id	sid	tid	token	lemma	pos
american_scientific_journal-761	1	1	american	american	PROPN
american_scientific_journal-761	1	2	scientific	scientific	ADJ
american_scientific_journal-761	1	3	research	research	NOUN
american_scientific_journal-761	1	4	journal	journal	NOUN
american_scientific_journal-761	1	5	for	for	ADP
american_scientific_journal-761	1	6	engineering	engineering	NOUN
american_scientific_journal-761	1	7	,	,	PUNCT
american_scientific_journal-761	1	8	technology	technology	NOUN
american_scientific_journal-761	1	9	,	,	PUNCT
american_scientific_journal-761	1	10	and	and	CCONJ
american_scientific_journal-761	1	11	sciences	science	NOUN
american_scientific_journal-761	1	12	(	(	PUNCT
american_scientific_journal-761	1	13	asrjets	asrjet	NOUN
american_scientific_journal-761	1	14	)	)	PUNCT
american_scientific_journal-761	1	15	issn	issn	PROPN
american_scientific_journal-761	1	16	(	(	PUNCT
american_scientific_journal-761	1	17	print	print	NOUN
american_scientific_journal-761	1	18	)	)	PUNCT
american_scientific_journal-761	1	19	2313	2313	NUM
american_scientific_journal-761	1	20	-	-	SYM
american_scientific_journal-761	1	21	4410	4410	NUM
american_scientific_journal-761	1	22	,	,	PUNCT
american_scientific_journal-761	1	23	issn	issn	PROPN
american_scientific_journal-761	1	24	(	(	PUNCT
american_scientific_journal-761	1	25	online	online	ADJ
american_scientific_journal-761	1	26	)	)	PUNCT
american_scientific_journal-761	1	27	2313	2313	NUM
american_scientific_journal-761	1	28	-	-	SYM
american_scientific_journal-761	1	29	4402	4402	NUM
american_scientific_journal-761	1	30	©	©	PROPN
american_scientific_journal-761	1	31	global	global	ADJ
american_scientific_journal-761	1	32	society	society	NOUN
american_scientific_journal-761	1	33	of	of	ADP
american_scientific_journal-761	1	34	scientific	scientific	ADJ
american_scientific_journal-761	1	35	research	research	NOUN
american_scientific_journal-761	1	36	and	and	CCONJ
american_scientific_journal-761	1	37	researchers	researcher	NOUN
american_scientific_journal-761	1	38	http://asrjetsjournal.org/	http://asrjetsjournal.org/	NOUN
american_scientific_journal-761	1	39	students	student	NOUN
american_scientific_journal-761	1	40	difficulties	difficulty	NOUN
american_scientific_journal-761	1	41	of	of	ADP
american_scientific_journal-761	1	42	solving	solve	VERB
american_scientific_journal-761	1	43	inequalities	inequality	NOUN
american_scientific_journal-761	1	44	in	in	ADP
american_scientific_journal-761	1	45	calculus	calculus	PROPN
american_scientific_journal-761	1	46	dejene	dejene	PROPN
american_scientific_journal-761	1	47	girma	girma	PROPN
american_scientific_journal-761	1	48	denbela	denbela	PROPN
american_scientific_journal-761	1	49	*	*	PROPN
american_scientific_journal-761	1	50	department	department	PROPN
american_scientific_journal-761	1	51	of	of	ADP
american_scientific_journal-761	1	52	mathematics	mathematic	NOUN
american_scientific_journal-761	1	53	,	,	PUNCT
american_scientific_journal-761	1	54	dilla	dilla	PROPN
american_scientific_journal-761	1	55	university	university	NOUN
american_scientific_journal-761	1	56	,	,	PUNCT
american_scientific_journal-761	1	57	dilla	dilla	PROPN
american_scientific_journal-761	1	58	p.o.box	p.o.box	PROPN
american_scientific_journal-761	1	59	,	,	PUNCT
american_scientific_journal-761	1	60	419	419	NUM
american_scientific_journal-761	1	61	,	,	PUNCT
american_scientific_journal-761	1	62	ethiopia	ethiopia	PROPN
american_scientific_journal-761	1	63	aemail	aemail	NOUN
american_scientific_journal-761	1	64	:	:	PUNCT
american_scientific_journal-761	2	1	dejene28@gmail.com	dejene28@gmail.com	X
american_scientific_journal-761	2	2	abstract	abstract	VERB
american_scientific_journal-761	2	3	the	the	DET
american_scientific_journal-761	2	4	study	study	NOUN
american_scientific_journal-761	2	5	tries	try	VERB
american_scientific_journal-761	2	6	to	to	PART
american_scientific_journal-761	2	7	analyze	analyze	VERB
american_scientific_journal-761	2	8	the	the	DET
american_scientific_journal-761	2	9	students	student	NOUN
american_scientific_journal-761	2	10	’	’	PART
american_scientific_journal-761	2	11	difficulties	difficulty	NOUN
american_scientific_journal-761	2	12	and	and	CCONJ
american_scientific_journal-761	2	13	explore	explore	VERB
american_scientific_journal-761	2	14	the	the	DET
american_scientific_journal-761	2	15	errors	error	NOUN
american_scientific_journal-761	2	16	done	do	VERB
american_scientific_journal-761	2	17	by	by	ADP
american_scientific_journal-761	2	18	the	the	DET
american_scientific_journal-761	2	19	students	student	NOUN
american_scientific_journal-761	2	20	when	when	SCONJ
american_scientific_journal-761	2	21	finding	find	VERB
american_scientific_journal-761	2	22	solution	solution	NOUN
american_scientific_journal-761	2	23	sets	set	NOUN
american_scientific_journal-761	2	24	for	for	ADP
american_scientific_journal-761	2	25	inequalities	inequality	NOUN
american_scientific_journal-761	2	26	.	.	PUNCT
american_scientific_journal-761	3	1	for	for	ADP
american_scientific_journal-761	3	2	these	these	DET
american_scientific_journal-761	3	3	purpose	purpose	NOUN
american_scientific_journal-761	3	4	a	a	DET
american_scientific_journal-761	3	5	test	test	NOUN
american_scientific_journal-761	3	6	was	be	AUX
american_scientific_journal-761	3	7	given	give	VERB
american_scientific_journal-761	3	8	to	to	ADP
american_scientific_journal-761	3	9	college	college	NOUN
american_scientific_journal-761	3	10	of	of	ADP
american_scientific_journal-761	3	11	natural	natural	ADJ
american_scientific_journal-761	3	12	and	and	CCONJ
american_scientific_journal-761	3	13	computational	computational	ADJ
american_scientific_journal-761	3	14	science	science	NOUN
american_scientific_journal-761	3	15	students	student	NOUN
american_scientific_journal-761	3	16	who	who	PRON
american_scientific_journal-761	3	17	have	have	AUX
american_scientific_journal-761	3	18	taken	take	VERB
american_scientific_journal-761	3	19	calculus	calculus	NOUN
american_scientific_journal-761	3	20	i	i	PRON
american_scientific_journal-761	3	21	or	or	CCONJ
american_scientific_journal-761	3	22	applied	apply	VERB
american_scientific_journal-761	3	23	mathematics	mathematic	NOUN
american_scientific_journal-761	3	24	i	i	PRON
american_scientific_journal-761	3	25	course	course	VERB
american_scientific_journal-761	3	26	in	in	ADP
american_scientific_journal-761	3	27	dilla	dilla	PROPN
american_scientific_journal-761	3	28	university	university	PROPN
american_scientific_journal-761	3	29	,	,	PUNCT
american_scientific_journal-761	3	30	ethiopia	ethiopia	PROPN
american_scientific_journal-761	3	31	.	.	PUNCT
american_scientific_journal-761	4	1	the	the	DET
american_scientific_journal-761	4	2	results	result	NOUN
american_scientific_journal-761	4	3	showed	show	VERB
american_scientific_journal-761	4	4	that	that	SCONJ
american_scientific_journal-761	4	5	the	the	DET
american_scientific_journal-761	4	6	students	student	NOUN
american_scientific_journal-761	4	7	are	be	AUX
american_scientific_journal-761	4	8	not	not	PART
american_scientific_journal-761	4	9	successful	successful	ADJ
american_scientific_journal-761	4	10	in	in	ADP
american_scientific_journal-761	4	11	solving	solve	VERB
american_scientific_journal-761	4	12	inequalities	inequality	NOUN
american_scientific_journal-761	4	13	.	.	PUNCT
american_scientific_journal-761	5	1	the	the	DET
american_scientific_journal-761	5	2	mostly	mostly	ADV
american_scientific_journal-761	5	3	observed	observe	VERB
american_scientific_journal-761	5	4	mistake	mistake	NOUN
american_scientific_journal-761	5	5	was	be	AUX
american_scientific_journal-761	5	6	to	to	PART
american_scientific_journal-761	5	7	multiply	multiply	VERB
american_scientific_journal-761	5	8	both	both	DET
american_scientific_journal-761	5	9	sides	side	NOUN
american_scientific_journal-761	5	10	of	of	ADP
american_scientific_journal-761	5	11	inequality	inequality	NOUN
american_scientific_journal-761	5	12	by	by	ADP
american_scientific_journal-761	5	13	expression	expression	NOUN
american_scientific_journal-761	5	14	that	that	PRON
american_scientific_journal-761	5	15	includes	include	VERB
american_scientific_journal-761	5	16	variable	variable	NOUN
american_scientific_journal-761	5	17	without	without	ADP
american_scientific_journal-761	5	18	paying	pay	VERB
american_scientific_journal-761	5	19	attention	attention	NOUN
american_scientific_journal-761	5	20	to	to	ADP
american_scientific_journal-761	5	21	the	the	DET
american_scientific_journal-761	5	22	sign	sign	NOUN
american_scientific_journal-761	5	23	of	of	ADP
american_scientific_journal-761	5	24	this	this	DET
american_scientific_journal-761	5	25	expression	expression	NOUN
american_scientific_journal-761	5	26	.	.	PUNCT
american_scientific_journal-761	6	1	moreover	moreover	ADV
american_scientific_journal-761	6	2	,	,	PUNCT
american_scientific_journal-761	6	3	significant	significant	ADJ
american_scientific_journal-761	6	4	number	number	NOUN
american_scientific_journal-761	6	5	of	of	ADP
american_scientific_journal-761	6	6	procedural	procedural	ADJ
american_scientific_journal-761	6	7	and	and	CCONJ
american_scientific_journal-761	6	8	technical	technical	ADJ
american_scientific_journal-761	6	9	errors	error	NOUN
american_scientific_journal-761	6	10	is	be	AUX
american_scientific_journal-761	6	11	made	make	VERB
american_scientific_journal-761	6	12	by	by	ADP
american_scientific_journal-761	6	13	the	the	DET
american_scientific_journal-761	6	14	students	student	NOUN
american_scientific_journal-761	6	15	.	.	PUNCT
american_scientific_journal-761	7	1	keywords	keyword	NOUN
american_scientific_journal-761	7	2	:	:	PUNCT
american_scientific_journal-761	7	3	inequalities	inequality	NOUN
american_scientific_journal-761	7	4	;	;	PUNCT
american_scientific_journal-761	7	5	solving	solve	VERB
american_scientific_journal-761	7	6	inequalities	inequality	NOUN
american_scientific_journal-761	7	7	;	;	PUNCT
american_scientific_journal-761	7	8	students	student	NOUN
american_scientific_journal-761	7	9	’	'	PUNCT
american_scientific_journal-761	7	10	mistakes	mistake	NOUN
american_scientific_journal-761	7	11	.	.	PUNCT
american_scientific_journal-761	8	1	1	1	X
american_scientific_journal-761	8	2	.	.	X
american_scientific_journal-761	8	3	introduction	introduction	NOUN
american_scientific_journal-761	8	4	the	the	DET
american_scientific_journal-761	8	5	concept	concept	NOUN
american_scientific_journal-761	8	6	“	"	PUNCT
american_scientific_journal-761	8	7	inequality	inequality	NOUN
american_scientific_journal-761	8	8	”	"	PUNCT
american_scientific_journal-761	8	9	and	and	CCONJ
american_scientific_journal-761	8	10	finding	find	VERB
american_scientific_journal-761	8	11	a	a	DET
american_scientific_journal-761	8	12	solution	solution	NOUN
american_scientific_journal-761	8	13	set	set	VERB
american_scientific_journal-761	8	14	for	for	ADP
american_scientific_journal-761	8	15	an	an	DET
american_scientific_journal-761	8	16	inequality	inequality	NOUN
american_scientific_journal-761	8	17	is	be	AUX
american_scientific_journal-761	8	18	an	an	DET
american_scientific_journal-761	8	19	important	important	ADJ
american_scientific_journal-761	8	20	issue	issue	NOUN
american_scientific_journal-761	8	21	in	in	ADP
american_scientific_journal-761	8	22	calculus	calculus	NOUN
american_scientific_journal-761	8	23	as	as	ADV
american_scientific_journal-761	8	24	well	well	ADV
american_scientific_journal-761	8	25	as	as	ADP
american_scientific_journal-761	8	26	for	for	ADP
american_scientific_journal-761	8	27	all	all	DET
american_scientific_journal-761	8	28	the	the	DET
american_scientific_journal-761	8	29	fields	field	NOUN
american_scientific_journal-761	8	30	of	of	ADP
american_scientific_journal-761	8	31	mathematics	mathematic	NOUN
american_scientific_journal-761	8	32	.	.	PUNCT
american_scientific_journal-761	9	1	because	because	SCONJ
american_scientific_journal-761	9	2	,	,	PUNCT
american_scientific_journal-761	9	3	the	the	DET
american_scientific_journal-761	9	4	main	main	ADJ
american_scientific_journal-761	9	5	concern	concern	NOUN
american_scientific_journal-761	9	6	of	of	ADP
american_scientific_journal-761	9	7	a	a	DET
american_scientific_journal-761	9	8	calculus	calculus	NOUN
american_scientific_journal-761	9	9	course	course	NOUN
american_scientific_journal-761	9	10	includes	include	VERB
american_scientific_journal-761	9	11	the	the	DET
american_scientific_journal-761	9	12	concept	concept	NOUN
american_scientific_journal-761	9	13	of	of	ADP
american_scientific_journal-761	9	14	“	"	PUNCT
american_scientific_journal-761	9	15	function	function	NOUN
american_scientific_journal-761	9	16	”	"	PUNCT
american_scientific_journal-761	9	17	and	and	CCONJ
american_scientific_journal-761	9	18	analyzing	analyze	VERB
american_scientific_journal-761	9	19	the	the	DET
american_scientific_journal-761	9	20	properties	property	NOUN
american_scientific_journal-761	9	21	of	of	ADP
american_scientific_journal-761	9	22	these	these	DET
american_scientific_journal-761	9	23	functions	function	NOUN
american_scientific_journal-761	9	24	.	.	PUNCT
american_scientific_journal-761	10	1	the	the	DET
american_scientific_journal-761	10	2	analysis	analysis	NOUN
american_scientific_journal-761	10	3	of	of	ADP
american_scientific_journal-761	10	4	some	some	DET
american_scientific_journal-761	10	5	properties	property	NOUN
american_scientific_journal-761	10	6	of	of	ADP
american_scientific_journal-761	10	7	functions	function	NOUN
american_scientific_journal-761	10	8	requires	require	VERB
american_scientific_journal-761	10	9	the	the	DET
american_scientific_journal-761	10	10	solutions	solution	NOUN
american_scientific_journal-761	10	11	of	of	ADP
american_scientific_journal-761	10	12	inequalities	inequality	NOUN
american_scientific_journal-761	10	13	.	.	PUNCT
american_scientific_journal-761	11	1	for	for	ADP
american_scientific_journal-761	11	2	instance	instance	NOUN
american_scientific_journal-761	11	3	,	,	PUNCT
american_scientific_journal-761	11	4	in	in	ADP
american_scientific_journal-761	11	5	order	order	NOUN
american_scientific_journal-761	11	6	to	to	PART
american_scientific_journal-761	11	7	find	find	VERB
american_scientific_journal-761	11	8	the	the	DET
american_scientific_journal-761	11	9	domains	domain	NOUN
american_scientific_journal-761	11	10	of	of	ADP
american_scientific_journal-761	11	11	the	the	DET
american_scientific_journal-761	11	12	functions	function	NOUN
american_scientific_journal-761	11	13	𝒇(𝒙	𝒇(𝒙	NUM
american_scientific_journal-761	11	14	)	)	PUNCT
american_scientific_journal-761	11	15	=	=	SYM
american_scientific_journal-761	12	1	√𝒙𝟐	√𝒙𝟐	PROPN
american_scientific_journal-761	13	1	+	+	NUM
american_scientific_journal-761	13	2	𝟐𝒙	𝟐𝒙	NOUN
american_scientific_journal-761	13	3	−	−	PROPN
american_scientific_journal-761	13	4	𝟐	𝟐	NUM
american_scientific_journal-761	13	5	and	and	CCONJ
american_scientific_journal-761	13	6	𝒉(𝒙	𝒉(𝒙	PROPN
american_scientific_journal-761	13	7	)	)	PUNCT
american_scientific_journal-761	13	8	=	=	PUNCT
american_scientific_journal-761	13	9	𝒍𝒏	𝒍𝒏	VERB
american_scientific_journal-761	13	10	𝒙	𝒙	PROPN
american_scientific_journal-761	13	11	𝒙−𝟐	𝒙−𝟐	PROPN
american_scientific_journal-761	13	12	,	,	PUNCT
american_scientific_journal-761	13	13	it	it	PRON
american_scientific_journal-761	13	14	is	be	AUX
american_scientific_journal-761	13	15	necessary	necessary	ADJ
american_scientific_journal-761	13	16	to	to	PART
american_scientific_journal-761	13	17	find	find	VERB
american_scientific_journal-761	13	18	the	the	DET
american_scientific_journal-761	13	19	solution	solution	NOUN
american_scientific_journal-761	13	20	sets	set	NOUN
american_scientific_journal-761	13	21	for	for	ADP
american_scientific_journal-761	13	22	the	the	DET
american_scientific_journal-761	13	23	inequalities	inequality	NOUN
american_scientific_journal-761	13	24	𝒙𝟐	𝒙𝟐	PROPN
american_scientific_journal-761	13	25	+	+	CCONJ
american_scientific_journal-761	13	26	𝟐𝒙	𝟐𝒙	NOUN
american_scientific_journal-761	13	27	−	−	PROPN
american_scientific_journal-761	13	28	𝟐	𝟐	NUM
american_scientific_journal-761	13	29	≥	≥	NOUN
american_scientific_journal-761	13	30	𝟎	𝟎	NUM
american_scientific_journal-761	13	31	and	and	CCONJ
american_scientific_journal-761	13	32	𝐱	𝐱	DET
american_scientific_journal-761	13	33	𝐱−𝟐	𝐱−𝟐	PROPN
american_scientific_journal-761	13	34	>	>	SYM
american_scientific_journal-761	13	35	𝟎	𝟎	PROPN
american_scientific_journal-761	13	36	.	.	PUNCT
american_scientific_journal-761	14	1	similarly	similarly	ADV
american_scientific_journal-761	14	2	,	,	PUNCT
american_scientific_journal-761	14	3	inequality	inequality	NOUN
american_scientific_journal-761	14	4	solutions	solution	NOUN
american_scientific_journal-761	14	5	are	be	AUX
american_scientific_journal-761	14	6	required	require	VERB
american_scientific_journal-761	14	7	to	to	PART
american_scientific_journal-761	14	8	determine	determine	VERB
american_scientific_journal-761	14	9	the	the	DET
american_scientific_journal-761	14	10	monotonicity	monotonicity	NOUN
american_scientific_journal-761	14	11	and	and	CCONJ
american_scientific_journal-761	14	12	concavity	concavity	NOUN
american_scientific_journal-761	14	13	of	of	ADP
american_scientific_journal-761	14	14	functions	function	NOUN
american_scientific_journal-761	14	15	by	by	ADP
american_scientific_journal-761	14	16	the	the	DET
american_scientific_journal-761	14	17	use	use	NOUN
american_scientific_journal-761	14	18	of	of	ADP
american_scientific_journal-761	14	19	derivative	derivative	NOUN
