120	28	anal	anal	NOUN
american_scientific_journal-3982	120	29	.	.	PUNCT
american_scientific_journal-3982	121	1	exchange,25,787–793,1999	exchange,25,787–793,1999	PROPN
american_scientific_journal-3982	121	2	[	[	X
american_scientific_journal-3982	121	3	8	8	NUM
american_scientific_journal-3982	121	4	]	]	X
american_scientific_journal-3982	121	5	takeuchi	takeuchi	PROPN
american_scientific_journal-3982	121	6	..	..	PUNCT
american_scientific_journal-3982	121	7	yu	yu	PROPN
american_scientific_journal-3982	121	8	“	"	PUNCT
american_scientific_journal-3982	121	9	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	121	10	’s	’s	PART
american_scientific_journal-3982	121	11	rule	rule	NOUN
american_scientific_journal-3982	121	12	for	for	ADP
american_scientific_journal-3982	121	13	series”,bol	series”,bol	PROPN
american_scientific_journal-3982	121	14	.	.	PUNCT
american_scientific_journal-3982	121	15	mat	mat	PROPN
american_scientific_journal-3982	121	16	.	.	PROPN
american_scientific_journal-3982	121	17	,	,	PUNCT
american_scientific_journal-3982	121	18	1,17–33,1995	1,17–33,1995	NUM
american_scientific_journal-3982	121	19	.	.	PUNCT
american_scientific_journal-3982	122	1	https://bidi.uam.mx:9284/mathscinet/search/journaldoc.html?id=3699	https://bidi.uam.mx:9284/mathscinet/search/journaldoc.html?id=3699	PROPN
american_scientific_journal-3982	122	2	https://bidi.uam.mx:9284/mathscinet/search/publications.html?pg1=issi&s1=185375	https://bidi.uam.mx:9284/mathscinet/search/publications.html?pg1=issi&s1=185375	PROPN
american_scientific_journal-3982	122	3	american	american	PROPN
american_scientific_journal-3982	122	4	scientific	scientific	ADJ
american_scientific_journal-3982	122	5	research	research	NOUN
american_scientific_journal-3982	122	6	journal	journal	NOUN
american_scientific_journal-3982	122	7	for	for	ADP
american_scientific_journal-3982	122	8	engineering	engineering	NOUN
american_scientific_journal-3982	122	9	,	,	PUNCT
american_scientific_journal-3982	122	10	technology	technology	NOUN
american_scientific_journal-3982	122	11	,	,	PUNCT
american_scientific_journal-3982	122	12	and	and	CCONJ
american_scientific_journal-3982	122	13	sciences	science	NOUN
american_scientific_journal-3982	122	14	(	(	PUNCT
american_scientific_journal-3982	122	15	asrjets	asrjet	NOUN
american_scientific_journal-3982	122	16	)	)	PUNCT
american_scientific_journal-3982	122	17	(	(	PUNCT
american_scientific_journal-3982	122	18	2018	2018	NUM
american_scientific_journal-3982	122	19	)	)	PUNCT
american_scientific_journal-3982	122	20	volume	volume	NOUN
american_scientific_journal-3982	122	21	41	41	NUM
american_scientific_journal-3982	122	22	,	,	PUNCT
american_scientific_journal-3982	122	23	no	no	DET
american_scientific_journal-3982	122	24	1	1	NUM
american_scientific_journal-3982	122	25	,	,	PUNCT
american_scientific_journal-3982	122	26	pp	pp	ADV
american_scientific_journal-3982	122	27	240	240	NUM
american_scientific_journal-3982	122	28	-	-	SYM
american_scientific_journal-3982	122	29	245	245	NUM
american_scientific_journal-3982	122	30	245	245	NUM
american_scientific_journal-3982	123	1	[	[	X
american_scientific_journal-3982	123	2	9	9	NUM
american_scientific_journal-3982	123	3	]	]	PUNCT
american_scientific_journal-3982	123	4	i.	i.	NOUN
american_scientific_journal-3982	123	5	muntean	muntean	PROPN
american_scientific_journal-3982	123	6	.	.	PUNCT
american_scientific_journal-3982	124	1	“	"	PUNCT
american_scientific_journal-3982	124	2	l,’hôpital	l,’hôpital	PROPN
american_scientific_journal-3982	124	3	’s	’s	PART
american_scientific_journal-3982	124	4	rules	rule	NOUN
american_scientific_journal-3982	124	5	with	with	ADP
american_scientific_journal-3982	124	6	extreme	extreme	ADJ
american_scientific_journal-3982	124	7	limits	limit	NOUN
american_scientific_journal-3982	124	8	”	"	PUNCT
american_scientific_journal-3982	124	9	in	in	ADP
american_scientific_journal-3982	124	10	seminar	seminar	NOUN
american_scientific_journal-3982	124	11	on	on	ADP
american_scientific_journal-3982	124	12	mathematical	mathematical	ADJ
american_scientific_journal-3982	124	13	analysis	analysis	NOUN
american_scientific_journal-3982	124	14	,	,	PUNCT
american_scientific_journal-3982	124	15	1993	1993	NUM
american_scientific_journal-3982	124	16	,	,	PUNCT