american_scientific_journal-761	14	20	(	(	PUNCT
american_scientific_journal-761	14	21	sandor	sandor	PROPN
american_scientific_journal-761	14	22	1997	1997	NUM
american_scientific_journal-761	14	23	)	)	PUNCT
american_scientific_journal-761	14	24	.	.	PUNCT
american_scientific_journal-761	15	1	for	for	ADP
american_scientific_journal-761	15	2	instance	instance	NOUN
american_scientific_journal-761	15	3	,	,	PUNCT
american_scientific_journal-761	15	4	for	for	ADP
american_scientific_journal-761	15	5	the	the	DET
american_scientific_journal-761	15	6	analyzing	analyzing	NOUN
american_scientific_journal-761	15	7	the	the	DET
american_scientific_journal-761	15	8	monotonocity	monotonocity	NOUN
american_scientific_journal-761	15	9	of	of	ADP
american_scientific_journal-761	15	10	the	the	DET
american_scientific_journal-761	15	11	function	function	NOUN
american_scientific_journal-761	15	12	𝒇(𝒙	𝒇(𝒙	NOUN
american_scientific_journal-761	15	13	)	)	PUNCT
american_scientific_journal-761	15	14	=	=	PUNCT
american_scientific_journal-761	15	15	𝒙𝟐+𝟐𝒙+𝟒	𝒙𝟐+𝟐𝒙+𝟒	NOUN
american_scientific_journal-761	15	16	𝟐𝒙	𝟐𝒙	NOUN
american_scientific_journal-761	15	17	it	it	PRON
american_scientific_journal-761	15	18	is	be	AUX
american_scientific_journal-761	15	19	necessary	necessary	ADJ
american_scientific_journal-761	15	20	to	to	PART
american_scientific_journal-761	15	21	find	find	VERB
american_scientific_journal-761	15	22	the	the	DET
american_scientific_journal-761	15	23	solution	solution	NOUN
american_scientific_journal-761	15	24	sets	set	NOUN
american_scientific_journal-761	15	25	of	of	ADP
american_scientific_journal-761	15	26	inequalities	inequality	NOUN
american_scientific_journal-761	15	27	𝒙	𝒙	PROPN
american_scientific_journal-761	15	28	𝟐−𝟒	𝟐−𝟒	PROPN
american_scientific_journal-761	15	29	𝟐𝒙𝟐	𝟐𝒙𝟐	X
american_scientific_journal-761	15	30	>	>	X
american_scientific_journal-761	15	31	𝟎	𝟎	PROPN
american_scientific_journal-761	15	32	and	and	CCONJ
american_scientific_journal-761	15	33	𝒙	𝒙	PROPN
american_scientific_journal-761	15	34	𝟐−𝟒	𝟐−𝟒	PROPN
american_scientific_journal-761	15	35	𝟐𝒙𝟐	𝟐𝒙𝟐	X
american_scientific_journal-761	15	36	<	<	X
american_scientific_journal-761	15	37	𝟎	𝟎	PROPN
american_scientific_journal-761	15	38	or	or	CCONJ
american_scientific_journal-761	15	39	𝒇′(𝒙	𝒇′(𝒙	NUM
american_scientific_journal-761	15	40	)	)	PUNCT
american_scientific_journal-761	15	41	>	>	X
american_scientific_journal-761	15	42	𝟎	𝟎	PROPN
american_scientific_journal-761	15	43	and	and	CCONJ
american_scientific_journal-761	15	44	𝒇′(𝒙	𝒇′(𝒙	PROPN
american_scientific_journal-761	15	45	)	)	PUNCT
american_scientific_journal-761	15	46	>	>	X
american_scientific_journal-761	15	47	𝟎	𝟎	NUM
american_scientific_journal-761	15	48	for	for	ADP
american_scientific_journal-761	15	49	the	the	DET
american_scientific_journal-761	15	50	concavity	concavity	NOUN
american_scientific_journal-761	15	51	the	the	DET
american_scientific_journal-761	15	52	inequalities	inequality	NOUN
american_scientific_journal-761	15	53	𝒇′′(𝒙	𝒇′′(𝒙	NOUN
american_scientific_journal-761	15	54	)	)	PUNCT
american_scientific_journal-761	15	55	<	<	X
american_scientific_journal-761	15	56	𝟎	𝟎	NUM
american_scientific_journal-761	15	57	and	and	CCONJ
american_scientific_journal-761	15	58	𝒇′′(𝒙	𝒇′′(𝒙	NOUN
american_scientific_journal-761	15	59	)	)	PUNCT
american_scientific_journal-761	15	60	>	>	X
american_scientific_journal-761	15	61	𝟎	𝟎	NUM
american_scientific_journal-761	15	62	which	which	PRON
american_scientific_journal-761	15	63	means	mean	VERB
american_scientific_journal-761	15	64	𝟒	𝟒	NUM
american_scientific_journal-761	15	65	𝒙𝟑	𝒙𝟑	PROPN
american_scientific_journal-761	15	66	>	>	X
american_scientific_journal-761	15	67	𝟎	𝟎	PROPN
american_scientific_journal-761	15	68	and	and	CCONJ
american_scientific_journal-761	15	69	𝟒	𝟒	NUM
american_scientific_journal-761	15	70	𝒙𝟑	𝒙𝟑	NOUN
american_scientific_journal-761	15	71	<	<	X
american_scientific_journal-761	15	72	𝟎	𝟎	PROPN
american_scientific_journal-761	15	73	.	.	PUNCT
american_scientific_journal-761	16	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-761	17	1	*	*	PUNCT
american_scientific_journal-761	17	2	corresponding	correspond	VERB
american_scientific_journal-761	17	3	author	author	NOUN
american_scientific_journal-761	17	4	.	.	PUNCT
american_scientific_journal-761	18	1	57	57	NUM
american_scientific_journal-761	18	2	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-761	18	3	american	american	ADJ
american_scientific_journal-761	18	4	scientific	scientific	ADJ
american_scientific_journal-761	18	5	research	research	NOUN
american_scientific_journal-761	18	6	journal	journal	NOUN
american_scientific_journal-761	18	7	for	for	ADP
american_scientific_journal-761	18	8	engineering	engineering	NOUN
american_scientific_journal-761	18	9	,	,	PUNCT
american_scientific_journal-761	18	10	technology	technology	NOUN
american_scientific_journal-761	18	11	,	,	PUNCT
american_scientific_journal-761	18	12	and	and	CCONJ
american_scientific_journal-761	18	13	sciences	science	NOUN
american_scientific_journal-761	18	14	(	(	PUNCT
american_scientific_journal-761	18	15	asrjets	asrjet	NOUN
american_scientific_journal-761	18	16	)	)	PUNCT
american_scientific_journal-761	18	17	(	(	PUNCT
american_scientific_journal-761	18	18	2013	2013	NUM
american_scientific_journal-761	18	19	)	)	PUNCT
american_scientific_journal-761	18	20	volume	volume	NOUN
american_scientific_journal-761	18	21	5	5	NUM
american_scientific_journal-761	18	22	,	,	PUNCT
american_scientific_journal-761	18	23	no	no	DET
american_scientific_journal-761	18	24	1	1	NUM
american_scientific_journal-761	18	25	,	,	PUNCT
american_scientific_journal-761	18	26	pp	pp	ADV
american_scientific_journal-761	18	27	57	57	NUM
american_scientific_journal-761	18	28	-	-	SYM
american_scientific_journal-761	18	29	62	62	NUM
american_scientific_journal-761	18	30	e	e	NOUN
american_scientific_journal-761	18	31	-	-	NOUN
american_scientific_journal-761	18	32	mail	mail	NOUN
american_scientific_journal-761	18	33	address	address	NOUN
american_scientific_journal-761	18	34	:	:	PUNCT
american_scientific_journal-761	18	35	dejene28@yahoo.com	dejene28@yahoo.com	PROPN
american_scientific_journal-761	18	36	.	.	PROPN
american_scientific_journal-761	18	37	therefore	therefore	ADV
american_scientific_journal-761	18	38	;	;	PUNCT
american_scientific_journal-761	18	39	calculus	calculus	NOUN
american_scientific_journal-761	18	40	text	text	NOUN
american_scientific_journal-761	18	41	books	book	NOUN
american_scientific_journal-761	18	42	introduce	introduce	VERB
american_scientific_journal-761	18	43	the	the	DET
american_scientific_journal-761	18	44	concept	concept	NOUN
american_scientific_journal-761	18	45	of	of	ADP
american_scientific_journal-761	18	46	inequality	inequality	NOUN
american_scientific_journal-761	18	47	before	before	SCONJ
american_scientific_journal-761	18	48	they	they	PRON
american_scientific_journal-761	18	49	cover	cover	VERB
american_scientific_journal-761	18	50	functions	function	NOUN
american_scientific_journal-761	18	51	and	and	CCONJ
american_scientific_journal-761	18	52	their	their	PRON
american_scientific_journal-761	18	53	properties	property	NOUN
american_scientific_journal-761	18	54	[	[	X
american_scientific_journal-761	18	55	1	1	NUM
american_scientific_journal-761	18	56	]	]	PUNCT
american_scientific_journal-761	18	57	,	,	PUNCT
american_scientific_journal-761	18	58	[	[	X
american_scientific_journal-761	18	59	6	6	NUM
american_scientific_journal-761	18	60	]	]	PUNCT
american_scientific_journal-761	18	61	.	.	PUNCT
american_scientific_journal-761	19	1	as	as	SCONJ
american_scientific_journal-761	19	2	these	these	DET
american_scientific_journal-761	19	3	examples	example	NOUN
american_scientific_journal-761	19	4	show	show	VERB
american_scientific_journal-761	19	5	,	,	PUNCT
american_scientific_journal-761	19	6	the	the	DET
american_scientific_journal-761	19	7	students	student	NOUN
american_scientific_journal-761	19	8	’	'	PUNCT
american_scientific_journal-761	19	9	performances	performance	NOUN
american_scientific_journal-761	19	10	in	in	ADP
american_scientific_journal-761	19	11	solving	solve	VERB
american_scientific_journal-761	19	12	inequalities	inequality	NOUN
american_scientific_journal-761	19	13	directly	directly	ADV
american_scientific_journal-761	19	14	affect	affect	VERB
american_scientific_journal-761	19	15	their	their	PRON
american_scientific_journal-761	19	16	success	success	NOUN
american_scientific_journal-761	19	17	in	in	ADP
american_scientific_journal-761	19	18	calculus	calculus	NOUN
american_scientific_journal-761	19	19	courses	course	NOUN
american_scientific_journal-761	19	20	.	.	PUNCT
american_scientific_journal-761	20	1	as	as	ADP
american_scientific_journal-761	20	2	a	a	DET
american_scientific_journal-761	20	3	result	result	NOUN
american_scientific_journal-761	20	4	,	,	PUNCT
american_scientific_journal-761	20	5	this	this	DET
american_scientific_journal-761	20	6	situation	situation	NOUN
american_scientific_journal-761	20	7	triggered	trigger	VERB
american_scientific_journal-761	20	8	a	a	DET
american_scientific_journal-761	20	9	considerable	considerable	ADJ
american_scientific_journal-761	20	10	number	number	NOUN
american_scientific_journal-761	20	11	of	of	ADP
american_scientific_journal-761	20	12	studies	study	NOUN
american_scientific_journal-761	20	13	on	on	ADP
american_scientific_journal-761	20	14	the	the	DET
american_scientific_journal-761	20	15	inequalities	inequality	NOUN
american_scientific_journal-761	20	16	topic	topic	NOUN
american_scientific_journal-761	20	17	[	[	X
american_scientific_journal-761	20	18	9	9	NUM
american_scientific_journal-761	20	19	]	]	PUNCT
american_scientific_journal-761	20	20	;	;	PUNCT
american_scientific_journal-761	21	1	[	[	X
american_scientific_journal-761	21	2	7	7	NUM
american_scientific_journal-761	21	3	]	]	PUNCT
american_scientific_journal-761	21	4	;	;	PUNCT
american_scientific_journal-761	22	1	[	[	X
american_scientific_journal-761	22	2	8	8	NUM
american_scientific_journal-761	22	3	]	]	PUNCT
american_scientific_journal-761	22	4	;	;	PUNCT
american_scientific_journal-761	22	5	[	[	X
american_scientific_journal-761	22	6	3	3	NUM
american_scientific_journal-761	22	7	]	]	PUNCT
american_scientific_journal-761	22	8	;	;	PUNCT
american_scientific_journal-761	23	1	[	[	X
american_scientific_journal-761	23	2	2	2	NUM
american_scientific_journal-761	23	3	]	]	PUNCT
american_scientific_journal-761	23	4	.	.	PUNCT
american_scientific_journal-761	24	1	moreover	moreover	ADV
american_scientific_journal-761	24	2	,	,	PUNCT
american_scientific_journal-761	24	3	due	due	ADP
american_scientific_journal-761	24	4	to	to	ADP
american_scientific_journal-761	24	5	not	not	PART
american_scientific_journal-761	24	6	the	the	DET
american_scientific_journal-761	24	7	problem	problem	NOUN
american_scientific_journal-761	24	8	of	of	ADP
american_scientific_journal-761	24	9	the	the	DET
american_scientific_journal-761	24	10	concept	concept	NOUN
american_scientific_journal-761	24	11	of	of	ADP
american_scientific_journal-761	24	12	monotonocity	monotonocity	NOUN
american_scientific_journal-761	24	13	or	or	CCONJ
american_scientific_journal-761	24	14	concavity	concavity	NOUN
american_scientific_journal-761	24	15	of	of	ADP
american_scientific_journal-761	24	16	the	the	DET
american_scientific_journal-761	24	17	function	function	NOUN
american_scientific_journal-761	24	18	students	student	NOUN
american_scientific_journal-761	24	19	fail	fail	VERB
american_scientific_journal-761	24	20	to	to	PART
american_scientific_journal-761	24	21	get	get	VERB
american_scientific_journal-761	24	22	the	the	DET
american_scientific_journal-761	24	23	correct	correct	ADJ
american_scientific_journal-761	24	24	answer	answer	NOUN
american_scientific_journal-761	24	25	of	of	ADP
american_scientific_journal-761	24	26	the	the	DET
american_scientific_journal-761	24	27	original	original	ADJ
american_scientific_journal-761	24	28	problem	problem	NOUN
american_scientific_journal-761	24	29	in	in	ADP
american_scientific_journal-761	24	30	the	the	DET
american_scientific_journal-761	24	31	course	course	NOUN
american_scientific_journal-761	24	32	.	.	PUNCT
american_scientific_journal-761	25	1	which	which	PRON
american_scientific_journal-761	25	2	is	be	AUX
american_scientific_journal-761	25	3	normally	normally	ADV
american_scientific_journal-761	25	4	an	an	DET
american_scientific_journal-761	25	5	error	error	NOUN
american_scientific_journal-761	25	6	due	due	ADP
american_scientific_journal-761	25	7	to	to	ADP
american_scientific_journal-761	25	8	lack	lack	NOUN
american_scientific_journal-761	25	9	of	of	ADP
american_scientific_journal-761	25	10	other	other	ADJ
american_scientific_journal-761	25	11	mathematics	mathematic	NOUN
american_scientific_journal-761	25	12	concept	concept	NOUN
american_scientific_journal-761	25	13	knowledge	knowledge	NOUN
american_scientific_journal-761	25	14	.	.	PUNCT
american_scientific_journal-761	26	1	according	accord	VERB
american_scientific_journal-761	26	2	to	to	ADP
american_scientific_journal-761	26	3	seah	seah	PROPN
american_scientific_journal-761	26	4	[	[	X
american_scientific_journal-761	26	5	5	5	X
american_scientific_journal-761	26	6	]	]	PUNCT
american_scientific_journal-761	26	7	there	there	PRON
american_scientific_journal-761	26	8	are	be	VERB
american_scientific_journal-761	26	9	two	two	NUM
american_scientific_journal-761	26	10	types	type	NOUN
american_scientific_journal-761	26	11	of	of	ADP
american_scientific_journal-761	26	12	errors	error	NOUN
american_scientific_journal-761	26	13	the	the	DET
american_scientific_journal-761	26	14	first	first	ADJ
american_scientific_journal-761	26	15	type	type	NOUN
american_scientific_journal-761	26	16	of	of	ADP
american_scientific_journal-761	26	17	error	error	NOUN
american_scientific_journal-761	26	18	is	be	AUX
american_scientific_journal-761	26	19	procedural	procedural	ADJ
american_scientific_journal-761	26	20	.	.	PUNCT
american_scientific_journal-761	27	1	procedural	procedural	ADJ
american_scientific_journal-761	27	2	errors	error	NOUN
american_scientific_journal-761	27	3	are	be	AUX
american_scientific_journal-761	27	4	those	those	PRON
american_scientific_journal-761	27	5	which	which	PRON
american_scientific_journal-761	27	6	arise	arise	VERB
american_scientific_journal-761	27	7	from	from	ADP
american_scientific_journal-761	27	8	failure	failure	NOUN
american_scientific_journal-761	27	9	to	to	PART
american_scientific_journal-761	27	10	carry	carry	VERB
american_scientific_journal-761	27	11	out	out	ADP
american_scientific_journal-761	27	12	manipulations	manipulation	NOUN
american_scientific_journal-761	27	13	or	or	CCONJ
american_scientific_journal-761	27	14	algorithms	algorithm	NOUN
american_scientific_journal-761	27	15	despite	despite	SCONJ
american_scientific_journal-761	27	16	having	having	AUX
american_scientific_journal-761	27	17	understood	understand	VERB
american_scientific_journal-761	27	18	the	the	DET
american_scientific_journal-761	27	19	concepts	concept	NOUN
american_scientific_journal-761	27	20	behind	behind	ADP
american_scientific_journal-761	27	21	the	the	DET
american_scientific_journal-761	27	22	problem	problem	NOUN
american_scientific_journal-761	27	23	.	.	PUNCT
american_scientific_journal-761	28	1	the	the	DET
american_scientific_journal-761	28	2	second	second	ADJ
american_scientific_journal-761	28	3	type	type	NOUN
american_scientific_journal-761	28	4	of	of	ADP
american_scientific_journal-761	28	5	error	error	NOUN
american_scientific_journal-761	28	6	is	be	AUX
american_scientific_journal-761	28	7	technical	technical	ADJ
american_scientific_journal-761	28	8	error	error	NOUN
american_scientific_journal-761	28	9	.	.	PUNCT
american_scientific_journal-761	29	1	it	it	PRON
american_scientific_journal-761	29	2	refers	refer	VERB
american_scientific_journal-761	29	3	to	to	ADP
american_scientific_journal-761	29	4	errors	error	NOUN
american_scientific_journal-761	29	5	due	due	ADP
american_scientific_journal-761	29	6	to	to	ADP
american_scientific_journal-761	29	7	a	a	DET
american_scientific_journal-761	29	8	lack	lack	NOUN
american_scientific_journal-761	29	9	of	of	ADP
american_scientific_journal-761	29	10	mathematical	mathematical	ADJ
american_scientific_journal-761	29	11	content	content	NOUN
american_scientific_journal-761	29	12	knowledge	knowledge	NOUN
american_scientific_journal-761	29	13	in	in	ADP
american_scientific_journal-761	29	14	other	other	ADJ
american_scientific_journal-761	29	15	topics	topic	NOUN
american_scientific_journal-761	29	16	or	or	CCONJ
american_scientific_journal-761	29	17	errors	error	NOUN
american_scientific_journal-761	29	18	due	due	ADJ
american_scientific_journal-761	29	19	to	to	ADP
american_scientific_journal-761	29	20	carelessness	carelessness	NOUN
american_scientific_journal-761	29	21	on	on	ADP
american_scientific_journal-761	29	22	the	the	DET
american_scientific_journal-761	29	23	basis	basis	NOUN
american_scientific_journal-761	29	24	of	of	ADP
american_scientific_journal-761	29	25	these	these	DET
american_scientific_journal-761	29	26	considerations	consideration	NOUN
american_scientific_journal-761	29	27	,	,	PUNCT
american_scientific_journal-761	29	28	this	this	DET
american_scientific_journal-761	29	29	study	study	NOUN
american_scientific_journal-761	29	30	aims	aim	VERB
american_scientific_journal-761	29	31	at	at	ADP
american_scientific_journal-761	29	32	analyzing	analyze	VERB
american_scientific_journal-761	29	33	the	the	DET
american_scientific_journal-761	29	34	students	student	NOUN
american_scientific_journal-761	29	35	’	’	PART
american_scientific_journal-761	29	36	difficulties	difficulty	NOUN
american_scientific_journal-761	29	37	and	and	CCONJ
american_scientific_journal-761	29	38	exploring	explore	VERB
american_scientific_journal-761	29	39	the	the	DET
american_scientific_journal-761	29	40	possible	possible	ADJ
american_scientific_journal-761	29	41	errors	error	NOUN
american_scientific_journal-761	29	42	done	do	VERB
american_scientific_journal-761	29	43	by	by	ADP
american_scientific_journal-761	29	44	the	the	DET
american_scientific_journal-761	29	45	students	student	NOUN
american_scientific_journal-761	29	46	taking	take	VERB
american_scientific_journal-761	29	47	calculus	calculus	NOUN
american_scientific_journal-761	29	48	course	course	NOUN
american_scientific_journal-761	29	49	in	in	ADP
american_scientific_journal-761	29	50	dilla	dilla	PROPN
american_scientific_journal-761	29	51	university	university	PROPN
american_scientific_journal-761	29	52	in	in	ADP
american_scientific_journal-761	29	53	ethiopia	ethiopia	PROPN
american_scientific_journal-761	29	54	while	while	SCONJ
american_scientific_journal-761	29	55	finding	find	VERB
american_scientific_journal-761	29	56	solution	solution	NOUN
american_scientific_journal-761	29	57	sets	set	NOUN
american_scientific_journal-761	29	58	for	for	ADP
american_scientific_journal-761	29	59	inequalities	inequality	NOUN
american_scientific_journal-761	29	60	.	.	PUNCT
american_scientific_journal-761	30	1	2	2	X
american_scientific_journal-761	30	2	.	.	X
american_scientific_journal-761	30	3	method	method	VERB
american_scientific_journal-761	30	4	the	the	DET
american_scientific_journal-761	30	5	subjects	subject	NOUN
american_scientific_journal-761	30	6	of	of	ADP
american_scientific_journal-761	30	7	this	this	DET
american_scientific_journal-761	30	8	study	study	NOUN
american_scientific_journal-761	30	9	are	be	AUX
american_scientific_journal-761	30	10	223	223	NUM
american_scientific_journal-761	30	11	first	first	ADJ
american_scientific_journal-761	30	12	year	year	NOUN
american_scientific_journal-761	30	13	students	student	NOUN
american_scientific_journal-761	30	14	attending	attend	VERB
american_scientific_journal-761	30	15	physics	physic	NOUN
american_scientific_journal-761	30	16	,	,	PUNCT
american_scientific_journal-761	30	17	chemistry	chemistry	NOUN
american_scientific_journal-761	30	18	and	and	CCONJ
american_scientific_journal-761	30	19	statistics	statistic	NOUN
american_scientific_journal-761	30	20	departments	department	NOUN
american_scientific_journal-761	30	21	at	at	ADP
american_scientific_journal-761	30	22	the	the	DET
american_scientific_journal-761	30	23	college	college	NOUN
american_scientific_journal-761	30	24	of	of	ADP
american_scientific_journal-761	30	25	natural	natural	ADJ
american_scientific_journal-761	30	26	and	and	CCONJ
american_scientific_journal-761	30	27	computational	computational	ADJ
american_scientific_journal-761	30	28	science	science	NOUN
american_scientific_journal-761	30	29	of	of	ADP
american_scientific_journal-761	30	30	dilla	dilla	PROPN
american_scientific_journal-761	30	31	university	university	PROPN
american_scientific_journal-761	30	32	in	in	ADP
american_scientific_journal-761	30	33	ethiopia	ethiopia	PROPN
american_scientific_journal-761	30	34	and	and	CCONJ
american_scientific_journal-761	30	35	also	also	ADV
american_scientific_journal-761	30	36	taking	take	VERB
american_scientific_journal-761	30	37	calculus	calculus	NOUN
american_scientific_journal-761	30	38	i	i	PRON
american_scientific_journal-761	30	39	/	/	SYM
american_scientific_journal-761	30	40	applied	apply	VERB
american_scientific_journal-761	30	41	mathematics	mathematic	NOUN
american_scientific_journal-761	31	1	i	i	PRON
american_scientific_journal-761	31	2	course	course	VERB
american_scientific_journal-761	31	3	.	.	PUNCT
american_scientific_journal-761	32	1	this	this	DET
american_scientific_journal-761	32	2	group	group	NOUN
american_scientific_journal-761	32	3	,	,	PUNCT
american_scientific_journal-761	32	4	are	be	AUX
american_scientific_journal-761	32	5	already	already	ADV
american_scientific_journal-761	32	6	been	be	AUX
american_scientific_journal-761	32	7	taught	teach	VERB
american_scientific_journal-761	32	8	how	how	SCONJ
american_scientific_journal-761	32	9	to	to	PART
american_scientific_journal-761	32	10	solve	solve	VERB
american_scientific_journal-761	32	11	inequalities	inequality	NOUN
american_scientific_journal-761	32	12	by	by	ADP
american_scientific_journal-761	32	13	using	use	VERB
american_scientific_journal-761	32	14	algebra	algebra	NOUN
american_scientific_journal-761	32	15	and	and	CCONJ
american_scientific_journal-761	32	16	geometric	geometric	ADJ
american_scientific_journal-761	32	17	methods	method	NOUN
american_scientific_journal-761	32	18	.	.	PUNCT
american_scientific_journal-761	33	1	in	in	ADP
american_scientific_journal-761	33	2	the	the	DET
american_scientific_journal-761	33	3	study	study	NOUN
american_scientific_journal-761	33	4	a	a	DET
american_scientific_journal-761	33	5	five	five	NUM
american_scientific_journal-761	33	6	-	-	PUNCT
american_scientific_journal-761	33	7	question	question	NOUN
american_scientific_journal-761	33	8	test	test	NOUN
american_scientific_journal-761	33	9	was	be	AUX
american_scientific_journal-761	33	10	administered	administer	VERB
american_scientific_journal-761	33	11	.	.	PUNCT
american_scientific_journal-761	34	1	2.1	2.1	NUM
american_scientific_journal-761	34	2	.	.	PUNCT
american_scientific_journal-761	35	1	a	a	DET
american_scientific_journal-761	35	2	test	test	NOUN
american_scientific_journal-761	35	3	administered	administer	VERB
american_scientific_journal-761	35	4	to	to	ADP
american_scientific_journal-761	35	5	the	the	DET
american_scientific_journal-761	35	6	subjects	subject	NOUN
american_scientific_journal-761	35	7	a	a	PRON
american_scientific_journal-761	35	8	)	)	PUNCT
american_scientific_journal-761	35	9	find	find	VERB
american_scientific_journal-761	35	10	the	the	DET
american_scientific_journal-761	35	11	solution	solution	NOUN
american_scientific_journal-761	35	12	set	set	VERB
american_scientific_journal-761	35	13	for	for	ADP
american_scientific_journal-761	35	14	the	the	DET
american_scientific_journal-761	35	15	inequality	inequality	NOUN
american_scientific_journal-761	35	16	|𝑥	|𝑥	PROPN
american_scientific_journal-761	35	17	+	+	CCONJ
american_scientific_journal-761	35	18	1|	1|	NUM
american_scientific_journal-761	35	19	>	>	PUNCT
american_scientific_journal-761	35	20	|𝑥	|𝑥	PROPN
american_scientific_journal-761	35	21	−	−	PROPN
american_scientific_journal-761	35	22	3|	3|	NUM
american_scientific_journal-761	35	23	in	in	ADP
american_scientific_journal-761	35	24	this	this	DET
american_scientific_journal-761	35	25	question	question	NOUN
american_scientific_journal-761	35	26	,	,	PUNCT
american_scientific_journal-761	35	27	the	the	DET
american_scientific_journal-761	35	28	students	student	NOUN
american_scientific_journal-761	35	29	are	be	AUX
american_scientific_journal-761	35	30	expected	expect	VERB
american_scientific_journal-761	35	31	to	to	PART
american_scientific_journal-761	35	32	find	find	VERB
american_scientific_journal-761	35	33	the	the	DET
american_scientific_journal-761	35	34	solution	solution	NOUN
american_scientific_journal-761	35	35	by	by	ADP
american_scientific_journal-761	35	36	considering	consider	VERB
american_scientific_journal-761	35	37	four	four	NUM
american_scientific_journal-761	35	38	situations	situation	NOUN
american_scientific_journal-761	35	39	occurred	occur	VERB
american_scientific_journal-761	35	40	due	due	ADP
american_scientific_journal-761	35	41	to	to	ADP
american_scientific_journal-761	35	42	the	the	DET
american_scientific_journal-761	35	43	properties	property	NOUN
american_scientific_journal-761	35	44	of	of	ADP
american_scientific_journal-761	35	45	the	the	DET
american_scientific_journal-761	35	46	absolute	absolute	ADJ
american_scientific_journal-761	35	47	value	value	NOUN
american_scientific_journal-761	35	48	.	.	PUNCT
american_scientific_journal-761	36	1	b	b	X
american_scientific_journal-761	36	2	)	)	PUNCT
american_scientific_journal-761	36	3	find	find	VERB
american_scientific_journal-761	36	4	the	the	DET
american_scientific_journal-761	36	5	solution	solution	NOUN
american_scientific_journal-761	36	6	set	set	VERB
american_scientific_journal-761	36	7	for	for	ADP
american_scientific_journal-761	36	8	the	the	DET
american_scientific_journal-761	36	9	inequality	inequality	NOUN
american_scientific_journal-761	36	10	2	2	NUM
american_scientific_journal-761	36	11	𝑥−1	𝑥−1	PROPN
american_scientific_journal-761	36	12	≥	≥	NOUN
american_scientific_journal-761	36	13	5	5	NUM
american_scientific_journal-761	36	14	in	in	ADP
american_scientific_journal-761	36	15	this	this	DET
american_scientific_journal-761	36	16	question	question	NOUN
american_scientific_journal-761	36	17	,	,	PUNCT
american_scientific_journal-761	36	18	the	the	DET
american_scientific_journal-761	36	19	students	student	NOUN
american_scientific_journal-761	36	20	are	be	AUX
american_scientific_journal-761	36	21	expected	expect	VERB
american_scientific_journal-761	36	22	to	to	PART
american_scientific_journal-761	36	23	find	find	VERB
american_scientific_journal-761	36	24	the	the	DET
american_scientific_journal-761	36	25	solution	solution	NOUN
american_scientific_journal-761	36	26	for	for	ADP
american_scientific_journal-761	36	27	the	the	DET
american_scientific_journal-761	36	28	inequality	inequality	NOUN
american_scientific_journal-761	36	29	paying	pay	VERB
american_scientific_journal-761	36	30	attention	attention	NOUN
american_scientific_journal-761	36	31	to	to	ADP
american_scientific_journal-761	36	32	the	the	DET
american_scientific_journal-761	36	33	sign	sign	NOUN
american_scientific_journal-761	36	34	of	of	ADP
american_scientific_journal-761	36	35	x	x	SYM
american_scientific_journal-761	36	36	−	−	PROPN
american_scientific_journal-761	36	37	1	1	NUM
american_scientific_journal-761	36	38	.	.	PUNCT
american_scientific_journal-761	37	1	c	c	X
american_scientific_journal-761	37	2	)	)	PUNCT
american_scientific_journal-761	37	3	find	find	VERB
american_scientific_journal-761	37	4	the	the	DET
american_scientific_journal-761	37	5	solution	solution	NOUN
american_scientific_journal-761	37	6	set	set	VERB
american_scientific_journal-761	37	7	for	for	ADP
american_scientific_journal-761	37	8	the	the	DET
american_scientific_journal-761	37	9	inequality	inequality	NOUN
american_scientific_journal-761	37	10	−2𝑥2	−2𝑥2	VERB
american_scientific_journal-761	37	11	+	+	CCONJ
american_scientific_journal-761	37	12	5𝑥	5𝑥	NUM
american_scientific_journal-761	38	1	+	+	CCONJ
american_scientific_journal-761	38	2	3	3	NUM
american_scientific_journal-761	38	3	<	<	X
american_scientific_journal-761	38	4	0	0	NUM
american_scientific_journal-761	39	1	in	in	ADP
american_scientific_journal-761	39	2	this	this	DET
american_scientific_journal-761	39	3	question	question	NOUN
american_scientific_journal-761	39	4	,	,	PUNCT
american_scientific_journal-761	39	5	the	the	DET
american_scientific_journal-761	39	6	students	student	NOUN
american_scientific_journal-761	39	7	are	be	AUX
american_scientific_journal-761	39	8	expected	expect	VERB
american_scientific_journal-761	39	9	to	to	PART
american_scientific_journal-761	39	10	find	find	VERB
american_scientific_journal-761	39	11	the	the	DET
american_scientific_journal-761	39	12	set	set	NOUN
american_scientific_journal-761	39	13	where	where	SCONJ
american_scientific_journal-761	39	14	the	the	DET
american_scientific_journal-761	39	15	second	second	ADJ
american_scientific_journal-761	39	16	degree	degree	NOUN
american_scientific_journal-761	39	17	polynomials	polynomial	NOUN
american_scientific_journal-761	39	18	get	get	VERB
american_scientific_journal-761	39	19	negative	negative	ADJ
american_scientific_journal-761	39	20	58	58	NUM
american_scientific_journal-761	39	21	american	american	ADJ
american_scientific_journal-761	39	22	scientific	scientific	ADJ
american_scientific_journal-761	39	23	research	research	NOUN
american_scientific_journal-761	39	24	journal	journal	NOUN
american_scientific_journal-761	39	25	for	for	ADP
american_scientific_journal-761	39	26	engineering	engineering	NOUN
american_scientific_journal-761	39	27	,	,	PUNCT
american_scientific_journal-761	39	28	technology	technology	NOUN
american_scientific_journal-761	39	29	,	,	PUNCT
american_scientific_journal-761	39	30	and	and	CCONJ
american_scientific_journal-761	39	31	sciences	science	NOUN
american_scientific_journal-761	39	32	(	(	PUNCT
american_scientific_journal-761	39	33	asrjets	asrjet	NOUN
american_scientific_journal-761	39	34	)	)	PUNCT
american_scientific_journal-761	39	35	(	(	PUNCT
american_scientific_journal-761	39	36	2013	2013	NUM
american_scientific_journal-761	39	37	)	)	PUNCT
american_scientific_journal-761	39	38	volume	volume	NOUN
american_scientific_journal-761	39	39	5	5	NUM
american_scientific_journal-761	39	40	,	,	PUNCT
american_scientific_journal-761	39	41	no	no	DET
american_scientific_journal-761	39	42	1	1	NUM
american_scientific_journal-761	39	43	,	,	PUNCT
american_scientific_journal-761	39	44	pp	pp	ADV
american_scientific_journal-761	39	45	57	57	NUM
american_scientific_journal-761	39	46	-	-	SYM
american_scientific_journal-761	39	47	62	62	NUM
american_scientific_journal-761	39	48	values	value	NOUN
american_scientific_journal-761	39	49	.	.	PUNCT
american_scientific_journal-761	40	1	d	d	X
american_scientific_journal-761	40	2	)	)	PUNCT
american_scientific_journal-761	40	3	find	find	VERB
american_scientific_journal-761	40	4	the	the	DET
american_scientific_journal-761	40	5	solution	solution	NOUN
american_scientific_journal-761	40	6	set	set	VERB
american_scientific_journal-761	40	7	for	for	ADP
american_scientific_journal-761	40	8	the	the	DET
american_scientific_journal-761	40	9	inequality	inequality	NOUN
american_scientific_journal-761	40	10	𝑥	𝑥	PROPN
american_scientific_journal-761	40	11	2	2	NUM
american_scientific_journal-761	40	12	≥	≥	NOUN
american_scientific_journal-761	40	13	1	1	NUM
american_scientific_journal-761	40	14	+	+	CCONJ
american_scientific_journal-761	40	15	4	4	NUM
american_scientific_journal-761	40	16	𝑥	𝑥	NOUN
american_scientific_journal-761	40	17	in	in	ADP
american_scientific_journal-761	40	18	this	this	DET
american_scientific_journal-761	40	19	question	question	NOUN
american_scientific_journal-761	40	20	,	,	PUNCT
american_scientific_journal-761	40	21	the	the	DET
american_scientific_journal-761	40	22	students	student	NOUN
american_scientific_journal-761	40	23	are	be	AUX
american_scientific_journal-761	40	24	expected	expect	VERB
american_scientific_journal-761	40	25	to	to	PART
american_scientific_journal-761	40	26	find	find	VERB
american_scientific_journal-761	40	27	the	the	DET
american_scientific_journal-761	40	28	solution	solution	NOUN
american_scientific_journal-761	40	29	by	by	ADP
american_scientific_journal-761	40	30	transforming	transform	VERB
american_scientific_journal-761	40	31	this	this	DET
american_scientific_journal-761	40	32	inequality	inequality	NOUN
american_scientific_journal-761	40	33	to	to	ADP
american_scientific_journal-761	40	34	a	a	DET
american_scientific_journal-761	40	35	rational	rational	ADJ
american_scientific_journal-761	40	36	expression	expression	NOUN
american_scientific_journal-761	40	37	after	after	ADP
american_scientific_journal-761	40	38	certain	certain	ADJ
american_scientific_journal-761	40	39	calculations	calculation	NOUN
american_scientific_journal-761	40	40	and	and	CCONJ
american_scientific_journal-761	40	41	by	by	ADP
american_scientific_journal-761	40	42	considering	consider	VERB
american_scientific_journal-761	40	43	the	the	DET
american_scientific_journal-761	40	44	signs	sign	NOUN
american_scientific_journal-761	40	45	of	of	ADP
american_scientific_journal-761	40	46	numerator	numerator	NOUN
american_scientific_journal-761	40	47	and	and	CCONJ
american_scientific_journal-761	40	48	denominator	denominator	NOUN
american_scientific_journal-761	40	49	.	.	PUNCT
american_scientific_journal-761	41	1	e	e	X
american_scientific_journal-761	41	2	)	)	PUNCT
american_scientific_journal-761	41	3	find	find	VERB
american_scientific_journal-761	41	4	the	the	DET
american_scientific_journal-761	41	5	solution	solution	NOUN
american_scientific_journal-761	41	6	set	set	VERB
american_scientific_journal-761	41	7	for	for	ADP
american_scientific_journal-761	41	8	the	the	DET
american_scientific_journal-761	41	9	inequality	inequality	NOUN
american_scientific_journal-761	41	10	49𝑥2	49𝑥2	NUM
american_scientific_journal-761	41	11	≤	≤	NUM
american_scientific_journal-761	41	12	64	64	NUM
american_scientific_journal-761	41	13	in	in	ADP
american_scientific_journal-761	41	14	this	this	DET
american_scientific_journal-761	41	15	question	question	NOUN
american_scientific_journal-761	41	16	,	,	PUNCT
american_scientific_journal-761	41	17	the	the	DET
american_scientific_journal-761	41	18	students	student	NOUN
american_scientific_journal-761	41	19	are	be	AUX
american_scientific_journal-761	41	20	expected	expect	VERB
american_scientific_journal-761	41	21	to	to	PART
american_scientific_journal-761	41	22	find	find	VERB
american_scientific_journal-761	41	23	the	the	DET
american_scientific_journal-761	41	24	solution	solution	NOUN