american_scientific_journal-3982	124	17	11	11	NUM
american_scientific_journal-3982	124	18	–	–	SYM
american_scientific_journal-3982	124	19	28	28	NUM
american_scientific_journal-3982	124	20	.	.	PUNCT
american_scientific_journal-3982	125	1	[	[	X
american_scientific_journal-3982	125	2	10	10	NUM
american_scientific_journal-3982	125	3	]	]	SYM
american_scientific_journal-3982	125	4	m.vianello	m.vianello	NOUN
american_scientific_journal-3982	125	5	.	.	PUNCT
american_scientific_journal-3982	126	1	“	"	PUNCT
american_scientific_journal-3982	126	2	a	a	DET
american_scientific_journal-3982	126	3	generalization	generalization	NOUN
american_scientific_journal-3982	126	4	of	of	ADP
american_scientific_journal-3982	126	5	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	126	6	’s	’s	PART
american_scientific_journal-3982	126	7	rule	rule	NOUN
american_scientific_journal-3982	126	8	via	via	ADP
american_scientific_journal-3982	126	9	absolute	absolute	ADJ
american_scientific_journal-3982	126	10	continuity	continuity	NOUN
american_scientific_journal-3982	126	11	and	and	CCONJ
american_scientific_journal-3982	126	12	banach	banach	NOUN
american_scientific_journal-3982	126	13	modules	module	NOUN
american_scientific_journal-3982	126	14	”	"	PUNCT
american_scientific_journal-3982	126	15	.	.	PUNCT
american_scientific_journal-3982	127	1	real	real	ADJ
american_scientific_journal-3982	127	2	anal	anal	PROPN
american_scientific_journal-3982	127	3	.	.	PUNCT
american_scientific_journal-3982	128	1	exchange	exchange	NOUN
american_scientific_journal-3982	128	2	,	,	PUNCT
american_scientific_journal-3982	128	3	18	18	NUM
american_scientific_journal-3982	128	4	,	,	PUNCT
american_scientific_journal-3982	128	5	557–567.1993	557–567.1993	NUM
american_scientific_journal-3982	128	6	.	.	PUNCT
american_scientific_journal-3982	129	1	[	[	X
american_scientific_journal-3982	129	2	11	11	NUM
american_scientific_journal-3982	129	3	]	]	X
american_scientific_journal-3982	129	4	y.x	y.x	PROPN
american_scientific_journal-3982	129	5	.	.	PROPN
american_scientific_journal-3982	129	6	tian	tian	PROPN
american_scientific_journal-3982	129	7	,	,	PUNCT
american_scientific_journal-3982	129	8	“	"	PUNCT
american_scientific_journal-3982	129	9	l’hôpital	l’hôpital	NOUN
american_scientific_journal-3982	129	10	rules	rule	NOUN
american_scientific_journal-3982	129	11	for	for	ADP
american_scientific_journal-3982	129	12	conjugate	conjugate	ADJ
american_scientific_journal-3982	129	13	analytic	analytic	ADJ
american_scientific_journal-3982	129	14	functions	function	NOUN
american_scientific_journal-3982	129	15	”	"	PUNCT
american_scientific_journal-3982	129	16	,	,	PUNCT
american_scientific_journal-3982	129	17	sichuan	sichuan	PROPN
american_scientific_journal-3982	129	18	shifan	shifan	PROPN
american_scientific_journal-3982	129	19	daxue	daxue	PROPN
american_scientific_journal-3982	129	20	xuebao	xuebao	PROPN
american_scientific_journal-3982	130	1	ziran	ziran	PROPN
american_scientific_journal-3982	130	2	kexue	kexue	PROPN
american_scientific_journal-3982	130	3	ban	ban	VERB
american_scientific_journal-3982	130	4	16,53–56,1993	16,53–56,1993	PRON
american_scientific_journal-3982	130	5	.	.	PUNCT
american_scientific_journal-3982	131	1	[	[	X
american_scientific_journal-3982	131	2	12	12	NUM
american_scientific_journal-3982	131	3	]	]	X
american_scientific_journal-3982	131	4	r.	r.	PROPN
american_scientific_journal-3982	131	5	spigler	spigler	PROPN
american_scientific_journal-3982	131	6	&	&	CCONJ
american_scientific_journal-3982	131	7	m.	m.	PROPN
american_scientific_journal-3982	131	8	vianello	vianello	PROPN
american_scientific_journal-3982	131	9	.	.	PUNCT
american_scientific_journal-3982	132	1	“	"	PUNCT
american_scientific_journal-3982	132	2	abstract	abstract	ADJ
american_scientific_journal-3982	132	3	abstract	abstract	ADJ
american_scientific_journal-3982	132	4	versions	version	NOUN
american_scientific_journal-3982	132	5	of	of	ADP
american_scientific_journal-3982	132	6	l'hôpital	l'hôpital	PROPN
american_scientific_journal-3982	132	7	's	's	PART
american_scientific_journal-3982	132	8	rule	rule	NOUN
american_scientific_journal-3982	132	9	for	for	ADP
american_scientific_journal-3982	132	10	holomorphic	holomorphic	ADJ
american_scientific_journal-3982	132	11	functions	function	NOUN