american_scientific_journal-761	41	25	set	set	VERB
american_scientific_journal-761	41	26	by	by	ADP
american_scientific_journal-761	41	27	keeping	keep	VERB
american_scientific_journal-761	41	28	the	the	DET
american_scientific_journal-761	41	29	equality	equality	NOUN
american_scientific_journal-761	41	30	√x2	√x2	PROPN
american_scientific_journal-761	41	31	=	=	SYM
american_scientific_journal-761	41	32	|x|	|x|	PROPN
american_scientific_journal-761	41	33	in	in	ADP
american_scientific_journal-761	41	34	mind	mind	NOUN
american_scientific_journal-761	41	35	.	.	PUNCT
american_scientific_journal-761	42	1	3	3	X
american_scientific_journal-761	42	2	.	.	NOUN
american_scientific_journal-761	42	3	results	result	NOUN
american_scientific_journal-761	42	4	table	table	VERB
american_scientific_journal-761	42	5	1	1	NUM
american_scientific_journal-761	42	6	:	:	PUNCT
american_scientific_journal-761	42	7	students	student	NOUN
american_scientific_journal-761	42	8	’	'	PUNCT
american_scientific_journal-761	42	9	performances	performance	VERB
american_scientific_journal-761	42	10	questions	question	NOUN
american_scientific_journal-761	42	11	1st	1st	ADJ
american_scientific_journal-761	42	12	question	question	NOUN
american_scientific_journal-761	42	13	2nd	2nd	ADJ
american_scientific_journal-761	42	14	question	question	NOUN
american_scientific_journal-761	42	15	3rd	3rd	ADJ
american_scientific_journal-761	42	16	question	question	NOUN
american_scientific_journal-761	42	17	4th	4th	ADJ
american_scientific_journal-761	42	18	question	question	NOUN
american_scientific_journal-761	42	19	5th	5th	ADJ
american_scientific_journal-761	42	20	question	question	NOUN
american_scientific_journal-761	42	21	the	the	DET
american_scientific_journal-761	42	22	percentages	percentage	NOUN
american_scientific_journal-761	42	23	for	for	ADP
american_scientific_journal-761	42	24	the	the	DET
american_scientific_journal-761	42	25	correct	correct	ADJ
american_scientific_journal-761	42	26	answers	answer	NOUN
american_scientific_journal-761	42	27	60	60	NUM
american_scientific_journal-761	42	28	30	30	NUM
american_scientific_journal-761	42	29	45	45	NUM
american_scientific_journal-761	42	30	20	20	NUM
american_scientific_journal-761	42	31	68	68	NUM
american_scientific_journal-761	42	32	60	60	NUM
american_scientific_journal-761	42	33	%	%	NOUN
american_scientific_journal-761	42	34	of	of	ADP
american_scientific_journal-761	42	35	the	the	DET
american_scientific_journal-761	42	36	students	student	NOUN
american_scientific_journal-761	42	37	gave	give	VERB
american_scientific_journal-761	42	38	the	the	DET
american_scientific_journal-761	42	39	correct	correct	ADJ
american_scientific_journal-761	42	40	answer	answer	NOUN
american_scientific_journal-761	42	41	to	to	ADP
american_scientific_journal-761	42	42	the	the	DET
american_scientific_journal-761	42	43	first	first	ADJ
american_scientific_journal-761	42	44	question	question	NOUN
american_scientific_journal-761	42	45	.	.	PUNCT
american_scientific_journal-761	43	1	in	in	ADP
american_scientific_journal-761	43	2	other	other	ADJ
american_scientific_journal-761	43	3	words	word	NOUN
american_scientific_journal-761	43	4	,	,	PUNCT
american_scientific_journal-761	43	5	40	40	NUM
american_scientific_journal-761	43	6	%	%	NOUN
american_scientific_journal-761	43	7	of	of	ADP
american_scientific_journal-761	43	8	the	the	DET
american_scientific_journal-761	43	9	students	student	NOUN
american_scientific_journal-761	43	10	were	be	AUX
american_scientific_journal-761	43	11	not	not	PART
american_scientific_journal-761	43	12	able	able	ADJ
american_scientific_journal-761	43	13	to	to	PART
american_scientific_journal-761	43	14	solve	solve	VERB
american_scientific_journal-761	43	15	the	the	DET
american_scientific_journal-761	43	16	inequality	inequality	NOUN
american_scientific_journal-761	43	17	correctly	correctly	ADV
american_scientific_journal-761	43	18	.	.	PUNCT
american_scientific_journal-761	44	1	in	in	ADP
american_scientific_journal-761	44	2	this	this	DET
american_scientific_journal-761	44	3	question	question	NOUN
american_scientific_journal-761	44	4	,	,	PUNCT
american_scientific_journal-761	44	5	the	the	DET
american_scientific_journal-761	44	6	students	student	NOUN
american_scientific_journal-761	44	7	could	could	AUX
american_scientific_journal-761	44	8	have	have	AUX
american_scientific_journal-761	44	9	found	find	VERB
american_scientific_journal-761	44	10	the	the	DET
american_scientific_journal-761	44	11	solution	solution	NOUN
american_scientific_journal-761	44	12	set	set	VERB
american_scientific_journal-761	44	13	by	by	ADP
american_scientific_journal-761	44	14	dividing	divide	VERB
american_scientific_journal-761	44	15	the	the	DET
american_scientific_journal-761	44	16	universe	universe	NOUN
american_scientific_journal-761	44	17	in	in	ADP
american_scientific_journal-761	44	18	to	to	ADP
american_scientific_journal-761	44	19	three	three	NUM
american_scientific_journal-761	44	20	sub	sub	NOUN
american_scientific_journal-761	44	21	sets	set	NOUN
american_scientific_journal-761	44	22	namely	namely	ADV
american_scientific_journal-761	44	23	:	:	PUNCT
american_scientific_journal-761	44	24	when	when	SCONJ
american_scientific_journal-761	44	25	𝒙	𝒙	PROPN
american_scientific_journal-761	44	26	∈	∈	PROPN
american_scientific_journal-761	44	27	(	(	PUNCT
american_scientific_journal-761	44	28	−∞,−𝟏	−∞,−𝟏	NUM
american_scientific_journal-761	44	29	)	)	PUNCT
american_scientific_journal-761	44	30	;	;	PUNCT
american_scientific_journal-761	44	31	∈	∈	PROPN
american_scientific_journal-761	45	1	[	[	X
american_scientific_journal-761	45	2	−𝟏,𝟑	−𝟏,𝟑	NOUN
american_scientific_journal-761	45	3	)	)	PUNCT
american_scientific_journal-761	45	4	;	;	PUNCT
american_scientific_journal-761	45	5	and	and	CCONJ
american_scientific_journal-761	45	6	𝒙	𝒙	NUM
american_scientific_journal-761	45	7	∈	∈	NOUN
american_scientific_journal-761	46	1	[	[	X
american_scientific_journal-761	46	2	𝟑	𝟑	NUM
american_scientific_journal-761	46	3	,	,	PUNCT
american_scientific_journal-761	46	4	+	+	NOUN
american_scientific_journal-761	46	5	∞	∞	NOUN
american_scientific_journal-761	46	6	)	)	PUNCT
american_scientific_journal-761	46	7	.	.	PUNCT
american_scientific_journal-761	47	1	when	when	SCONJ
american_scientific_journal-761	47	2	the	the	DET
american_scientific_journal-761	47	3	calculations	calculation	NOUN
american_scientific_journal-761	47	4	made	make	VERB
american_scientific_journal-761	47	5	by	by	ADP
american_scientific_journal-761	47	6	the	the	DET
american_scientific_journal-761	47	7	students	student	NOUN
american_scientific_journal-761	47	8	who	who	PRON
american_scientific_journal-761	47	9	gave	give	VERB
american_scientific_journal-761	47	10	the	the	DET
american_scientific_journal-761	47	11	wrong	wrong	ADJ
american_scientific_journal-761	47	12	answer	answer	NOUN
american_scientific_journal-761	47	13	were	be	AUX
american_scientific_journal-761	47	14	analyzed	analyze	VERB
american_scientific_journal-761	47	15	,	,	PUNCT
american_scientific_journal-761	47	16	consider	consider	VERB
american_scientific_journal-761	47	17	sample	sample	NOUN
american_scientific_journal-761	47	18	student	student	NOUN
american_scientific_journal-761	47	19	did	do	VERB
american_scientific_journal-761	47	20	on	on	ADP
american_scientific_journal-761	47	21	this	this	DET
american_scientific_journal-761	47	22	question	question	NOUN
american_scientific_journal-761	47	23	.	.	PUNCT
american_scientific_journal-761	48	1	sample	sample	NOUN
american_scientific_journal-761	48	2	1	1	NUM
american_scientific_journal-761	48	3	:	:	PUNCT
american_scientific_journal-761	48	4	the	the	DET
american_scientific_journal-761	48	5	solution	solution	NOUN
american_scientific_journal-761	48	6	given	give	VERB
american_scientific_journal-761	48	7	by	by	ADP
american_scientific_journal-761	48	8	one	one	NUM
american_scientific_journal-761	48	9	of	of	ADP
american_scientific_journal-761	48	10	the	the	DET
american_scientific_journal-761	48	11	students	student	NOUN
american_scientific_journal-761	48	12	who	who	PRON
american_scientific_journal-761	48	13	failed	fail	VERB
american_scientific_journal-761	48	14	to	to	PART
american_scientific_journal-761	48	15	give	give	VERB
american_scientific_journal-761	48	16	the	the	DET
american_scientific_journal-761	48	17	correct	correct	ADJ
american_scientific_journal-761	48	18	answer	answer	NOUN
american_scientific_journal-761	48	19	to	to	ADP
american_scientific_journal-761	48	20	the	the	DET
american_scientific_journal-761	48	21	first	first	ADJ
american_scientific_journal-761	48	22	question	question	NOUN
american_scientific_journal-761	48	23	.	.	PUNCT
american_scientific_journal-761	49	1	|𝑥	|𝑥	NOUN
american_scientific_journal-761	49	2	+	+	CCONJ
american_scientific_journal-761	49	3	1|	1|	NUM
american_scientific_journal-761	49	4	>	>	PUNCT
american_scientific_journal-761	49	5	|𝑥	|𝑥	PROPN
american_scientific_journal-761	49	6	−	−	PROPN
american_scientific_journal-761	49	7	3|	3|	NUM
american_scientific_journal-761	49	8	𝑙𝑒𝑡	𝑙𝑒𝑡	NOUN
american_scientific_journal-761	49	9	𝑥	𝑥	PROPN
american_scientific_journal-761	49	10	≥	≥	NUM
american_scientific_journal-761	49	11	3	3	NUM
american_scientific_journal-761	49	12	⇒	⇒	NOUN
american_scientific_journal-761	50	1	𝑥	𝑥	PROPN
american_scientific_journal-761	51	1	+	+	CCONJ
american_scientific_journal-761	51	2	1	1	NUM
american_scientific_journal-761	51	3	>	>	SYM
american_scientific_journal-761	51	4	𝑥	𝑥	X
american_scientific_journal-761	52	1	−	−	NUM
american_scientific_journal-761	52	2	3	3	NUM
american_scientific_journal-761	52	3	⟹	⟹	NUM
american_scientific_journal-761	52	4	0	0	NUM
american_scientific_journal-761	52	5	>	>	X
american_scientific_journal-761	53	1	−4	−4	X
american_scientific_journal-761	53	2	⟹	⟹	X
american_scientific_journal-761	53	3	𝑆.	𝑆.	ADJ
american_scientific_journal-761	53	4	𝑆1	𝑆1	NOUN
american_scientific_journal-761	53	5	=	=	SYM
american_scientific_journal-761	53	6	ℝ	ℝ	PROPN
american_scientific_journal-761	53	7	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
american_scientific_journal-761	53	8	𝑙𝑒𝑡	𝑙𝑒𝑡	ADV
american_scientific_journal-761	54	1	𝑥	𝑥	X
american_scientific_journal-761	54	2	<	<	X
american_scientific_journal-761	54	3	1	1	NUM
american_scientific_journal-761	54	4	⟹−𝑥	⟹−𝑥	ADP
american_scientific_journal-761	54	5	−	−	PROPN
american_scientific_journal-761	54	6	1	1	NUM
american_scientific_journal-761	54	7	>	>	PUNCT
american_scientific_journal-761	54	8	−𝑥	−𝑥	NOUN
american_scientific_journal-761	55	1	+	+	CCONJ
american_scientific_journal-761	55	2	3	3	NUM
american_scientific_journal-761	55	3	⇒	⇒	NOUN
american_scientific_journal-761	55	4	0	0	PUNCT
american_scientific_journal-761	55	5	>	>	SYM
american_scientific_journal-761	55	6	4	4	NUM
american_scientific_journal-761	55	7	⟹	⟹	ADV
american_scientific_journal-761	55	8	𝑆.	𝑆.	NOUN
american_scientific_journal-761	55	9	𝑆2	𝑆2	NOUN
american_scientific_journal-761	55	10	=	=	PUNCT
american_scientific_journal-761	55	11	∅	∅	NOUN
american_scientific_journal-761	55	12	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
american_scientific_journal-761	55	13	𝑙𝑒𝑡	𝑙𝑒𝑡	PROPN
american_scientific_journal-761	55	14	−	−	PROPN
american_scientific_journal-761	55	15	1	1	NUM
american_scientific_journal-761	55	16	≤	≤	NUM
american_scientific_journal-761	56	1	𝑥	𝑥	PRON
american_scientific_journal-761	56	2	<	<	X
american_scientific_journal-761	56	3	3	3	NUM
american_scientific_journal-761	56	4	⇒	⇒	NOUN
american_scientific_journal-761	56	5	𝑥	𝑥	X
american_scientific_journal-761	57	1	+	+	CCONJ
american_scientific_journal-761	57	2	1	1	NUM
american_scientific_journal-761	57	3	>	>	PUNCT
american_scientific_journal-761	57	4	−𝑥	−𝑥	NOUN
american_scientific_journal-761	57	5	+	+	CCONJ
american_scientific_journal-761	57	6	3	3	NUM
american_scientific_journal-761	57	7	⇒	⇒	NOUN
american_scientific_journal-761	57	8	𝑥	𝑥	X
american_scientific_journal-761	57	9	>	>	SYM
american_scientific_journal-761	57	10	2	2	NUM
american_scientific_journal-761	57	11	⇒	⇒	NOUN
american_scientific_journal-761	57	12	𝑆.	𝑆.	PROPN
american_scientific_journal-761	57	13	𝑆3	𝑆3	PROPN
american_scientific_journal-761	57	14	=	=	SYM
american_scientific_journal-761	57	15	(	(	PUNCT
american_scientific_journal-761	57	16	2	2	NUM
american_scientific_journal-761	57	17	,	,	PUNCT
american_scientific_journal-761	57	18	+	+	NOUN
american_scientific_journal-761	57	19	∞	∞	NOUN
american_scientific_journal-761	57	20	)	)	PUNCT
american_scientific_journal-761	58	1	finally	finally	ADV
american_scientific_journal-761	58	2	he	he	PRON
american_scientific_journal-761	58	3	came	come	VERB
american_scientific_journal-761	58	4	to	to	ADP
american_scientific_journal-761	58	5	final	final	ADJ
american_scientific_journal-761	58	6	solution	solution	NOUN
american_scientific_journal-761	58	7	𝑆.	𝑆.	PROPN
american_scientific_journal-761	58	8	𝑆	𝑆	PROPN
american_scientific_journal-761	59	1	=	=	SYM
american_scientific_journal-761	59	2	𝑆.	𝑆.	PROPN
american_scientific_journal-761	59	3	𝑆1	𝑆1	NOUN
american_scientific_journal-761	59	4	∪	∪	ADP
american_scientific_journal-761	59	5	𝑆.	𝑆.	ADJ
american_scientific_journal-761	59	6	𝑆2	𝑆2	NOUN
american_scientific_journal-761	59	7	∪	∪	ADP
american_scientific_journal-761	59	8	𝑆.	𝑆.	PROPN
american_scientific_journal-761	59	9	𝑆3	𝑆3	NOUN
american_scientific_journal-761	59	10	=	=	SYM
american_scientific_journal-761	59	11	ℝ	ℝ	PROPN
american_scientific_journal-761	59	12	this	this	PRON
american_scientific_journal-761	59	13	is	be	AUX
american_scientific_journal-761	59	14	normally	normally	ADV
american_scientific_journal-761	59	15	without	without	ADP
american_scientific_journal-761	59	16	considering	consider	VERB
american_scientific_journal-761	59	17	intersection	intersection	NOUN
american_scientific_journal-761	59	18	of	of	ADP
american_scientific_journal-761	59	19	each	each	DET
american_scientific_journal-761	59	20	finding	finding	NOUN
american_scientific_journal-761	59	21	with	with	ADP
american_scientific_journal-761	59	22	subsets	subset	NOUN
american_scientific_journal-761	59	23	of	of	ADP
american_scientific_journal-761	59	24	the	the	DET
american_scientific_journal-761	59	25	universe	universe	NOUN
american_scientific_journal-761	59	26	.	.	PUNCT
american_scientific_journal-761	60	1	which	which	PRON
american_scientific_journal-761	60	2	is	be	AUX
american_scientific_journal-761	60	3	a	a	DET
american_scientific_journal-761	60	4	procedural	procedural	ADJ
american_scientific_journal-761	60	5	error	error	NOUN
american_scientific_journal-761	60	6	as	as	ADP
american_scientific_journal-761	60	7	a	a	DET
american_scientific_journal-761	60	8	result	result	NOUN
american_scientific_journal-761	60	9	of	of	ADP
american_scientific_journal-761	60	10	failure	failure	NOUN
american_scientific_journal-761	60	11	to	to	PART
american_scientific_journal-761	60	12	carry	carry	VERB
american_scientific_journal-761	60	13	out	out	ADP
american_scientific_journal-761	60	14	manipulation	manipulation	NOUN
american_scientific_journal-761	60	15	or	or	CCONJ
american_scientific_journal-761	60	16	algorithmic	algorithmic	ADJ
american_scientific_journal-761	60	17	despite	despite	SCONJ
american_scientific_journal-761	60	18	having	having	AUX
american_scientific_journal-761	60	19	understand	understand	VERB
american_scientific_journal-761	60	20	the	the	DET
american_scientific_journal-761	60	21	content	content	NOUN
american_scientific_journal-761	60	22	behind	behind	ADP
american_scientific_journal-761	60	23	the	the	DET
american_scientific_journal-761	60	24	problem	problem	NOUN
american_scientific_journal-761	60	25	.	.	PUNCT
american_scientific_journal-761	61	1	the	the	DET
american_scientific_journal-761	61	2	second	second	ADJ
american_scientific_journal-761	61	3	question	question	NOUN
american_scientific_journal-761	61	4	was	be	AUX
american_scientific_journal-761	61	5	given	give	VERB
american_scientific_journal-761	61	6	a	a	DET
american_scientific_journal-761	61	7	correct	correct	ADJ
american_scientific_journal-761	61	8	answer	answer	NOUN
american_scientific_journal-761	61	9	by	by	ADP
american_scientific_journal-761	61	10	30	30	NUM
american_scientific_journal-761	61	11	%	%	NOUN
american_scientific_journal-761	61	12	of	of	ADP
american_scientific_journal-761	61	13	the	the	DET
american_scientific_journal-761	61	14	students	student	NOUN
american_scientific_journal-761	61	15	.	.	PUNCT
american_scientific_journal-761	62	1	according	accord	VERB
american_scientific_journal-761	62	2	to	to	ADP
american_scientific_journal-761	62	3	this	this	DET
american_scientific_journal-761	62	4	result	result	NOUN
american_scientific_journal-761	62	5	,	,	PUNCT
american_scientific_journal-761	62	6	one	one	PRON
american_scientific_journal-761	62	7	might	might	AUX
american_scientific_journal-761	62	8	conclude	conclude	VERB
american_scientific_journal-761	62	9	that	that	SCONJ
american_scientific_journal-761	62	10	a	a	DET
american_scientific_journal-761	62	11	considerable	considerable	ADJ
american_scientific_journal-761	62	12	number	number	NOUN
american_scientific_journal-761	62	13	of	of	ADP
american_scientific_journal-761	62	14	students	student	NOUN
american_scientific_journal-761	62	15	failed	fail	VERB
american_scientific_journal-761	62	16	to	to	PART
american_scientific_journal-761	62	17	answer	answer	VERB
american_scientific_journal-761	62	18	this	this	DET
american_scientific_journal-761	62	19	question	question	NOUN
american_scientific_journal-761	62	20	correctly	correctly	ADV