american_scientific_journal-3982	132	12	in	in	ADP
american_scientific_journal-3982	132	13	the	the	DET
american_scientific_journal-3982	132	14	framework	framework	NOUN
american_scientific_journal-3982	132	15	of	of	ADP
american_scientific_journal-3982	132	16	complex	complex	ADJ
american_scientific_journal-3982	132	17	b	b	NOUN
american_scientific_journal-3982	132	18	-	-	PUNCT
american_scientific_journal-3982	132	19	modules	module	NOUN
american_scientific_journal-3982	132	20	”	"	PUNCT
american_scientific_journal-3982	132	21	j.	j.	PROPN
american_scientific_journal-3982	132	22	math	math	PROPN
american_scientific_journal-3982	132	23	.	.	PUNCT
american_scientific_journal-3982	133	1	anal	anal	PROPN
american_scientific_journal-3982	133	2	.	.	PUNCT
american_scientific_journal-3982	134	1	appl,17–28,1993	appl,17–28,1993	PROPN
american_scientific_journal-3982	134	2	.	.	PUNCT
american_scientific_journal-3982	135	1	[	[	X
american_scientific_journal-3982	135	2	13	13	NUM
american_scientific_journal-3982	135	3	]	]	SYM
american_scientific_journal-3982	135	4	a.	a.	NOUN
american_scientific_journal-3982	135	5	l.	l.	PROPN
american_scientific_journal-3982	135	6	durán	durán	PROPN
american_scientific_journal-3982	135	7	.	.	PUNCT
american_scientific_journal-3982	136	1	“	"	PUNCT
american_scientific_journal-3982	136	2	the	the	DET
american_scientific_journal-3982	136	3	converse	converse	NOUN
american_scientific_journal-3982	136	4	of	of	ADP
american_scientific_journal-3982	136	5	de	de	PROPN
american_scientific_journal-3982	136	6	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	136	7	’s	’s	PART
american_scientific_journal-3982	136	8	rule	rule	NOUN
american_scientific_journal-3982	136	9	”	"	PUNCT
american_scientific_journal-3982	136	10	.	.	PUNCT
american_scientific_journal-3982	137	1	cienc	cienc	PROPN
american_scientific_journal-3982	137	2	.	.	PUNCT
american_scientific_journal-3982	138	1	tecn	tecn	PROPN
american_scientific_journal-3982	138	2	.	.	PUNCT
american_scientific_journal-3982	139	1	,	,	PUNCT
american_scientific_journal-3982	139	2	16	16	NUM
american_scientific_journal-3982	139	3	,	,	PUNCT
american_scientific_journal-3982	139	4	111–119	111–119	NUM
american_scientific_journal-3982	139	5	.	.	NOUN
american_scientific_journal-3982	139	6	1992	1992	NUM
american_scientific_journal-3982	139	7	.	.	PUNCT
american_scientific_journal-3982	140	1	[	[	X
american_scientific_journal-3982	140	2	14	14	NUM
american_scientific_journal-3982	140	3	]	]	SYM
american_scientific_journal-3982	140	4	hartig	hartig	NOUN
american_scientific_journal-3982	140	5	,	,	PUNCT
american_scientific_journal-3982	140	6	donald	donald	PROPN
american_scientific_journal-3982	140	7	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	140	8	’s	’s	PART
american_scientific_journal-3982	140	9	rule	rule	NOUN
american_scientific_journal-3982	140	10	via	via	ADP
american_scientific_journal-3982	140	11	integration	integration	NOUN
american_scientific_journal-3982	140	12	.	.	PUNCT
american_scientific_journal-3982	141	1	amer	amer	PROPN
american_scientific_journal-3982	141	2	.	.	PUNCT
american_scientific_journal-3982	141	3	math	math	PROPN
american_scientific_journal-3982	141	4	.	.	PUNCT
american_scientific_journal-3982	142	1	monthly	monthly	ADJ
american_scientific_journal-3982	142	2	98	98	NUM
american_scientific_journal-3982	142	3	(	(	PUNCT
american_scientific_journal-3982	142	4	1991	1991	NUM
american_scientific_journal-3982	142	5	)	)	PUNCT
american_scientific_journal-3982	142	6	,	,	PUNCT
american_scientific_journal-3982	142	7	no	no	INTJ
american_scientific_journal-3982	142	8	.	.	NOUN
american_scientific_journal-3982	142	9	2	2	NUM
american_scientific_journal-3982	142	10	,	,	PUNCT
american_scientific_journal-3982	142	11	156–157	156–157	NUM
american_scientific_journal-3982	142	12	.	.	PUNCT
american_scientific_journal-3982	143	1	[	[	X
american_scientific_journal-3982	143	2	15	15	NUM
american_scientific_journal-3982	143	3	]	]	X
american_scientific_journal-3982	143	4	shishkina	shishkina	NOUN
american_scientific_journal-3982	143	5	,	,	PUNCT
american_scientific_journal-3982	143	6	a.	a.	NOUN
american_scientific_journal-3982	143	7	v.	v.	ADV
american_scientific_journal-3982	143	8	on	on	ADP
american_scientific_journal-3982	143	9	the	the	DET