american_scientific_journal-761	62	21	.	.	PUNCT
american_scientific_journal-761	63	1	59	59	NUM
american_scientific_journal-761	63	2	american	american	ADJ
american_scientific_journal-761	63	3	scientific	scientific	ADJ
american_scientific_journal-761	63	4	research	research	NOUN
american_scientific_journal-761	63	5	journal	journal	NOUN
american_scientific_journal-761	63	6	for	for	ADP
american_scientific_journal-761	63	7	engineering	engineering	NOUN
american_scientific_journal-761	63	8	,	,	PUNCT
american_scientific_journal-761	63	9	technology	technology	NOUN
american_scientific_journal-761	63	10	,	,	PUNCT
american_scientific_journal-761	63	11	and	and	CCONJ
american_scientific_journal-761	63	12	sciences	science	NOUN
american_scientific_journal-761	63	13	(	(	PUNCT
american_scientific_journal-761	63	14	asrjets	asrjet	NOUN
american_scientific_journal-761	63	15	)	)	PUNCT
american_scientific_journal-761	63	16	(	(	PUNCT
american_scientific_journal-761	63	17	2013	2013	NUM
american_scientific_journal-761	63	18	)	)	PUNCT
american_scientific_journal-761	63	19	volume	volume	NOUN
american_scientific_journal-761	63	20	5	5	NUM
american_scientific_journal-761	63	21	,	,	PUNCT
american_scientific_journal-761	63	22	no	no	DET
american_scientific_journal-761	63	23	1	1	NUM
american_scientific_journal-761	63	24	,	,	PUNCT
american_scientific_journal-761	63	25	pp	pp	ADV
american_scientific_journal-761	63	26	57	57	NUM
american_scientific_journal-761	63	27	-	-	SYM
american_scientific_journal-761	63	28	62	62	NUM
american_scientific_journal-761	63	29	the	the	DET
american_scientific_journal-761	63	30	question	question	NOUN
american_scientific_journal-761	63	31	was	be	AUX
american_scientific_journal-761	63	32	2	2	NUM
american_scientific_journal-761	63	33	𝑥−1	𝑥−1	NOUN
american_scientific_journal-761	63	34	≥	≥	NOUN
american_scientific_journal-761	63	35	5	5	NUM
american_scientific_journal-761	63	36	.	.	PUNCT
american_scientific_journal-761	64	1	in	in	ADP
american_scientific_journal-761	64	2	this	this	DET
american_scientific_journal-761	64	3	question	question	NOUN
american_scientific_journal-761	64	4	,	,	PUNCT
american_scientific_journal-761	64	5	the	the	DET
american_scientific_journal-761	64	6	students	student	NOUN
american_scientific_journal-761	64	7	are	be	AUX
american_scientific_journal-761	64	8	expected	expect	VERB
american_scientific_journal-761	64	9	to	to	PART
american_scientific_journal-761	64	10	find	find	VERB
american_scientific_journal-761	64	11	the	the	DET
american_scientific_journal-761	64	12	solution	solution	NOUN
american_scientific_journal-761	64	13	for	for	ADP
american_scientific_journal-761	64	14	the	the	DET
american_scientific_journal-761	64	15	inequality	inequality	NOUN
american_scientific_journal-761	64	16	paying	pay	VERB
american_scientific_journal-761	64	17	attention	attention	NOUN
american_scientific_journal-761	64	18	to	to	ADP
american_scientific_journal-761	64	19	the	the	DET
american_scientific_journal-761	64	20	sign	sign	NOUN
american_scientific_journal-761	64	21	of	of	ADP
american_scientific_journal-761	64	22	x	x	SYM
american_scientific_journal-761	64	23	−	−	PROPN
american_scientific_journal-761	64	24	1	1	NUM
american_scientific_journal-761	64	25	.	.	PUNCT
american_scientific_journal-761	65	1	but	but	CCONJ
american_scientific_journal-761	65	2	one	one	NUM
american_scientific_journal-761	65	3	of	of	ADP
american_scientific_journal-761	65	4	the	the	DET
american_scientific_journal-761	65	5	sample	sample	NOUN
american_scientific_journal-761	65	6	students	student	NOUN
american_scientific_journal-761	65	7	who	who	PRON
american_scientific_journal-761	65	8	filed	file	VERB
american_scientific_journal-761	65	9	to	to	PART
american_scientific_journal-761	65	10	find	find	VERB
american_scientific_journal-761	65	11	the	the	DET
american_scientific_journal-761	65	12	correct	correct	ADJ
american_scientific_journal-761	65	13	answer	answer	NOUN
american_scientific_journal-761	65	14	simply	simply	ADV
american_scientific_journal-761	65	15	multiplied	multiply	VERB
american_scientific_journal-761	65	16	both	both	DET
american_scientific_journal-761	65	17	side	side	NOUN
american_scientific_journal-761	65	18	of	of	ADP
american_scientific_journal-761	65	19	2	2	NUM
american_scientific_journal-761	65	20	𝑥−1	𝑥−1	NOUN
american_scientific_journal-761	65	21	≥	≥	NOUN
american_scientific_journal-761	65	22	5	5	NUM
american_scientific_journal-761	65	23	by	by	ADP
american_scientific_journal-761	65	24	𝑥	𝑥	NOUN
american_scientific_journal-761	65	25	−	−	PROPN
american_scientific_journal-761	65	26	1	1	NUM
american_scientific_journal-761	65	27	and	and	CCONJ
american_scientific_journal-761	65	28	obtained	obtain	VERB
american_scientific_journal-761	65	29	the	the	DET
american_scientific_journal-761	65	30	inequality	inequality	NOUN
american_scientific_journal-761	65	31	2	2	NUM
american_scientific_journal-761	65	32	≥	≥	NOUN
american_scientific_journal-761	65	33	5(𝑥	5(𝑥	NUM
american_scientific_journal-761	65	34	−	−	NUM
american_scientific_journal-761	65	35	1)𝑎𝑛𝑑	1)𝑎𝑛𝑑	NUM
american_scientific_journal-761	65	36	𝑜𝑏𝑡𝑎𝑖𝑛𝑒𝑑	𝑜𝑏𝑡𝑎𝑖𝑛𝑒𝑑	VERB
american_scientific_journal-761	65	37	the	the	DET
american_scientific_journal-761	65	38	result	result	NOUN
american_scientific_journal-761	65	39	𝑥	𝑥	X
american_scientific_journal-761	65	40	≤	≤	NUM
american_scientific_journal-761	65	41	7	7	NUM
american_scientific_journal-761	65	42	5	5	NUM
american_scientific_journal-761	65	43	.	.	PUNCT
american_scientific_journal-761	66	1	in	in	ADP
american_scientific_journal-761	66	2	this	this	DET
american_scientific_journal-761	66	3	question	question	NOUN
american_scientific_journal-761	66	4	students	student	NOUN
american_scientific_journal-761	66	5	did	do	AUX
american_scientific_journal-761	66	6	n’t	not	PART
american_scientific_journal-761	66	7	realized	realize	VERB
american_scientific_journal-761	66	8	the	the	DET
american_scientific_journal-761	66	9	situations	situation	NOUN
american_scientific_journal-761	66	10	𝑥	𝑥	X
american_scientific_journal-761	66	11	<	<	X
american_scientific_journal-761	66	12	1	1	NUM
american_scientific_journal-761	66	13	𝑎𝑛𝑑	𝑎𝑛𝑑	NOUN
american_scientific_journal-761	66	14	𝑥	𝑥	PROPN
american_scientific_journal-761	66	15	>	>	X
american_scientific_journal-761	66	16	1	1	NUM
american_scientific_journal-761	66	17	,	,	PUNCT
american_scientific_journal-761	66	18	so	so	SCONJ
american_scientific_journal-761	66	19	that	that	SCONJ
american_scientific_journal-761	66	20	they	they	PRON
american_scientific_journal-761	66	21	could	could	AUX
american_scientific_journal-761	66	22	not	not	PART
american_scientific_journal-761	66	23	find	find	VERB
american_scientific_journal-761	66	24	the	the	DET
american_scientific_journal-761	66	25	correct	correct	ADJ
american_scientific_journal-761	66	26	answer	answer	NOUN
american_scientific_journal-761	66	27	𝑖.	𝑖.	ADV
american_scientific_journal-761	66	28	𝑒	𝑒	PROPN
american_scientific_journal-761	66	29	(	(	PUNCT
american_scientific_journal-761	66	30	1	1	NUM
american_scientific_journal-761	66	31	,	,	PUNCT
american_scientific_journal-761	66	32	7	7	NUM
american_scientific_journal-761	66	33	2	2	NUM
american_scientific_journal-761	66	34	]	]	PUNCT
american_scientific_journal-761	66	35	.	.	PUNCT
american_scientific_journal-761	67	1	in	in	ADP
american_scientific_journal-761	67	2	the	the	DET
american_scientific_journal-761	67	3	third	third	ADJ
american_scientific_journal-761	67	4	question	question	NOUN
american_scientific_journal-761	67	5	,	,	PUNCT
american_scientific_journal-761	67	6	nearly	nearly	ADV
american_scientific_journal-761	67	7	45	45	NUM
american_scientific_journal-761	67	8	%	%	NOUN
american_scientific_journal-761	67	9	of	of	ADP
american_scientific_journal-761	67	10	the	the	DET
american_scientific_journal-761	67	11	students	student	NOUN
american_scientific_journal-761	67	12	found	find	VERB
american_scientific_journal-761	67	13	the	the	DET
american_scientific_journal-761	67	14	correct	correct	ADJ
american_scientific_journal-761	67	15	solution	solution	NOUN
american_scientific_journal-761	67	16	set	set	VERB
american_scientific_journal-761	67	17	.	.	PUNCT
american_scientific_journal-761	68	1	in	in	ADP
american_scientific_journal-761	68	2	other	other	ADJ
american_scientific_journal-761	68	3	words	word	NOUN
american_scientific_journal-761	68	4	,	,	PUNCT
american_scientific_journal-761	68	5	55	55	NUM
american_scientific_journal-761	68	6	%	%	NOUN
american_scientific_journal-761	68	7	of	of	ADP
american_scientific_journal-761	68	8	the	the	DET
american_scientific_journal-761	68	9	students	student	NOUN
american_scientific_journal-761	68	10	were	be	AUX
american_scientific_journal-761	68	11	not	not	PART
american_scientific_journal-761	68	12	able	able	ADJ
american_scientific_journal-761	68	13	to	to	PART
american_scientific_journal-761	68	14	find	find	VERB
american_scientific_journal-761	68	15	the	the	DET
american_scientific_journal-761	68	16	correct	correct	ADJ
american_scientific_journal-761	68	17	solution	solution	NOUN
american_scientific_journal-761	68	18	set	set	VERB
american_scientific_journal-761	68	19	.	.	PUNCT
american_scientific_journal-761	69	1	these	these	DET
american_scientific_journal-761	69	2	students	student	NOUN
american_scientific_journal-761	69	3	mostly	mostly	ADV
american_scientific_journal-761	69	4	focused	focus	VERB
american_scientific_journal-761	69	5	on	on	ADP
american_scientific_journal-761	69	6	the	the	DET
american_scientific_journal-761	69	7	negative	negative	ADJ
american_scientific_journal-761	69	8	and	and	CCONJ
american_scientific_journal-761	69	9	positive	positive	ADJ
american_scientific_journal-761	69	10	values	value	NOUN
american_scientific_journal-761	69	11	of	of	ADP
american_scientific_journal-761	69	12	the	the	DET
american_scientific_journal-761	69	13	polynomial	polynomial	ADJ
american_scientific_journal-761	69	14	−2𝑥2	−2𝑥2	PROPN
american_scientific_journal-761	69	15	+	+	CCONJ
american_scientific_journal-761	70	1	5𝑥	5𝑥	NUM
american_scientific_journal-761	71	1	+	+	CCONJ
american_scientific_journal-761	71	2	3	3	NUM
american_scientific_journal-761	71	3	.they	.they	PRON
american_scientific_journal-761	71	4	reached	reach	VERB
american_scientific_journal-761	71	5	the	the	DET
american_scientific_journal-761	71	6	incorrect	incorrect	ADJ
american_scientific_journal-761	71	7	answer	answer	NOUN
american_scientific_journal-761	71	8	due	due	ADP
american_scientific_journal-761	71	9	to	to	ADP
american_scientific_journal-761	71	10	the	the	DET
american_scientific_journal-761	71	11	reason	reason	NOUN
american_scientific_journal-761	71	12	that	that	PRON
american_scientific_journal-761	71	13	they	they	PRON
american_scientific_journal-761	71	14	did	do	AUX
american_scientific_journal-761	71	15	n’t	not	PART
american_scientific_journal-761	71	16	realized	realize	VERB
american_scientific_journal-761	71	17	that	that	SCONJ
american_scientific_journal-761	71	18	the	the	DET
american_scientific_journal-761	71	19	equations	equation	NOUN
american_scientific_journal-761	71	20	−2x2	−2x2	PUNCT
american_scientific_journal-761	72	1	+	+	X
american_scientific_journal-761	72	2	5x	5x	NOUN
american_scientific_journal-761	72	3	+	+	CCONJ
american_scientific_journal-761	72	4	3	3	NUM
american_scientific_journal-761	72	5	=	=	SYM
american_scientific_journal-761	72	6	0	0	NUM
american_scientific_journal-761	72	7	and	and	CCONJ
american_scientific_journal-761	72	8	2x2	2x2	NUM
american_scientific_journal-761	72	9	−	−	NOUN
american_scientific_journal-761	72	10	5x	5x	NUM
american_scientific_journal-761	72	11	−	−	PROPN
american_scientific_journal-761	72	12	3	3	NUM
american_scientific_journal-761	72	13	=	=	SYM
american_scientific_journal-761	72	14	0	0	NUM
american_scientific_journal-761	72	15	have	have	VERB
american_scientific_journal-761	72	16	the	the	DET
american_scientific_journal-761	72	17	same	same	ADJ
american_scientific_journal-761	72	18	solution	solution	NOUN
american_scientific_journal-761	72	19	.	.	PUNCT
american_scientific_journal-761	73	1	the	the	DET
american_scientific_journal-761	73	2	correct	correct	ADJ
american_scientific_journal-761	73	3	solution	solution	NOUN
american_scientific_journal-761	73	4	set	set	VERB
american_scientific_journal-761	73	5	for	for	ADP
american_scientific_journal-761	73	6	the	the	DET
american_scientific_journal-761	73	7	fourth	fourth	ADJ
american_scientific_journal-761	73	8	question	question	NOUN
american_scientific_journal-761	73	9	was	be	AUX
american_scientific_journal-761	73	10	found	find	VERB
american_scientific_journal-761	73	11	by	by	ADP
american_scientific_journal-761	73	12	20	20	NUM
american_scientific_journal-761	73	13	%	%	NOUN
american_scientific_journal-761	73	14	of	of	ADP
american_scientific_journal-761	73	15	the	the	DET
american_scientific_journal-761	73	16	students	student	NOUN
american_scientific_journal-761	73	17	.	.	PUNCT
american_scientific_journal-761	74	1	the	the	DET
american_scientific_journal-761	74	2	majority	majority	NOUN
american_scientific_journal-761	74	3	of	of	ADP
american_scientific_journal-761	74	4	the	the	DET
american_scientific_journal-761	74	5	students	student	NOUN
american_scientific_journal-761	74	6	gave	give	VERB
american_scientific_journal-761	74	7	the	the	DET
american_scientific_journal-761	74	8	wrong	wrong	ADJ
american_scientific_journal-761	74	9	answer	answer	NOUN
american_scientific_journal-761	74	10	to	to	ADP
american_scientific_journal-761	74	11	this	this	DET
american_scientific_journal-761	74	12	question	question	NOUN
american_scientific_journal-761	74	13	.	.	PUNCT
american_scientific_journal-761	75	1	these	these	DET
american_scientific_journal-761	75	2	students	student	NOUN
american_scientific_journal-761	75	3	particularly	particularly	ADV
american_scientific_journal-761	75	4	did	do	AUX
american_scientific_journal-761	75	5	n’t	not	PART
american_scientific_journal-761	75	6	consider	consider	VERB
american_scientific_journal-761	75	7	the	the	DET
american_scientific_journal-761	75	8	variable	variable	NOUN
american_scientific_journal-761	75	9	x	x	NOUN
american_scientific_journal-761	75	10	in	in	ADP
american_scientific_journal-761	75	11	the	the	DET
american_scientific_journal-761	75	12	denominator	denominator	NOUN
american_scientific_journal-761	75	13	in	in	ADP
american_scientific_journal-761	75	14	the	the	DET
american_scientific_journal-761	75	15	later	later	ADJ
american_scientific_journal-761	75	16	calculation	calculation	NOUN
american_scientific_journal-761	75	17	.	.	PUNCT
american_scientific_journal-761	76	1	obtained	obtain	VERB
american_scientific_journal-761	76	2	x	x	PROPN
american_scientific_journal-761	76	3	2	2	NUM
american_scientific_journal-761	76	4	−	−	NUM
american_scientific_journal-761	76	5	4	4	NUM
american_scientific_journal-761	76	6	x	x	SYM
american_scientific_journal-761	76	7	−	−	PROPN
american_scientific_journal-761	76	8	1	1	NUM
american_scientific_journal-761	76	9	≥	≥	NOUN
american_scientific_journal-761	76	10	0	0	NUM
american_scientific_journal-761	76	11	from	from	ADP
american_scientific_journal-761	76	12	𝑥	𝑥	DET
american_scientific_journal-761	76	13	2	2	NUM
american_scientific_journal-761	76	14	≥	≥	NOUN
american_scientific_journal-761	76	15	1	1	NUM
american_scientific_journal-761	76	16	+	+	CCONJ
american_scientific_journal-761	76	17	4	4	NUM
american_scientific_journal-761	76	18	x	x	NOUN
american_scientific_journal-761	76	19	and	and	CCONJ
american_scientific_journal-761	76	20	this	this	PRON
american_scientific_journal-761	76	21	led	lead	VERB
american_scientific_journal-761	76	22	them	they	PRON
american_scientific_journal-761	76	23	to	to	PART
american_scientific_journal-761	76	24	find	find	VERB
american_scientific_journal-761	76	25	the	the	DET
american_scientific_journal-761	76	26	inequality	inequality	NOUN
american_scientific_journal-761	76	27	x	x	PROPN
american_scientific_journal-761	76	28	2−2x−8	2−2x−8	NUM
american_scientific_journal-761	76	29	2x	2x	NUM
american_scientific_journal-761	76	30	≥	≥	NOUN
american_scientific_journal-761	76	31	0	0	NUM
american_scientific_journal-761	76	32	.	.	PUNCT
american_scientific_journal-761	77	1	this	this	PRON
american_scientific_journal-761	77	2	was	be	AUX
american_scientific_journal-761	77	3	basically	basically	ADV
american_scientific_journal-761	77	4	acquired	acquire	VERB
american_scientific_journal-761	77	5	by	by	ADP
american_scientific_journal-761	77	6	making	make	VERB
american_scientific_journal-761	77	7	the	the	DET
american_scientific_journal-761	77	8	denominator	denominator	NOUN
american_scientific_journal-761	77	9	equal	equal	ADJ
american_scientific_journal-761	77	10	up	up	ADP
american_scientific_journal-761	77	11	to	to	ADP
american_scientific_journal-761	77	12	this	this	DET
american_scientific_journal-761	77	13	step	step	NOUN
american_scientific_journal-761	77	14	what	what	PRON
american_scientific_journal-761	77	15	they	they	PRON
american_scientific_journal-761	77	16	did	do	AUX
american_scientific_journal-761	77	17	is	be	AUX
american_scientific_journal-761	77	18	arithmetically	arithmetically	ADV
american_scientific_journal-761	77	19	correct	correct	ADJ
american_scientific_journal-761	77	20	.	.	PUNCT
american_scientific_journal-761	78	1	next	next	ADV
american_scientific_journal-761	78	2	,	,	PUNCT
american_scientific_journal-761	78	3	ignoring	ignore	VERB
american_scientific_journal-761	78	4	the	the	DET
american_scientific_journal-761	78	5	possibility	possibility	NOUN
american_scientific_journal-761	78	6	that	that	SCONJ
american_scientific_journal-761	78	7	x	x	PRON
american_scientific_journal-761	78	8	may	may	AUX
american_scientific_journal-761	78	9	take	take	VERB
american_scientific_journal-761	78	10	both	both	PRON
american_scientific_journal-761	78	11	negative	negative	ADJ
american_scientific_journal-761	78	12	and	and	CCONJ
american_scientific_journal-761	78	13	positive	positive	ADJ
american_scientific_journal-761	78	14	values	value	NOUN
american_scientific_journal-761	78	15	,	,	PUNCT
american_scientific_journal-761	78	16	they	they	PRON
american_scientific_journal-761	78	17	multiplied	multiply	VERB
american_scientific_journal-761	78	18	x	x	PUNCT
american_scientific_journal-761	78	19	by	by	ADP
american_scientific_journal-761	78	20	both	both	DET
american_scientific_journal-761	78	21	sides	side	NOUN
american_scientific_journal-761	78	22	of	of	ADP
american_scientific_journal-761	78	23	x	x	PROPN
american_scientific_journal-761	78	24	2−2x−8	2−2x−8	NUM
american_scientific_journal-761	78	25	2x	2x	NUM
american_scientific_journal-761	78	26	≥	≥	NOUN
american_scientific_journal-761	78	27	0	0	NUM
american_scientific_journal-761	78	28	and	and	CCONJ
american_scientific_journal-761	78	29	obtained	obtain	VERB
american_scientific_journal-761	78	30	the	the	DET
american_scientific_journal-761	78	31	quadratic	quadratic	ADJ
american_scientific_journal-761	78	32	inequality	inequality	NOUN
american_scientific_journal-761	79	1	x2	x2	PRON
american_scientific_journal-761	79	2	−	−	PROPN
american_scientific_journal-761	80	1	2x	2x	NUM
american_scientific_journal-761	80	2	−	−	PROPN
american_scientific_journal-761	80	3	8	8	NUM
american_scientific_journal-761	80	4	≥	≥	NOUN
american_scientific_journal-761	80	5	0	0	NUM
american_scientific_journal-761	81	1	this	this	PRON
american_scientific_journal-761	81	2	was	be	AUX
american_scientific_journal-761	81	3	led	lead	VERB
american_scientific_journal-761	81	4	them	they	PRON
american_scientific_journal-761	81	5	solution	solution	NOUN
american_scientific_journal-761	81	6	set	set	VERB
american_scientific_journal-761	81	7	of	of	ADP
american_scientific_journal-761	81	8	(	(	PUNCT
american_scientific_journal-761	81	9	−∞,−2	−∞,−2	NUM
american_scientific_journal-761	81	10	]	]	PUNCT
american_scientific_journal-761	81	11	∪	∪	ADP
american_scientific_journal-761	81	12	[	[	X
american_scientific_journal-761	81	13	4,∞	4,∞	NUM
american_scientific_journal-761	81	14	)	)	PUNCT
american_scientific_journal-761	81	15	this	this	DET
american_scientific_journal-761	81	16	solution	solution	NOUN
american_scientific_journal-761	81	17	became	became	AUX
american_scientific_journal-761	81	18	considered	consider	VERB
american_scientific_journal-761	81	19	the	the	DET
american_scientific_journal-761	81	20	solution	solution	NOUN
american_scientific_journal-761	81	21	for	for	ADP
american_scientific_journal-761	81	22	the	the	DET
american_scientific_journal-761	81	23	original	original	ADJ
american_scientific_journal-761	81	24	inequality	inequality	NOUN
american_scientific_journal-761	81	25	𝑥	𝑥	PROPN
american_scientific_journal-761	81	26	2	2	NUM
american_scientific_journal-761	81	27	≥	≥	NOUN
american_scientific_journal-761	81	28	1	1	NUM
american_scientific_journal-761	81	29	+	+	CCONJ
american_scientific_journal-761	81	30	4	4	NUM
american_scientific_journal-761	81	31	x	x	NOUN
american_scientific_journal-761	81	32	.	.	PUNCT
american_scientific_journal-761	82	1	unfortunately	unfortunately	ADV
american_scientific_journal-761	82	2	,	,	PUNCT
american_scientific_journal-761	82	3	this	this	PRON
american_scientific_journal-761	82	4	was	be	AUX
american_scientific_journal-761	82	5	the	the	DET
american_scientific_journal-761	82	6	incorrect	incorrect	ADJ
american_scientific_journal-761	82	7	solution	solution	NOUN
american_scientific_journal-761	82	8	set	set	VERB
american_scientific_journal-761	82	9	.	.	PUNCT
american_scientific_journal-761	83	1	most	most	ADJ
american_scientific_journal-761	83	2	of	of	ADP
american_scientific_journal-761	83	3	the	the	DET
american_scientific_journal-761	83	4	students	student	NOUN
american_scientific_journal-761	83	5	were	be	AUX
american_scientific_journal-761	83	6	successful	successful	ADJ
american_scientific_journal-761	83	7	in	in	ADP
american_scientific_journal-761	83	8	finding	find	VERB
american_scientific_journal-761	83	9	the	the	DET
american_scientific_journal-761	83	10	correct	correct	ADJ
american_scientific_journal-761	83	11	answer	answer	NOUN
american_scientific_journal-761	83	12	to	to	ADP
american_scientific_journal-761	83	13	the	the	DET
american_scientific_journal-761	83	14	fifth	fifth	ADJ
american_scientific_journal-761	83	15	question	question	NOUN
american_scientific_journal-761	83	16	68	68	NUM
american_scientific_journal-761	83	17	%	%	NOUN
american_scientific_journal-761	83	18	.	.	PUNCT
american_scientific_journal-761	84	1	when	when	SCONJ
american_scientific_journal-761	84	2	compared	compare	VERB
american_scientific_journal-761	84	3	with	with	ADP
american_scientific_journal-761	84	4	other	other	ADJ
american_scientific_journal-761	84	5	questions	question	NOUN
american_scientific_journal-761	84	6	,	,	PUNCT
american_scientific_journal-761	84	7	the	the	DET
american_scientific_journal-761	84	8	students	student	NOUN
american_scientific_journal-761	84	9	can	can	AUX
american_scientific_journal-761	84	10	be	be	AUX
american_scientific_journal-761	84	11	said	say	VERB
american_scientific_journal-761	84	12	to	to	PART
american_scientific_journal-761	84	13	have	have	AUX
american_scientific_journal-761	84	14	been	be	AUX
american_scientific_journal-761	84	15	more	more	ADV
american_scientific_journal-761	84	16	successful	successful	ADJ
american_scientific_journal-761	84	17	in	in	ADP
american_scientific_journal-761	84	18	this	this	DET
american_scientific_journal-761	84	19	question	question	NOUN
american_scientific_journal-761	84	20	.	.	PUNCT
american_scientific_journal-761	85	1	it	it	PRON
american_scientific_journal-761	85	2	could	could	AUX
american_scientific_journal-761	85	3	be	be	AUX
american_scientific_journal-761	85	4	the	the	DET
american_scientific_journal-761	85	5	reason	reason	NOUN
american_scientific_journal-761	85	6	that	that	SCONJ
american_scientific_journal-761	85	7	the	the	DET
american_scientific_journal-761	85	8	inequality	inequality	NOUN
american_scientific_journal-761	85	9	49𝑥2	49𝑥2	PRON
american_scientific_journal-761	85	10	≤	≤	NUM
american_scientific_journal-761	85	11	64	64	NUM
american_scientific_journal-761	85	12	has	have	VERB
american_scientific_journal-761	85	13	positive	positive	ADJ
american_scientific_journal-761	85	14	coefficient	coefficient	NOUN
american_scientific_journal-761	85	15	.	.	PUNCT
american_scientific_journal-761	86	1	but	but	CCONJ
american_scientific_journal-761	86	2	32	32	NUM
american_scientific_journal-761	86	3	%	%	NOUN
american_scientific_journal-761	86	4	of	of	ADP
american_scientific_journal-761	86	5	students	student	NOUN
american_scientific_journal-761	86	6	still	still	ADV
american_scientific_journal-761	86	7	have	have	VERB
american_scientific_journal-761	86	8	a	a	DET
american_scientific_journal-761	86	9	gap	gap	NOUN
american_scientific_journal-761	86	10	on	on	ADP
american_scientific_journal-761	86	11	this	this	DET
american_scientific_journal-761	86	12	problem	problem	NOUN
american_scientific_journal-761	86	13	too	too	ADV
american_scientific_journal-761	86	14	.	.	PUNCT
american_scientific_journal-761	87	1	4	4	X
american_scientific_journal-761	87	2	.	.	X
american_scientific_journal-761	87	3	discussion	discussion	NOUN
american_scientific_journal-761	87	4	when	when	SCONJ
american_scientific_journal-761	87	5	the	the	DET
american_scientific_journal-761	87	6	overall	overall	ADJ
american_scientific_journal-761	87	7	student	student	NOUN
american_scientific_journal-761	87	8	performances	performance	NOUN
american_scientific_journal-761	87	9	are	be	AUX
american_scientific_journal-761	87	10	considered	consider	VERB
american_scientific_journal-761	87	11	for	for	ADP
american_scientific_journal-761	87	12	all	all	DET
american_scientific_journal-761	87	13	five	five	NUM
american_scientific_journal-761	87	14	questions	question	NOUN
american_scientific_journal-761	87	15	,	,	PUNCT
american_scientific_journal-761	87	16	the	the	DET
american_scientific_journal-761	87	17	students	student	NOUN
american_scientific_journal-761	87	18	can	can	AUX
american_scientific_journal-761	87	19	not	not	PART
american_scientific_journal-761	87	20	be	be	AUX
american_scientific_journal-761	87	21	said	say	VERB
american_scientific_journal-761	87	22	to	to	PART
american_scientific_journal-761	87	23	have	have	AUX
american_scientific_journal-761	87	24	been	be	AUX
american_scientific_journal-761	87	25	successful	successful	ADJ
american_scientific_journal-761	87	26	in	in	ADP
american_scientific_journal-761	87	27	finding	find	VERB
american_scientific_journal-761	87	28	the	the	DET
american_scientific_journal-761	87	29	correct	correct	ADJ
american_scientific_journal-761	87	30	solution	solution	NOUN
american_scientific_journal-761	87	31	sets	set	NOUN
american_scientific_journal-761	87	32	for	for	ADP
american_scientific_journal-761	87	33	inequalities	inequality	NOUN
american_scientific_journal-761	87	34	.	.	PUNCT
american_scientific_journal-761	88	1	i	i	PRON
american_scientific_journal-761	88	2	believe	believe	VERB
american_scientific_journal-761	88	3	that	that	SCONJ
american_scientific_journal-761	88	4	this	this	DET
american_scientific_journal-761	88	5	situation	situation	NOUN
american_scientific_journal-761	88	6	might	might	AUX
american_scientific_journal-761	88	7	negatively	negatively	ADV
american_scientific_journal-761	88	8	affect	affect	VERB
american_scientific_journal-761	88	9	their	their	PRON
american_scientific_journal-761	88	10	success	success	NOUN
american_scientific_journal-761	88	11	in	in	ADP
american_scientific_journal-761	88	12	calculus	calculus	NOUN
american_scientific_journal-761	88	13	courses	course	NOUN
american_scientific_journal-761	88	14	.	.	PUNCT
american_scientific_journal-761	89	1	according	accord	VERB
american_scientific_journal-761	89	2	of	of	ADP
american_scientific_journal-761	89	3	the	the	DET
american_scientific_journal-761	89	4	record	record	NOUN
american_scientific_journal-761	89	5	of	of	ADP
american_scientific_journal-761	89	6	mathematics	mathematics	PROPN
american_scientific_journal-761	89	7	department	department	PROPN
american_scientific_journal-761	89	8	yearly	yearly	ADV
american_scientific_journal-761	89	9	we	we	PRON
american_scientific_journal-761	89	10	see	see	VERB
american_scientific_journal-761	89	11	among	among	ADP
american_scientific_journal-761	89	12	students	student	NOUN
american_scientific_journal-761	89	13	taking	take	VERB
american_scientific_journal-761	89	14	calculus	calculus	NOUN
american_scientific_journal-761	89	15	i	i	PRON
american_scientific_journal-761	89	16	or	or	CCONJ
american_scientific_journal-761	89	17	applied	apply	VERB
american_scientific_journal-761	89	18	mathematics	mathematic	NOUN
american_scientific_journal-761	89	19	i	i	PRON
american_scientific_journal-761	89	20	more	more	ADJ
american_scientific_journal-761	89	21	than	than	ADP
american_scientific_journal-761	89	22	half	half	NOUN
american_scientific_journal-761	89	23	students	student	NOUN
american_scientific_journal-761	89	24	grade	grade	NOUN
american_scientific_journal-761	89	25	is	be	AUX
american_scientific_journal-761	89	26	less	less	ADJ
american_scientific_journal-761	89	27	than	than	ADP
american_scientific_journal-761	89	28	“	"	PUNCT
american_scientific_journal-761	89	29	c	c	NOUN
american_scientific_journal-761	89	30	”	"	PUNCT
american_scientific_journal-761	89	31	grades	grade	NOUN
american_scientific_journal-761	89	32	.	.	PUNCT
american_scientific_journal-761	90	1	yearly	yearly	ADV
american_scientific_journal-761	90	2	an	an	DET
american_scientific_journal-761	90	3	average	average	NOUN
american_scientific_journal-761	90	4	of	of	ADP
american_scientific_journal-761	90	5	nearly	nearly	ADV
american_scientific_journal-761	90	6	2000	2000	NUM
american_scientific_journal-761	90	7	students	student	NOUN
american_scientific_journal-761	90	8	is	be	AUX
american_scientific_journal-761	90	9	register	register	ADJ
american_scientific_journal-761	90	10	to	to	PART
american_scientific_journal-761	90	11	take	take	VERB
american_scientific_journal-761	90	12	the	the	DET
american_scientific_journal-761	90	13	above	above	ADJ
american_scientific_journal-761	90	14	course	course	NOUN
american_scientific_journal-761	90	15	in	in	ADP
american_scientific_journal-761	90	16	dilla	dilla	PROPN
american_scientific_journal-761	90	17	university	university	NOUN
american_scientific_journal-761	90	18	.	.	PUNCT
american_scientific_journal-761	91	1	60	60	NUM
american_scientific_journal-761	91	2	american	american	ADJ
american_scientific_journal-761	91	3	scientific	scientific	ADJ
american_scientific_journal-761	91	4	research	research	NOUN
american_scientific_journal-761	91	5	journal	journal	NOUN
american_scientific_journal-761	91	6	for	for	ADP
american_scientific_journal-761	91	7	engineering	engineering	NOUN
american_scientific_journal-761	91	8	,	,	PUNCT
american_scientific_journal-761	91	9	technology	technology	NOUN
american_scientific_journal-761	91	10	,	,	PUNCT
american_scientific_journal-761	91	11	and	and	CCONJ
american_scientific_journal-761	91	12	sciences	science	NOUN
american_scientific_journal-761	91	13	(	(	PUNCT
american_scientific_journal-761	91	14	asrjets	asrjet	NOUN
american_scientific_journal-761	91	15	)	)	PUNCT
american_scientific_journal-761	91	16	(	(	PUNCT
american_scientific_journal-761	91	17	2013	2013	NUM
american_scientific_journal-761	91	18	)	)	PUNCT
american_scientific_journal-761	91	19	volume	volume	NOUN
american_scientific_journal-761	91	20	5	5	NUM
american_scientific_journal-761	91	21	,	,	PUNCT
american_scientific_journal-761	91	22	no	no	DET
american_scientific_journal-761	91	23	1	1	NUM
american_scientific_journal-761	91	24	,	,	PUNCT
american_scientific_journal-761	91	25	pp	pp	ADV
american_scientific_journal-761	91	26	57	57	NUM
american_scientific_journal-761	91	27	-	-	SYM
american_scientific_journal-761	91	28	62	62	NUM
american_scientific_journal-761	91	29	in	in	ADP
american_scientific_journal-761	91	30	addition	addition	NOUN
american_scientific_journal-761	91	31	,	,	PUNCT
american_scientific_journal-761	91	32	when	when	SCONJ
american_scientific_journal-761	91	33	the	the	DET
american_scientific_journal-761	91	34	calculations	calculation	NOUN
american_scientific_journal-761	91	35	of	of	ADP
american_scientific_journal-761	91	36	all	all	DET
american_scientific_journal-761	91	37	the	the	DET
american_scientific_journal-761	91	38	students	student	NOUN
american_scientific_journal-761	91	39	(	(	PUNCT
american_scientific_journal-761	91	40	those	those	PRON
american_scientific_journal-761	91	41	who	who	PRON
american_scientific_journal-761	91	42	found	find	VERB
american_scientific_journal-761	91	43	or	or	CCONJ
american_scientific_journal-761	91	44	failed	fail	VERB
american_scientific_journal-761	91	45	to	to	PART
american_scientific_journal-761	91	46	find	find	VERB
american_scientific_journal-761	91	47	the	the	DET
american_scientific_journal-761	91	48	correct	correct	ADJ
american_scientific_journal-761	91	49	solution	solution	NOUN
american_scientific_journal-761	91	50	set	set	NOUN
american_scientific_journal-761	91	51	)	)	PUNCT
american_scientific_journal-761	91	52	are	be	AUX
american_scientific_journal-761	91	53	analyzed	analyze	VERB
american_scientific_journal-761	91	54	,	,	PUNCT
american_scientific_journal-761	91	55	it	it	PRON
american_scientific_journal-761	91	56	was	be	AUX
american_scientific_journal-761	91	57	observed	observe	VERB
american_scientific_journal-761	91	58	that	that	SCONJ
american_scientific_journal-761	91	59	the	the	DET
american_scientific_journal-761	91	60	students	student	NOUN
american_scientific_journal-761	91	61	only	only	ADV
american_scientific_journal-761	91	62	perceive	perceive	VERB
american_scientific_journal-761	91	63	the	the	DET
american_scientific_journal-761	91	64	solution	solution	NOUN
american_scientific_journal-761	91	65	to	to	ADP
american_scientific_journal-761	91	66	the	the	DET
american_scientific_journal-761	91	67	problem	problem	NOUN
american_scientific_journal-761	91	68	as	as	ADP
american_scientific_journal-761	91	69	a	a	DET
american_scientific_journal-761	91	70	series	series	NOUN
american_scientific_journal-761	91	71	of	of	ADP
american_scientific_journal-761	91	72	algebraic	algebraic	ADJ
american_scientific_journal-761	91	73	calculations	calculation	NOUN
american_scientific_journal-761	91	74	without	without	ADP
american_scientific_journal-761	91	75	considering	consider	VERB
american_scientific_journal-761	91	76	what	what	PRON
american_scientific_journal-761	91	77	the	the	DET
american_scientific_journal-761	91	78	solution	solution	NOUN
american_scientific_journal-761	91	79	set	set	VERB
american_scientific_journal-761	91	80	of	of	ADP
american_scientific_journal-761	91	81	an	an	DET
american_scientific_journal-761	91	82	inequality	inequality	NOUN
american_scientific_journal-761	91	83	means	mean	VERB
american_scientific_journal-761	91	84	.	.	PUNCT
american_scientific_journal-761	92	1	in	in	ADP
american_scientific_journal-761	92	2	other	other	ADJ
american_scientific_journal-761	92	3	words	word	NOUN
american_scientific_journal-761	92	4	,	,	PUNCT
american_scientific_journal-761	92	5	they	they	PRON