american_scientific_journal-3982	143	10	inversion	inversion	NOUN
american_scientific_journal-3982	143	11	of	of	ADP
american_scientific_journal-3982	143	12	the	the	DET
american_scientific_journal-3982	143	13	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	143	14	rule	rule	NOUN
american_scientific_journal-3982	143	15	for	for	ADP
american_scientific_journal-3982	143	16	functions	function	NOUN
american_scientific_journal-3982	143	17	holomorphic	holomorphic	ADJ
american_scientific_journal-3982	143	18	in	in	ADP
american_scientific_journal-3982	143	19	the	the	DET
american_scientific_journal-3982	143	20	ball	ball	NOUN
american_scientific_journal-3982	143	21	.	.	PUNCT
american_scientific_journal-3982	144	1	(	(	PUNCT
american_scientific_journal-3982	144	2	russian	russian	ADJ
american_scientific_journal-3982	144	3	)	)	PUNCT
american_scientific_journal-3982	144	4	izv	izv	PROPN
american_scientific_journal-3982	144	5	.	.	PROPN
american_scientific_journal-3982	144	6	vyssh	vyssh	PROPN
american_scientific_journal-3982	144	7	.	.	PUNCT
american_scientific_journal-3982	145	1	uchebn	uchebn	NOUN
american_scientific_journal-3982	145	2	.	.	PUNCT
american_scientific_journal-3982	146	1	zaved	zave	VERB
american_scientific_journal-3982	146	2	.	.	PUNCT
american_scientific_journal-3982	147	1	mat	mat	NOUN
american_scientific_journal-3982	147	2	.	.	NOUN
american_scientific_journal-3982	148	1	2006	2006	NUM
american_scientific_journal-3982	148	2	,	,	PUNCT
american_scientific_journal-3982	148	3	no	no	INTJ
american_scientific_journal-3982	148	4	.	.	NOUN
american_scientific_journal-3982	148	5	6	6	NUM
american_scientific_journal-3982	148	6	,	,	PUNCT
american_scientific_journal-3982	148	7	78	78	NUM
american_scientific_journal-3982	148	8	-	-	SYM
american_scientific_journal-3982	148	9	-84	-84	NUM
american_scientific_journal-3982	148	10	;	;	PUNCT
american_scientific_journal-3982	148	11	translation	translation	NOUN
american_scientific_journal-3982	148	12	in	in	ADP
american_scientific_journal-3982	148	13	russian	russian	ADJ
american_scientific_journal-3982	148	14	math	math	NOUN
american_scientific_journal-3982	148	15	.	.	PUNCT
american_scientific_journal-3982	149	1	(	(	PUNCT
american_scientific_journal-3982	149	2	iz	iz	INTJ
american_scientific_journal-3982	149	3	.	.	PUNCT
american_scientific_journal-3982	149	4	vuz	vuz	PROPN
american_scientific_journal-3982	149	5	)	)	PUNCT
american_scientific_journal-3982	149	6	50	50	NUM
american_scientific_journal-3982	149	7	(	(	PUNCT
american_scientific_journal-3982	149	8	2006	2006	NUM
american_scientific_journal-3982	149	9	)	)	PUNCT
american_scientific_journal-3982	149	10	,	,	PUNCT
american_scientific_journal-3982	149	11	no	no	INTJ
american_scientific_journal-3982	149	12	.	.	NOUN
american_scientific_journal-3982	149	13	6	6	NUM
american_scientific_journal-3982	149	14	,	,	PUNCT
american_scientific_journal-3982	149	15	76–82	76–82	NUM
american_scientific_journal-3982	149	16	(	(	PUNCT
american_scientific_journal-3982	149	17	2007	2007	NUM
american_scientific_journal-3982	149	18	)	)	PUNCT
american_scientific_journal-3982	149	19	(	(	PUNCT
american_scientific_journal-3982	149	20	reviewer	reviewer	NOUN
american_scientific_journal-3982	149	21	:	:	PUNCT
american_scientific_journal-3982	149	22	sergey	sergey	PROPN
american_scientific_journal-3982	149	23	ivashkovich	ivashkovich	PROPN
american_scientific_journal-3982	149	24	)	)	PUNCT
american_scientific_journal-3982	149	25	32a10	32a10	NUM
american_scientific_journal-3982	149	26	.	.	PUNCT
american_scientific_journal-3982	150	1	[	[	X
american_scientific_journal-3982	150	2	16	16	NUM
american_scientific_journal-3982	150	3	]	]	X
american_scientific_journal-3982	150	4	popa	popa	NOUN
american_scientific_journal-3982	150	5	,	,	PUNCT
american_scientific_journal-3982	150	6	dumitru	dumitru	NOUN
american_scientific_journal-3982	150	7	on	on	ADP
american_scientific_journal-3982	150	8	the	the	DET
american_scientific_journal-3982	150	9	vector	vector	NOUN
american_scientific_journal-3982	150	10	form	form	NOUN
american_scientific_journal-3982	150	11	of	of	ADP
american_scientific_journal-3982	150	12	the	the	DET
american_scientific_journal-3982	150	13	lagrange	lagrange	NOUN
american_scientific_journal-3982	150	14	formula	formula	NOUN
american_scientific_journal-3982	150	15	,	,	PUNCT