american_scientific_journal-761	92	6	did	do	AUX
american_scientific_journal-761	92	7	not	not	PART
american_scientific_journal-761	92	8	check	check	VERB
american_scientific_journal-761	92	9	whether	whether	SCONJ
american_scientific_journal-761	92	10	an	an	DET
american_scientific_journal-761	92	11	“	"	PUNCT
american_scientific_journal-761	92	12	x	x	NOUN
american_scientific_journal-761	92	13	”	"	PUNCT
american_scientific_journal-761	92	14	real	real	ADJ
american_scientific_journal-761	92	15	number	number	NOUN
american_scientific_journal-761	92	16	in	in	ADP
american_scientific_journal-761	92	17	the	the	DET
american_scientific_journal-761	92	18	solution	solution	NOUN
american_scientific_journal-761	92	19	set	set	VERB
american_scientific_journal-761	92	20	proves	prove	VERB
american_scientific_journal-761	92	21	the	the	DET
american_scientific_journal-761	92	22	inequality	inequality	NOUN
american_scientific_journal-761	92	23	.	.	PUNCT
american_scientific_journal-761	93	1	as	as	ADP
american_scientific_journal-761	93	2	a	a	DET
american_scientific_journal-761	93	3	result	result	NOUN
american_scientific_journal-761	93	4	of	of	ADP
american_scientific_journal-761	93	5	this	this	DET
american_scientific_journal-761	93	6	problem	problem	NOUN
american_scientific_journal-761	93	7	they	they	PRON
american_scientific_journal-761	93	8	usually	usually	ADV
american_scientific_journal-761	93	9	fail	fail	VERB
american_scientific_journal-761	93	10	to	to	PART
american_scientific_journal-761	93	11	correctly	correctly	ADV
american_scientific_journal-761	93	12	answer	answer	VERB
american_scientific_journal-761	93	13	the	the	DET
american_scientific_journal-761	93	14	question	question	NOUN
american_scientific_journal-761	93	15	of	of	ADP
american_scientific_journal-761	93	16	increasing	increase	VERB
american_scientific_journal-761	93	17	/	/	SYM
american_scientific_journal-761	93	18	decreasing	decrease	VERB
american_scientific_journal-761	93	19	and	and	CCONJ
american_scientific_journal-761	93	20	concavity	concavity	NOUN
american_scientific_journal-761	93	21	of	of	ADP
american_scientific_journal-761	93	22	function	function	NOUN
american_scientific_journal-761	93	23	.	.	PUNCT
american_scientific_journal-761	94	1	this	this	PRON
american_scientific_journal-761	94	2	is	be	AUX
american_scientific_journal-761	94	3	a	a	DET
american_scientific_journal-761	94	4	procedural	procedural	ADJ
american_scientific_journal-761	94	5	and	and	CCONJ
american_scientific_journal-761	94	6	technical	technical	ADJ
american_scientific_journal-761	94	7	error	error	NOUN
american_scientific_journal-761	94	8	[	[	X
american_scientific_journal-761	94	9	5	5	NUM
american_scientific_journal-761	94	10	]	]	PUNCT
american_scientific_journal-761	94	11	.	.	PUNCT
american_scientific_journal-761	95	1	so	so	ADV
american_scientific_journal-761	95	2	here	here	ADV
american_scientific_journal-761	95	3	students	student	NOUN
american_scientific_journal-761	95	4	are	be	AUX
american_scientific_journal-761	95	5	commuted	commute	VERB
american_scientific_journal-761	95	6	both	both	CCONJ
american_scientific_journal-761	95	7	procedural	procedural	ADJ
american_scientific_journal-761	95	8	and	and	CCONJ
american_scientific_journal-761	95	9	technical	technical	ADJ
american_scientific_journal-761	95	10	errors	error	NOUN
american_scientific_journal-761	95	11	.	.	PUNCT
american_scientific_journal-761	96	1	so	so	ADV
american_scientific_journal-761	96	2	that	that	SCONJ
american_scientific_journal-761	96	3	,	,	PUNCT
american_scientific_journal-761	96	4	if	if	SCONJ
american_scientific_journal-761	96	5	the	the	DET
american_scientific_journal-761	96	6	students	student	NOUN
american_scientific_journal-761	96	7	had	have	AUX
american_scientific_journal-761	96	8	followed	follow	VERB
american_scientific_journal-761	96	9	this	this	DET
american_scientific_journal-761	96	10	checking	check	VERB
american_scientific_journal-761	96	11	procedure	procedure	NOUN
american_scientific_journal-761	96	12	,	,	PUNCT
american_scientific_journal-761	96	13	they	they	PRON
american_scientific_journal-761	96	14	could	could	AUX
american_scientific_journal-761	96	15	have	have	AUX
american_scientific_journal-761	96	16	found	find	VERB
american_scientific_journal-761	96	17	some	some	DET
american_scientific_journal-761	96	18	clues	clue	NOUN
american_scientific_journal-761	96	19	to	to	PART
american_scientific_journal-761	96	20	help	help	VERB
american_scientific_journal-761	96	21	them	they	PRON
american_scientific_journal-761	96	22	find	find	VERB
american_scientific_journal-761	96	23	the	the	DET
american_scientific_journal-761	96	24	correct	correct	ADJ
american_scientific_journal-761	96	25	solution	solution	NOUN
american_scientific_journal-761	96	26	set	set	VERB
american_scientific_journal-761	96	27	as	as	ADV
american_scientific_journal-761	96	28	well	well	ADV
american_scientific_journal-761	96	29	as	as	ADP
american_scientific_journal-761	96	30	the	the	DET
american_scientific_journal-761	96	31	calculus	calculus	NOUN
american_scientific_journal-761	96	32	i	i	PRON
american_scientific_journal-761	96	33	problem	problem	VERB
american_scientific_journal-761	96	34	as	as	ADV
american_scientific_journal-761	96	35	well	well	ADV
american_scientific_journal-761	96	36	.	.	PUNCT
american_scientific_journal-761	97	1	5	5	X
american_scientific_journal-761	97	2	.	.	X
american_scientific_journal-761	97	3	implication	implication	NOUN
american_scientific_journal-761	97	4	the	the	DET
american_scientific_journal-761	97	5	results	result	NOUN
american_scientific_journal-761	97	6	of	of	ADP
american_scientific_journal-761	97	7	the	the	DET
american_scientific_journal-761	97	8	study	study	NOUN
american_scientific_journal-761	97	9	have	have	AUX
american_scientific_journal-761	97	10	shown	show	VERB
american_scientific_journal-761	97	11	that	that	SCONJ
american_scientific_journal-761	97	12	students	student	NOUN
american_scientific_journal-761	97	13	mostly	mostly	ADV
american_scientific_journal-761	97	14	registering	register	VERB
american_scientific_journal-761	97	15	calculus	calculus	NOUN
american_scientific_journal-761	97	16	i	i	PRON
american_scientific_journal-761	97	17	course	course	VERB
american_scientific_journal-761	97	18	without	without	ADP
american_scientific_journal-761	97	19	proper	proper	ADJ
american_scientific_journal-761	97	20	understanding	understanding	NOUN
american_scientific_journal-761	97	21	of	of	ADP
american_scientific_journal-761	97	22	inequality	inequality	NOUN
american_scientific_journal-761	97	23	concepts	concept	NOUN
american_scientific_journal-761	97	24	.	.	PUNCT
american_scientific_journal-761	98	1	therefore	therefore	ADV
american_scientific_journal-761	98	2	diagnosing	diagnose	VERB
american_scientific_journal-761	98	3	students	student	NOUN
american_scientific_journal-761	98	4	’	'	PUNCT
american_scientific_journal-761	98	5	level	level	NOUN
american_scientific_journal-761	98	6	of	of	ADP
american_scientific_journal-761	98	7	understanding	understanding	NOUN
american_scientific_journal-761	98	8	of	of	ADP
american_scientific_journal-761	98	9	pre	pre	ADJ
american_scientific_journal-761	98	10	-	-	ADJ
american_scientific_journal-761	98	11	calculus	calculus	ADJ
american_scientific_journal-761	98	12	concept	concept	NOUN
american_scientific_journal-761	98	13	is	be	AUX
american_scientific_journal-761	98	14	vital	vital	ADJ
american_scientific_journal-761	98	15	.	.	PUNCT
american_scientific_journal-761	99	1	mathematics	mathematic	NOUN
american_scientific_journal-761	99	2	instructors	instructor	NOUN
american_scientific_journal-761	99	3	who	who	PRON
american_scientific_journal-761	99	4	are	be	AUX
american_scientific_journal-761	99	5	teaching	teach	VERB
american_scientific_journal-761	99	6	this	this	DET
american_scientific_journal-761	99	7	course	course	NOUN
american_scientific_journal-761	99	8	shall	shall	AUX
american_scientific_journal-761	99	9	understand	understand	VERB
american_scientific_journal-761	99	10	students	student	NOUN
american_scientific_journal-761	99	11	’	'	PUNCT
american_scientific_journal-761	99	12	gap	gap	NOUN
american_scientific_journal-761	99	13	and	and	CCONJ
american_scientific_journal-761	99	14	provide	provide	VERB
american_scientific_journal-761	99	15	remedial	remedial	NOUN
american_scientific_journal-761	99	16	on	on	ADP
american_scientific_journal-761	99	17	the	the	DET
american_scientific_journal-761	99	18	concept	concept	NOUN
american_scientific_journal-761	99	19	of	of	ADP
american_scientific_journal-761	99	20	inequality	inequality	NOUN
american_scientific_journal-761	99	21	before	before	ADP
american_scientific_journal-761	99	22	discussing	discuss	VERB
american_scientific_journal-761	99	23	related	relate	VERB
american_scientific_journal-761	99	24	concepts	concept	NOUN
american_scientific_journal-761	99	25	in	in	ADP
american_scientific_journal-761	99	26	calculus	calculus	NOUN
american_scientific_journal-761	99	27	.	.	PUNCT
american_scientific_journal-761	100	1	6	6	X
american_scientific_journal-761	100	2	.	.	X
american_scientific_journal-761	100	3	limitation	limitation	NOUN
american_scientific_journal-761	100	4	of	of	ADP
american_scientific_journal-761	100	5	the	the	DET
american_scientific_journal-761	100	6	study	study	NOUN
american_scientific_journal-761	100	7	the	the	DET
american_scientific_journal-761	100	8	following	follow	VERB
american_scientific_journal-761	100	9	limitations	limitation	NOUN
american_scientific_journal-761	100	10	were	be	AUX
american_scientific_journal-761	100	11	identified	identify	VERB
american_scientific_journal-761	100	12	from	from	ADP
american_scientific_journal-761	100	13	the	the	DET
american_scientific_journal-761	100	14	study	study	NOUN
american_scientific_journal-761	100	15	:	:	PUNCT
american_scientific_journal-761	100	16	•	•	ADP
american_scientific_journal-761	100	17	the	the	DET
american_scientific_journal-761	100	18	study	study	NOUN
american_scientific_journal-761	100	19	result	result	NOUN
american_scientific_journal-761	100	20	is	be	AUX
american_scientific_journal-761	100	21	limited	limit	VERB
american_scientific_journal-761	100	22	to	to	ADP
american_scientific_journal-761	100	23	the	the	DET
american_scientific_journal-761	100	24	above	above	ADJ
american_scientific_journal-761	100	25	mentioned	mention	VERB
american_scientific_journal-761	100	26	students	student	NOUN
american_scientific_journal-761	100	27	;	;	PUNCT
american_scientific_journal-761	100	28	the	the	DET
american_scientific_journal-761	100	29	result	result	NOUN
american_scientific_journal-761	100	30	could	could	AUX
american_scientific_journal-761	100	31	be	be	AUX
american_scientific_journal-761	100	32	different	different	ADJ
american_scientific_journal-761	100	33	for	for	ADP
american_scientific_journal-761	100	34	other	other	ADJ
american_scientific_journal-761	100	35	group	group	NOUN
american_scientific_journal-761	100	36	of	of	ADP
american_scientific_journal-761	100	37	students	student	NOUN
american_scientific_journal-761	100	38	.	.	PUNCT
american_scientific_journal-761	101	1	•	•	ADP
american_scientific_journal-761	101	2	to	to	PART
american_scientific_journal-761	101	3	determine	determine	VERB
american_scientific_journal-761	101	4	more	more	ADJ
american_scientific_journal-761	101	5	consistence	consistence	NOUN
american_scientific_journal-761	101	6	result	result	NOUN
american_scientific_journal-761	101	7	,	,	PUNCT
american_scientific_journal-761	101	8	it	it	PRON
american_scientific_journal-761	101	9	is	be	AUX
american_scientific_journal-761	101	10	necessary	necessary	ADJ
american_scientific_journal-761	101	11	to	to	PART
american_scientific_journal-761	101	12	consider	consider	VERB
american_scientific_journal-761	101	13	different	different	ADJ
american_scientific_journal-761	101	14	batch	batch	NOUN
american_scientific_journal-761	101	15	;	;	PUNCT
american_scientific_journal-761	101	16	•	•	X
american_scientific_journal-761	101	17	it	it	PRON
american_scientific_journal-761	101	18	only	only	ADV
american_scientific_journal-761	101	19	limited	limit	VERB
american_scientific_journal-761	101	20	to	to	ADP
american_scientific_journal-761	101	21	solving	solve	VERB
american_scientific_journal-761	101	22	inequality	inequality	NOUN
american_scientific_journal-761	101	23	problems	problem	NOUN
american_scientific_journal-761	101	24	in	in	ADP
american_scientific_journal-761	101	25	relation	relation	NOUN
american_scientific_journal-761	101	26	to	to	ADP
american_scientific_journal-761	101	27	calculus	calculus	NOUN
american_scientific_journal-761	101	28	,	,	PUNCT
american_scientific_journal-761	101	29	but	but	CCONJ
american_scientific_journal-761	101	30	other	other	ADJ
american_scientific_journal-761	101	31	concepts	concept	NOUN
american_scientific_journal-761	101	32	like	like	ADP
american_scientific_journal-761	101	33	function	function	NOUN
american_scientific_journal-761	101	34	concepts	concept	NOUN
american_scientific_journal-761	101	35	could	could	AUX
american_scientific_journal-761	101	36	also	also	ADV
american_scientific_journal-761	101	37	be	be	AUX
american_scientific_journal-761	101	38	sources	source	NOUN
american_scientific_journal-761	101	39	of	of	ADP
american_scientific_journal-761	101	40	students	student	NOUN
american_scientific_journal-761	101	41	’	'	PUNCT
american_scientific_journal-761	101	42	failure	failure	NOUN
american_scientific_journal-761	101	43	in	in	ADP
american_scientific_journal-761	101	44	calculus	calculus	NOUN
american_scientific_journal-761	101	45	.	.	PUNCT
american_scientific_journal-761	102	1	•	•	ADP
american_scientific_journal-761	102	2	a	a	DET
american_scientific_journal-761	102	3	test	test	NOUN
american_scientific_journal-761	102	4	is	be	AUX
american_scientific_journal-761	102	5	the	the	DET
american_scientific_journal-761	102	6	major	major	ADJ
american_scientific_journal-761	102	7	source	source	NOUN
american_scientific_journal-761	102	8	of	of	ADP
american_scientific_journal-761	102	9	data	datum	NOUN
american_scientific_journal-761	102	10	;	;	PUNCT
american_scientific_journal-761	102	11	if	if	SCONJ
american_scientific_journal-761	102	12	it	it	PRON
american_scientific_journal-761	102	13	is	be	AUX
american_scientific_journal-761	102	14	supplemented	supplement	VERB
american_scientific_journal-761	102	15	by	by	ADP
american_scientific_journal-761	102	16	multiple	multiple	ADJ
american_scientific_journal-761	102	17	data	datum	NOUN
american_scientific_journal-761	102	18	source	source	NOUN
american_scientific_journal-761	102	19	more	more	ADJ
american_scientific_journal-761	102	20	result	result	NOUN
american_scientific_journal-761	102	21	could	could	AUX
american_scientific_journal-761	102	22	be	be	AUX
american_scientific_journal-761	102	23	obtained	obtain	VERB
american_scientific_journal-761	102	24	.	.	PUNCT
american_scientific_journal-761	103	1	7	7	X
american_scientific_journal-761	103	2	.	.	X
american_scientific_journal-761	103	3	recommendation	recommendation	VERB
american_scientific_journal-761	103	4	the	the	DET
american_scientific_journal-761	103	5	following	follow	VERB
american_scientific_journal-761	103	6	recommendations	recommendation	NOUN
american_scientific_journal-761	103	7	were	be	AUX
american_scientific_journal-761	103	8	made	make	VERB
american_scientific_journal-761	103	9	on	on	ADP
american_scientific_journal-761	103	10	the	the	DET
american_scientific_journal-761	103	11	basis	basis	NOUN
american_scientific_journal-761	103	12	of	of	ADP
american_scientific_journal-761	103	13	the	the	DET
american_scientific_journal-761	103	14	findings	finding	NOUN
american_scientific_journal-761	103	15	of	of	ADP
american_scientific_journal-761	103	16	the	the	DET
american_scientific_journal-761	103	17	study	study	NOUN
american_scientific_journal-761	103	18	:	:	PUNCT
american_scientific_journal-761	103	19	•	•	ADP
american_scientific_journal-761	103	20	this	this	DET
american_scientific_journal-761	103	21	study	study	NOUN
american_scientific_journal-761	103	22	proved	prove	VERB
american_scientific_journal-761	103	23	that	that	SCONJ
american_scientific_journal-761	103	24	the	the	DET
american_scientific_journal-761	103	25	students	student	NOUN
american_scientific_journal-761	103	26	can	can	AUX
american_scientific_journal-761	103	27	not	not	PART
american_scientific_journal-761	103	28	be	be	AUX
american_scientific_journal-761	103	29	said	say	VERB
american_scientific_journal-761	103	30	to	to	PART
american_scientific_journal-761	103	31	have	have	AUX
american_scientific_journal-761	103	32	been	be	AUX
american_scientific_journal-761	103	33	successful	successful	ADJ
american_scientific_journal-761	103	34	in	in	ADP
american_scientific_journal-761	103	35	finding	find	VERB
american_scientific_journal-761	103	36	the	the	DET
american_scientific_journal-761	103	37	correct	correct	ADJ
american_scientific_journal-761	103	38	solution	solution	NOUN
american_scientific_journal-761	103	39	sets	set	NOUN
american_scientific_journal-761	103	40	for	for	ADP
american_scientific_journal-761	103	41	inequalities	inequality	NOUN
american_scientific_journal-761	103	42	.therefore	.therefore	ADP
american_scientific_journal-761	103	43	,	,	PUNCT
american_scientific_journal-761	103	44	calculus	calculus	NOUN
american_scientific_journal-761	103	45	instructor	instructor	NOUN
american_scientific_journal-761	103	46	should	should	AUX
american_scientific_journal-761	103	47	consider	consider	VERB
american_scientific_journal-761	103	48	the	the	DET
american_scientific_journal-761	103	49	main	main	ADJ