american_scientific_journal-3982	150	16	the	the	DET
american_scientific_journal-3982	150	17	darboux	darboux	ADJ
american_scientific_journal-3982	150	18	property	property	NOUN
american_scientific_journal-3982	150	19	and	and	CCONJ
american_scientific_journal-3982	150	20	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	150	21	’s	’s	PART
american_scientific_journal-3982	150	22	rule	rule	NOUN
american_scientific_journal-3982	150	23	.	.	PUNCT
american_scientific_journal-3982	151	1	[	[	X
american_scientific_journal-3982	151	2	17	17	NUM
american_scientific_journal-3982	151	3	]	]	X
american_scientific_journal-3982	151	4	takeuchi	takeuchi	PROPN
american_scientific_journal-3982	151	5	,	,	PUNCT
american_scientific_journal-3982	151	6	yu	yu	PROPN
american_scientific_journal-3982	151	7	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	151	8	’s	’s	PART
american_scientific_journal-3982	151	9	rule	rule	NOUN
american_scientific_journal-3982	151	10	for	for	ADP
american_scientific_journal-3982	151	11	series	series	NOUN
american_scientific_journal-3982	151	12	.	.	PUNCT
american_scientific_journal-3982	152	1	(	(	PUNCT
american_scientific_journal-3982	152	2	spanish	spanish	ADJ
american_scientific_journal-3982	152	3	)	)	PUNCT
american_scientific_journal-3982	152	4	bol	bol	NOUN
american_scientific_journal-3982	152	5	.	.	PUNCT
american_scientific_journal-3982	153	1	mat	mat	NOUN
american_scientific_journal-3982	153	2	.	.	NOUN
american_scientific_journal-3982	153	3	1/2	1/2	NUM
american_scientific_journal-3982	153	4	(	(	PUNCT
american_scientific_journal-3982	153	5	1995	1995	NUM
american_scientific_journal-3982	153	6	)	)	PUNCT
american_scientific_journal-3982	153	7	,	,	PUNCT
american_scientific_journal-3982	153	8	no	no	INTJ
american_scientific_journal-3982	153	9	.	.	NOUN
american_scientific_journal-3982	153	10	2	2	NUM
american_scientific_journal-3982	153	11	-	-	SYM
american_scientific_journal-3982	153	12	1	1	NUM
american_scientific_journal-3982	153	13	,	,	PUNCT
american_scientific_journal-3982	153	14	17–33	17–33	NUM
american_scientific_journal-3982	153	15	.	.	PUNCT
american_scientific_journal-3982	154	1	[	[	X
american_scientific_journal-3982	154	2	18	18	NUM
american_scientific_journal-3982	154	3	]	]	SYM
american_scientific_journal-3982	154	4	muntean	muntean	PROPN
american_scientific_journal-3982	154	5	,	,	PUNCT
american_scientific_journal-3982	154	6	ioan	ioan	PROPN
american_scientific_journal-3982	154	7	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	154	8	’s	’s	PART
american_scientific_journal-3982	154	9	rules	rule	NOUN
american_scientific_journal-3982	154	10	with	with	ADP
american_scientific_journal-3982	154	11	extreme	extreme	ADJ
american_scientific_journal-3982	154	12	limits	limit	NOUN
american_scientific_journal-3982	154	13	.	.	PUNCT
american_scientific_journal-3982	155	1	seminar	seminar	NOUN
american_scientific_journal-3982	155	2	on	on	ADP
american_scientific_journal-3982	155	3	mathematical	mathematical	ADJ
american_scientific_journal-3982	155	4	analysis	analysis	NOUN
american_scientific_journal-3982	155	5	(	(	PUNCT
american_scientific_journal-3982	155	6	clujnapoca	clujnapoca	NOUN
american_scientific_journal-3982	155	7	,	,	PUNCT
american_scientific_journal-3982	155	8	1992–1993	1992–1993	NUM
american_scientific_journal-3982	155	9	)	)	PUNCT
american_scientific_journal-3982	155	10	,	,	PUNCT
american_scientific_journal-3982	155	11	11–28	11–28	NUM
american_scientific_journal-3982	155	12	,	,	PUNCT
american_scientific_journal-3982	155	13	preprint	preprint	NOUN
american_scientific_journal-3982	155	14	,	,	PUNCT
american_scientific_journal-3982	155	15	93	93	NUM
american_scientific_journal-3982	155	16	-	-	SYM
american_scientific_journal-3982	155	17	7	7	NUM
american_scientific_journal-3982	155	18	,	,	PUNCT
american_scientific_journal-3982	155	19	"	"	PUNCT
american_scientific_journal-3982	155	20	babe	babe	NOUN
american_scientific_journal-3982	155	21	-	-	PUNCT
american_scientific_journal-3982	155	22	bolyai	bolyai	NOUN
american_scientific_journal-3982	155	23	”	"	PUNCT
american_scientific_journal-3982	155	24	univ	univ	PROPN
american_scientific_journal-3982	155	25	.	.	PROPN
american_scientific_journal-3982	155	26	,	,	PUNCT
american_scientific_journal-3982	155	27	cluj	cluj	PROPN
american_scientific_journal-3982	155	28	-	-	PUNCT
american_scientific_journal-3982	155	29	napoca	napoca	NOUN
american_scientific_journal-3982	155	30	,	,	PUNCT
american_scientific_journal-3982	155	31	1993	1993	NUM
american_scientific_journal-3982	155	32	.	.	PUNCT
american_scientific_journal-3982	156	1	[	[	X
american_scientific_journal-3982	156	2	19	19	NUM
american_scientific_journal-3982	156	3	]	]	SYM
american_scientific_journal-3982	156	4	spigler	spigler	NOUN
american_scientific_journal-3982	156	5	,	,	PUNCT
american_scientific_journal-3982	156	6	renato	renato	PROPN
american_scientific_journal-3982	156	7	;	;	PUNCT
american_scientific_journal-3982	156	8	vianello	vianello	PROPN
american_scientific_journal-3982	156	9	,	,	PUNCT
american_scientific_journal-3982	156	10	marco	marco	PROPN
american_scientific_journal-3982	156	11	abstract	abstract	ADJ
american_scientific_journal-3982	156	12	versions	version	NOUN
american_scientific_journal-3982	156	13	of	of	ADP
american_scientific_journal-3982	156	14	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	156	15	’s	’s	PART
american_scientific_journal-3982	156	16	rule	rule	NOUN
american_scientific_journal-3982	156	17	for	for	ADP
american_scientific_journal-3982	156	18	holomorphic	holomorphic	ADJ
american_scientific_journal-3982	156	19	functions	function	NOUN
american_scientific_journal-3982	156	20	in	in	ADP
american_scientific_journal-3982	156	21	the	the	DET
american_scientific_journal-3982	156	22	framework	framework	NOUN
american_scientific_journal-3982	156	23	of	of	ADP
american_scientific_journal-3982	156	24	complex	complex	ADJ
american_scientific_journal-3982	156	25	b	b	NOUN
american_scientific_journal-3982	156	26	-	-	PUNCT
american_scientific_journal-3982	156	27	modules	module	NOUN
american_scientific_journal-3982	156	28	.	.	PUNCT
american_scientific_journal-3982	157	1	j.	j.	PROPN
american_scientific_journal-3982	157	2	math	math	PROPN
american_scientific_journal-3982	157	3	.	.	PUNCT
american_scientific_journal-3982	158	1	anal	anal	PROPN
american_scientific_journal-3982	158	2	.	.	PUNCT
american_scientific_journal-3982	159	1	appl	appl	PROPN
american_scientific_journal-3982	159	2	.	.	PROPN
american_scientific_journal-3982	160	1	180	180	NUM
american_scientific_journal-3982	160	2	(	(	PUNCT
american_scientific_journal-3982	160	3	1993	1993	NUM
american_scientific_journal-3982	160	4	)	)	PUNCT
american_scientific_journal-3982	160	5	,	,	PUNCT
american_scientific_journal-3982	160	6	no	no	INTJ
american_scientific_journal-3982	160	7	.	.	NOUN
american_scientific_journal-3982	160	8	1	1	NUM
american_scientific_journal-3982	160	9	,	,	PUNCT
american_scientific_journal-3982	160	10	17–28	17–28	NUM
american_scientific_journal-3982	160	11	.	.	PUNCT
american_scientific_journal-3982	161	1	[	[	X
american_scientific_journal-3982	161	2	20	20	NUM
american_scientific_journal-3982	161	3	]	]	PUNCT
american_scientific_journal-3982	161	4	d.	d.	PROPN
american_scientific_journal-3982	161	5	hartig	hartig	PROPN
american_scientific_journal-3982	161	6	.	.	PUNCT
american_scientific_journal-3982	162	1	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	162	2	’s	’s	PART
american_scientific_journal-3982	162	3	rule	rule	NOUN
american_scientific_journal-3982	162	4	via	via	ADP
american_scientific_journal-3982	162	5	integration	integration	NOUN
american_scientific_journal-3982	162	6	”	"	PUNCT
american_scientific_journal-3982	162	7	,	,	PUNCT
american_scientific_journal-3982	162	8	amer	amer	PROPN
american_scientific_journal-3982	162	9	.	.	PROPN
american_scientific_journal-3982	162	10	math	math	PROPN
american_scientific_journal-3982	162	11	.	.	PUNCT
american_scientific_journal-3982	163	1	monthly	monthly	ADJ
american_scientific_journal-3982	163	2	,	,	PUNCT
american_scientific_journal-3982	163	3	98	98	NUM
american_scientific_journal-3982	163	4	,	,	PUNCT
american_scientific_journal-3982	163	5	156–157	156–157	NUM
american_scientific_journal-3982	163	6	.	.	NOUN
american_scientific_journal-3982	163	7	199	199	NUM
american_scientific_journal-3982	163	8	.	.	PUNCT
american_scientific_journal-3982	164	1	[	[	X
american_scientific_journal-3982	164	2	21	21	NUM
american_scientific_journal-3982	164	3	]	]	PUNCT
american_scientific_journal-3982	164	4	j.	j.	PROPN
american_scientific_journal-3982	164	5	aczél	aczél	PROPN
american_scientific_journal-3982	164	6	.	.	PUNCT
american_scientific_journal-3982	165	1	“	"	PUNCT
american_scientific_journal-3982	165	2	functional	functional	ADJ
american_scientific_journal-3982	165	3	equations	equation	NOUN
american_scientific_journal-3982	165	4	and	and	CCONJ
american_scientific_journal-3982	165	5	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	165	6	’s	’s	PART
american_scientific_journal-3982	165	7	rule	rule	NOUN
american_scientific_journal-3982	165	8	in	in	ADP
american_scientific_journal-3982	165	9	an	an	DET
american_scientific_journal-3982	165	10	exact	exact	ADJ
american_scientific_journal-3982	165	11	poisson	poisson	NOUN
american_scientific_journal-3982	165	12	derivation	derivation	NOUN
american_scientific_journal-3982	165	13	”	"	PUNCT
american_scientific_journal-3982	165	14	,	,	PUNCT
american_scientific_journal-3982	165	15	amer	amer	PROPN
american_scientific_journal-3982	165	16	.	.	PROPN
american_scientific_journal-3982	165	17	math	math	PROPN
american_scientific_journal-3982	165	18	.	.	PUNCT
american_scientific_journal-3982	166	1	monthly	monthly	ADJ
american_scientific_journal-3982	166	2	,	,	PUNCT
american_scientific_journal-3982	166	3	97	97	NUM
american_scientific_journal-3982	166	4	,	,	PUNCT
american_scientific_journal-3982	166	5	423–426	423–426	NUM
american_scientific_journal-3982	166	6	.	.	NOUN
american_scientific_journal-3982	166	7	1990	1990	NUM
american_scientific_journal-3982	166	8	.	.	PUNCT
american_scientific_journal-3982	167	1	22	22	NUM
american_scientific_journal-3982	167	2	]	]	PUNCT
american_scientific_journal-3982	167	3	g.	g.	PROPN
american_scientific_journal-3982	167	4	szabó	szabó	PROPN
american_scientific_journal-3982	167	5	,	,	PUNCT
american_scientific_journal-3982	167	6	"	"	PUNCT
american_scientific_journal-3982	167	7	a	a	DET
american_scientific_journal-3982	167	8	note	note	NOUN
american_scientific_journal-3982	167	9	on	on	ADP
american_scientific_journal-3982	167	10	the	the	DET
american_scientific_journal-3982	167	11	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	167	12	’s	’s	PART
american_scientific_journal-3982	167	13	rule	rule	NOUN
american_scientific_journal-3982	167	14	"	"	PUNCT
american_scientific_journal-3982	167	15	,	,	PUNCT
american_scientific_journal-3982	167	16	elem	elem	NOUN
american_scientific_journal-3982	167	17	.	.	PUNCT
american_scientific_journal-3982	168	1	math	math	NOUN
american_scientific_journal-3982	168	2	.	.	PUNCT
american_scientific_journal-3982	169	1	44	44	NUM
american_scientific_journal-3982	169	2	,	,	PUNCT
american_scientific_journal-3982	169	3	150–153,1989	150–153,1989	NUM
american_scientific_journal-3982	169	4	.	.	PUNCT
american_scientific_journal-3982	170	1	[	[	X
american_scientific_journal-3982	170	2	23	23	NUM
american_scientific_journal-3982	170	3	]	]	X
american_scientific_journal-3982	170	4	r.	r.	PROPN
american_scientific_journal-3982	170	5	výborný	výborný	PROPN
american_scientific_journal-3982	170	6	&	&	CCONJ
american_scientific_journal-3982	170	7	r.	r.	PROPN
american_scientific_journal-3982	170	8	nester	nester	NOUN
american_scientific_journal-3982	170	9	,	,	PUNCT
american_scientific_journal-3982	170	10	"	"	PUNCT
american_scientific_journal-3982	170	11	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	170	12	’s	’s	PART
american_scientific_journal-3982	170	13	rule	rule	NOUN
american_scientific_journal-3982	170	14	,	,	PUNCT
american_scientific_journal-3982	170	15	a	a	DET
american_scientific_journal-3982	170	16	counterexample	counterexample	NOUN
american_scientific_journal-3982	170	17	"	"	PUNCT
american_scientific_journal-3982	170	18	.	.	PUNCT
american_scientific_journal-3982	170	19	elem	elem	NOUN
american_scientific_journal-3982	170	20	.	.	PUNCT
american_scientific_journal-3982	171	1	math	math	NOUN
american_scientific_journal-3982	171	2	.	.	PUNCT
american_scientific_journal-3982	172	1	44	44	NUM
american_scientific_journal-3982	172	2	,	,	PUNCT
american_scientific_journal-3982	172	3	116–121,1989	116–121,1989	NUM
american_scientific_journal-3982	172	4	.	.	PUNCT
american_scientific_journal-3982	173	1	[	[	X
american_scientific_journal-3982	173	2	24]w	24]w	NUM
american_scientific_journal-3982	173	3	.	.	PUNCT
american_scientific_journal-3982	174	1	p	p	PROPN
american_scientific_journal-3982	174	2	cooke	cooke	PROPN
american_scientific_journal-3982	174	3	,	,	PUNCT
american_scientific_journal-3982	174	4	"	"	PUNCT
american_scientific_journal-3982	174	5	the	the	DET
american_scientific_journal-3982	174	6	teaching	teaching	NOUN
american_scientific_journal-3982	174	7	of	of	ADP
american_scientific_journal-3982	174	8	mathematics	mathematic	NOUN
american_scientific_journal-3982	174	9	:	:	PUNCT
american_scientific_journal-3982	174	10	l’hopital	l’hopital	PROPN
american_scientific_journal-3982	174	11	’s	’s	PART
american_scientific_journal-3982	174	12	rule	rule	NOUN
american_scientific_journal-3982	174	13	in	in	ADP
american_scientific_journal-3982	174	14	a	a	DET
american_scientific_journal-3982	174	15	poisson	poisson	NOUN
american_scientific_journal-3982	174	16	derivation	derivation	NOUN
american_scientific_journal-3982	174	17	"	"	PUNCT
american_scientific_journal-3982	174	18	.	.	PUNCT
american_scientific_journal-3982	175	1	amer	amer	PROPN
american_scientific_journal-3982	175	2	.	.	PUNCT
american_scientific_journal-3982	175	3	math	math	PROPN
american_scientific_journal-3982	175	4	.	.	PUNCT
american_scientific_journal-3982	176	1	monthly	monthly	ADJ
american_scientific_journal-3982	176	2	95	95	NUM
american_scientific_journal-3982	176	3	,	,	PUNCT
american_scientific_journal-3982	176	4	253–254.1988	253–254.1988	NUM
american_scientific_journal-3982	176	5	.	.	PUNCT
american_scientific_journal-3982	177	1	[	[	X
american_scientific_journal-3982	177	2	25	25	NUM
american_scientific_journal-3982	177	3	]	]	PUNCT
american_scientific_journal-3982	177	4	x.	x.	PROPN
american_scientific_journal-3982	177	5	c.	c.	PROPN
american_scientific_journal-3982	177	6	huang	huang	PROPN
american_scientific_journal-3982	177	7	,	,	PUNCT
american_scientific_journal-3982	177	8	"	"	PUNCT
american_scientific_journal-3982	177	9	a	a	DET
american_scientific_journal-3982	177	10	discrete	discrete	ADJ
american_scientific_journal-3982	177	11	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	177	12	’s	’s	PART
american_scientific_journal-3982	177	13	rule",college	rule",college	PROPN
american_scientific_journal-3982	177	14	math	math	NOUN
american_scientific_journal-3982	177	15	.	.	PUNCT
american_scientific_journal-3982	178	1	j.	j.	PROPN
american_scientific_journal-3982	178	2	,	,	PUNCT
american_scientific_journal-3982	178	3	19	19	NUM
american_scientific_journal-3982	178	4	,	,	PUNCT
american_scientific_journal-3982	178	5	321–329,1988	321–329,1988	NUM
american_scientific_journal-3982	178	6	.	.	PUNCT
american_scientific_journal-3982	179	1	https://bidi.uam.mx:9284/mathscinet/search/journaldoc.html?id=3591	https://bidi.uam.mx:9284/mathscinet/search/journaldoc.html?id=3591	NOUN
american_scientific_journal-3982	179	2	about	about	ADP
american_scientific_journal-3982	179	3	the	the	DET
american_scientific_journal-3982	179	4	proof	proof	NOUN
american_scientific_journal-3982	179	5	of	of	ADP
american_scientific_journal-3982	179	6	the	the	DET
american_scientific_journal-3982	179	7	l’hôpital	l’hôpital	PROPN
american_scientific_journal-3982	179	8	's	's	PART
american_scientific_journal-3982	179	9	rule	rule	NOUN
american_scientific_journal-3982	179	10	2	2	NUM
american_scientific_journal-3982	179	11	.	.	PUNCT
american_scientific_journal-3982	180	1	definitions	definition	NOUN
american_scientific_journal-3982	180	2	y	y	PROPN
american_scientific_journal-3982	180	3	results	result	VERB
american_scientific_journal-3982	180	4	on	on	ADP
american_scientific_journal-3982	180	5	continuity	continuity	NOUN
american_scientific_journal-3982	180	6	and	and	CCONJ
american_scientific_journal-3982	180	7	derivation	derivation	NOUN
american_scientific_journal-3982	180	8	of	of	ADP
american_scientific_journal-3982	180	9	locally	locally	ADV
american_scientific_journal-3982	180	10	defined	define	VERB
american_scientific_journal-3982	180	11	functions	function	NOUN
american_scientific_journal-3982	180	12	3	3	NUM
american_scientific_journal-3982	180	13	.	.	PUNCT
american_scientific_journal-3982	180	14	main	main	ADJ
american_scientific_journal-3982	180	15	results	result	NOUN
american_scientific_journal-3982	180	16	5	5	NUM
american_scientific_journal-3982	180	17	.	.	PUNCT
american_scientific_journal-3982	180	18	conclusions	conclusion	NOUN