american_scientific_journal-761	103	50	source	source	NOUN
american_scientific_journal-761	103	51	of	of	ADP
american_scientific_journal-761	103	52	students	student	NOUN
american_scientific_journal-761	103	53	’	'	PUNCT
american_scientific_journal-761	103	54	failure	failure	NOUN
american_scientific_journal-761	103	55	in	in	ADP
american_scientific_journal-761	103	56	calculus	calculus	NOUN
american_scientific_journal-761	103	57	in	in	ADP
american_scientific_journal-761	103	58	their	their	PRON
american_scientific_journal-761	103	59	teaching	teaching	NOUN
american_scientific_journal-761	103	60	.	.	PUNCT
american_scientific_journal-761	104	1	•	•	NUM
american_scientific_journal-761	104	2	the	the	DET
american_scientific_journal-761	104	3	government	government	NOUN
american_scientific_journal-761	104	4	should	should	AUX
american_scientific_journal-761	104	5	revise	revise	VERB
american_scientific_journal-761	104	6	the	the	DET
american_scientific_journal-761	104	7	curriculum	curriculum	NOUN
american_scientific_journal-761	104	8	;	;	PUNCT
american_scientific_journal-761	104	9	so	so	SCONJ
american_scientific_journal-761	104	10	that	that	SCONJ
american_scientific_journal-761	104	11	students	student	NOUN
american_scientific_journal-761	104	12	did	do	AUX
american_scientific_journal-761	104	13	n’t	not	PART
american_scientific_journal-761	104	14	completely	completely	ADV
american_scientific_journal-761	104	15	understood	understand	VERB
american_scientific_journal-761	104	16	pre	pre	ADJ
american_scientific_journal-761	104	17	calculus	calculus	NOUN
american_scientific_journal-761	104	18	concepts	concept	NOUN
american_scientific_journal-761	104	19	should	should	AUX
american_scientific_journal-761	104	20	take	take	VERB
american_scientific_journal-761	104	21	remedial	remedial	ADJ
american_scientific_journal-761	104	22	courses	course	NOUN
american_scientific_journal-761	104	23	by	by	ADP
american_scientific_journal-761	104	24	preparing	prepare	VERB
american_scientific_journal-761	104	25	a	a	DET
american_scientific_journal-761	104	26	test	test	NOUN
american_scientific_journal-761	104	27	to	to	PART
american_scientific_journal-761	104	28	separate	separate	VERB
american_scientific_journal-761	104	29	the	the	DET
american_scientific_journal-761	104	30	students	student	NOUN
american_scientific_journal-761	104	31	in	in	ADP
american_scientific_journal-761	104	32	different	different	ADJ
american_scientific_journal-761	104	33	levels	level	NOUN
american_scientific_journal-761	104	34	.	.	PUNCT
american_scientific_journal-761	105	1	•	•	NUM
american_scientific_journal-761	105	2	students	student	NOUN
american_scientific_journal-761	105	3	taking	take	VERB
american_scientific_journal-761	105	4	calculus	calculus	NOUN
american_scientific_journal-761	105	5	courses	course	NOUN
american_scientific_journal-761	105	6	should	should	AUX
american_scientific_journal-761	105	7	fill	fill	VERB
american_scientific_journal-761	105	8	their	their	PRON
american_scientific_journal-761	105	9	gap	gap	NOUN
american_scientific_journal-761	105	10	on	on	ADP
american_scientific_journal-761	105	11	different	different	ADJ
american_scientific_journal-761	105	12	pre	pre	ADJ
american_scientific_journal-761	105	13	-	-	ADJ
american_scientific_journal-761	105	14	calculus	calculus	ADJ
american_scientific_journal-761	105	15	concepts	concept	NOUN
american_scientific_journal-761	105	16	before	before	ADP
american_scientific_journal-761	105	17	encounter	encounter	NOUN
american_scientific_journal-761	105	18	calculus	calculus	NOUN
american_scientific_journal-761	105	19	course	course	NOUN
american_scientific_journal-761	105	20	.	.	PUNCT
american_scientific_journal-761	106	1	61	61	NUM
american_scientific_journal-761	106	2	american	american	ADJ
american_scientific_journal-761	106	3	scientific	scientific	ADJ
american_scientific_journal-761	106	4	research	research	NOUN
american_scientific_journal-761	106	5	journal	journal	NOUN
american_scientific_journal-761	106	6	for	for	ADP
american_scientific_journal-761	106	7	engineering	engineering	NOUN
american_scientific_journal-761	106	8	,	,	PUNCT
american_scientific_journal-761	106	9	technology	technology	NOUN
american_scientific_journal-761	106	10	,	,	PUNCT
american_scientific_journal-761	106	11	and	and	CCONJ
american_scientific_journal-761	106	12	sciences	science	NOUN
american_scientific_journal-761	106	13	(	(	PUNCT
american_scientific_journal-761	106	14	asrjets	asrjet	NOUN
american_scientific_journal-761	106	15	)	)	PUNCT
american_scientific_journal-761	106	16	(	(	PUNCT
american_scientific_journal-761	106	17	2013	2013	NUM
american_scientific_journal-761	106	18	)	)	PUNCT
american_scientific_journal-761	106	19	volume	volume	NOUN
american_scientific_journal-761	106	20	5	5	NUM
american_scientific_journal-761	106	21	,	,	PUNCT
american_scientific_journal-761	106	22	no	no	DET
american_scientific_journal-761	106	23	1	1	NUM
american_scientific_journal-761	106	24	,	,	PUNCT
american_scientific_journal-761	106	25	pp	pp	ADV
american_scientific_journal-761	106	26	57	57	NUM
american_scientific_journal-761	106	27	-	-	SYM
american_scientific_journal-761	106	28	62	62	NUM
american_scientific_journal-761	106	29	references	reference	NOUN
american_scientific_journal-761	106	30	[	[	X
american_scientific_journal-761	106	31	1	1	NUM
american_scientific_journal-761	106	32	]	]	X
american_scientific_journal-761	106	33	adams	adams	PROPN
american_scientific_journal-761	106	34	,	,	PUNCT
american_scientific_journal-761	106	35	r.a	r.a	PROPN
american_scientific_journal-761	106	36	.	.	PROPN
american_scientific_journal-761	106	37	calculus	calculus	PROPN
american_scientific_journal-761	106	38	.	.	PUNCT
american_scientific_journal-761	107	1	pearson	pearson	PROPN
american_scientific_journal-761	107	2	education	education	PROPN
american_scientific_journal-761	107	3	canada	canada	PROPN
american_scientific_journal-761	107	4	inc	inc	PROPN
american_scientific_journal-761	107	5	.	.	PROPN
american_scientific_journal-761	107	6	,	,	PUNCT
american_scientific_journal-761	107	7	toronto	toronto	PROPN
american_scientific_journal-761	107	8	,	,	PUNCT
american_scientific_journal-761	107	9	ontario	ontario	PROPN
american_scientific_journal-761	107	10	.	.	PUNCT
american_scientific_journal-761	108	1	5th	5th	ADJ
american_scientific_journal-761	108	2	ed	ed	NOUN
american_scientific_journal-761	108	3	,	,	PUNCT
american_scientific_journal-761	108	4	2003	2003	NUM
american_scientific_journal-761	108	5	.	.	PUNCT
american_scientific_journal-761	109	1	[	[	X
american_scientific_journal-761	109	2	2	2	NUM
american_scientific_journal-761	109	3	]	]	X
american_scientific_journal-761	109	4	dreyfus	dreyfus	PROPN
american_scientific_journal-761	109	5	,	,	PUNCT
american_scientific_journal-761	109	6	t.	t.	PROPN
american_scientific_journal-761	109	7	&	&	CCONJ
american_scientific_journal-761	109	8	eisenberg	eisenberg	PROPN
american_scientific_journal-761	109	9	,	,	PUNCT
american_scientific_journal-761	109	10	t.	t.	PROPN
american_scientific_journal-761	109	11	a	a	DET
american_scientific_journal-761	109	12	graphical	graphical	ADJ
american_scientific_journal-761	109	13	approach	approach	NOUN
american_scientific_journal-761	109	14	to	to	ADP
american_scientific_journal-761	109	15	solving	solve	VERB
american_scientific_journal-761	109	16	inequalities	inequality	NOUN
american_scientific_journal-761	109	17	.	.	PUNCT
american_scientific_journal-761	110	1	school	school	NOUN
american_scientific_journal-761	110	2	science	science	NOUN
american_scientific_journal-761	110	3	and	and	CCONJ
american_scientific_journal-761	110	4	mathematics	mathematic	NOUN
american_scientific_journal-761	110	5	,	,	PUNCT
american_scientific_journal-761	110	6	addison	addison	PROPN
american_scientific_journal-761	110	7	wesley	wesley	PROPN
american_scientific_journal-761	110	8	longman	longman	PROPN
american_scientific_journal-761	110	9	,	,	PUNCT
american_scientific_journal-761	110	10	1985,pp	1985,pp	NUM
american_scientific_journal-761	110	11	.651	.651	NUM
american_scientific_journal-761	110	12	-	-	SYM
american_scientific_journal-761	110	13	662	662	NUM
american_scientific_journal-761	110	14	.	.	PUNCT
american_scientific_journal-761	111	1	[	[	X
american_scientific_journal-761	111	2	3	3	NUM
american_scientific_journal-761	111	3	]	]	X
american_scientific_journal-761	111	4	linchevski	linchevski	NOUN
american_scientific_journal-761	111	5	,	,	PUNCT
american_scientific_journal-761	111	6	l.	l.	PROPN
american_scientific_journal-761	111	7	&	&	CCONJ
american_scientific_journal-761	111	8	sfard	sfard	PROPN
american_scientific_journal-761	111	9	,	,	PUNCT
american_scientific_journal-761	111	10	a.	a.	NOUN
american_scientific_journal-761	111	11	“	"	PUNCT
american_scientific_journal-761	111	12	rules	rule	VERB
american_scientific_journal-761	111	13	without	without	ADP
american_scientific_journal-761	111	14	reasons	reason	NOUN
american_scientific_journal-761	111	15	as	as	ADP
american_scientific_journal-761	111	16	process	process	NOUN
american_scientific_journal-761	111	17	without	without	ADP
american_scientific_journal-761	111	18	objects	object	NOUN
american_scientific_journal-761	111	19	-	-	PUNCT
american_scientific_journal-761	111	20	the	the	DET
american_scientific_journal-761	111	21	case	case	NOUN
american_scientific_journal-761	111	22	of	of	ADP
american_scientific_journal-761	111	23	equations	equation	NOUN
american_scientific_journal-761	111	24	and	and	CCONJ
american_scientific_journal-761	111	25	inequalities	inequality	NOUN
american_scientific_journal-761	111	26	”	"	PUNCT
american_scientific_journal-761	111	27	.	.	PUNCT
american_scientific_journal-761	112	1	proceedings	proceeding	NOUN
american_scientific_journal-761	112	2	of	of	ADP
american_scientific_journal-761	112	3	15th	15th	ADJ
american_scientific_journal-761	112	4	international	international	ADJ
american_scientific_journal-761	112	5	conference	conference	NOUN
american_scientific_journal-761	112	6	for	for	ADP
american_scientific_journal-761	112	7	the	the	DET
american_scientific_journal-761	112	8	psychology	psychology	NOUN
american_scientific_journal-761	112	9	of	of	ADP
american_scientific_journal-761	112	10	mathematics	mathematics	PROPN
american_scientific_journal-761	112	11	education	education	NOUN
american_scientific_journal-761	112	12	,	,	PUNCT
american_scientific_journal-761	112	13	asisi	asisi	ADJ
american_scientific_journal-761	112	14	,	,	PUNCT
american_scientific_journal-761	112	15	italy	italy	PROPN
american_scientific_journal-761	112	16	vol	vol	NOUN
american_scientific_journal-761	112	17	:	:	PUNCT
american_scientific_journal-761	112	18	ii	ii	PROPN
american_scientific_journal-761	112	19	,	,	PUNCT
american_scientific_journal-761	112	20	1991	1991	NUM
american_scientific_journal-761	112	21	,	,	PUNCT
american_scientific_journal-761	112	22	pp	pp	ADJ
american_scientific_journal-761	112	23	.	.	PUNCT
american_scientific_journal-761	113	1	317	317	NUM
american_scientific_journal-761	113	2	-	-	SYM
american_scientific_journal-761	113	3	324	324	NUM
american_scientific_journal-761	113	4	.	.	PUNCT
american_scientific_journal-761	114	1	[	[	X
american_scientific_journal-761	114	2	4	4	X
american_scientific_journal-761	114	3	]	]	X
american_scientific_journal-761	114	4	sandor	sandor	PROPN
american_scientific_journal-761	114	5	,	,	PUNCT
american_scientific_journal-761	114	6	j.	j.	PROPN
american_scientific_journal-761	114	7	“	"	PUNCT
american_scientific_journal-761	114	8	on	on	ADP
american_scientific_journal-761	114	9	means	mean	NOUN
american_scientific_journal-761	114	10	generated	generate	VERB
american_scientific_journal-761	114	11	by	by	ADP
american_scientific_journal-761	114	12	derivatives	derivative	NOUN
american_scientific_journal-761	114	13	of	of	ADP
american_scientific_journal-761	114	14	functions	function	NOUN
american_scientific_journal-761	114	15	”	"	PUNCT
american_scientific_journal-761	114	16	,	,	PUNCT
american_scientific_journal-761	114	17	international	international	ADJ
american_scientific_journal-761	114	18	journal	journal	NOUN
american_scientific_journal-761	114	19	of	of	ADP
american_scientific_journal-761	114	20	mathematical	mathematical	ADJ
american_scientific_journal-761	114	21	education	education	NOUN
american_scientific_journal-761	114	22	in	in	ADP
american_scientific_journal-761	114	23	science	science	NOUN
american_scientific_journal-761	114	24	and	and	CCONJ
american_scientific_journal-761	114	25	technology	technology	NOUN
american_scientific_journal-761	114	26	,	,	PUNCT
american_scientific_journal-761	114	27	vol	vol	NOUN
american_scientific_journal-761	114	28	.	.	PROPN
american_scientific_journal-761	114	29	28	28	NUM
american_scientific_journal-761	114	30	,	,	PUNCT
american_scientific_journal-761	114	31	no.1	no.1	NUM
american_scientific_journal-761	114	32	,	,	PUNCT
american_scientific_journal-761	114	33	pp.146	pp.146	NOUN
american_scientific_journal-761	114	34	-	-	PUNCT
american_scientific_journal-761	114	35	148,1997	148,1997	NOUN
american_scientific_journal-761	114	36	.	.	PUNCT
american_scientific_journal-761	115	1	[	[	X
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american_scientific_journal-761	115	3	]	]	PUNCT
american_scientific_journal-761	115	4	seah	seah	PROPN
american_scientific_journal-761	115	5	e	e	PROPN
american_scientific_journal-761	115	6	,	,	PUNCT
american_scientific_journal-761	115	7	k.	k.	PUNCT
american_scientific_journal-761	115	8	“	"	PUNCT
american_scientific_journal-761	115	9	analysis	analysis	NOUN
american_scientific_journal-761	115	10	of	of	ADP
american_scientific_journal-761	115	11	students	student	NOUN
american_scientific_journal-761	115	12	’	’	PART
american_scientific_journal-761	115	13	difficulties	difficulty	NOUN
american_scientific_journal-761	115	14	in	in	ADP
american_scientific_journal-761	115	15	solving	solve	VERB
american_scientific_journal-761	115	16	integration	integration	NOUN
american_scientific_journal-761	115	17	problems	problem	NOUN
american_scientific_journal-761	115	18	”	"	PUNCT
american_scientific_journal-761	115	19	.	.	PUNCT
american_scientific_journal-761	116	1	the	the	DET
american_scientific_journal-761	116	2	mathematics	mathematics	NOUN
american_scientific_journal-761	116	3	educator	educator	NOUN
american_scientific_journal-761	116	4	,	,	PUNCT
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american_scientific_journal-761	116	6	,	,	PUNCT
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american_scientific_journal-761	116	8	-	-	PUNCT
american_scientific_journal-761	116	9	59	59	NUM
american_scientific_journal-761	116	10	,	,	PUNCT
american_scientific_journal-761	116	11	2005	2005	NUM
american_scientific_journal-761	116	12	.	.	PUNCT
american_scientific_journal-761	117	1	[	[	X
american_scientific_journal-761	117	2	6	6	NUM
american_scientific_journal-761	117	3	]	]	SYM
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american_scientific_journal-761	117	5	,	,	PUNCT
american_scientific_journal-761	117	6	b.	b.	PROPN
american_scientific_journal-761	117	7	g.	g.	PROPN
american_scientific_journal-761	117	8	&	&	CCONJ
american_scientific_journal-761	117	9	finney	finney	PROPN
american_scientific_journal-761	117	10	,	,	PUNCT
american_scientific_journal-761	117	11	r.	r.	PROPN
american_scientific_journal-761	117	12	l.	l.	PROPN
american_scientific_journal-761	117	13	calculus	calculus	PROPN
american_scientific_journal-761	117	14	and	and	CCONJ
american_scientific_journal-761	117	15	analytic	analytic	ADJ
american_scientific_journal-761	117	16	geometry	geometry	NOUN
american_scientific_journal-761	117	17	.	.	PUNCT
american_scientific_journal-761	118	1	addison	addison	PROPN
american_scientific_journal-761	118	2	-	-	PUNCT
american_scientific_journal-761	118	3	wesley	wesley	PROPN
american_scientific_journal-761	118	4	publishing	publishing	PROPN
american_scientific_journal-761	118	5	company	company	NOUN
american_scientific_journal-761	118	6	,	,	PUNCT
american_scientific_journal-761	118	7	9th	9th	ADJ
american_scientific_journal-761	118	8	ed	ed	NOUN
american_scientific_journal-761	118	9	.	.	PROPN
american_scientific_journal-761	118	10	,	,	PUNCT
american_scientific_journal-761	118	11	1996	1996	NUM
american_scientific_journal-761	118	12	.	.	PUNCT
american_scientific_journal-761	119	1	[	[	X
american_scientific_journal-761	119	2	7	7	NUM
american_scientific_journal-761	119	3	]	]	PUNCT
american_scientific_journal-761	119	4	tsamir	tsamir	NOUN
american_scientific_journal-761	119	5	,	,	PUNCT
american_scientific_journal-761	119	6	p.	p.	PROPN
american_scientific_journal-761	119	7	&	&	CCONJ
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american_scientific_journal-761	119	9	,	,	PUNCT
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american_scientific_journal-761	119	11	“	"	PUNCT
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american_scientific_journal-761	119	13	’	'	PUNCT
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american_scientific_journal-761	119	17	:	:	PUNCT
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american_scientific_journal-761	119	24	.	.	PUNCT
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american_scientific_journal-761	120	10	,	,	PUNCT
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american_scientific_journal-761	120	12	.	.	PROPN
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american_scientific_journal-761	120	14	,	,	PUNCT
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american_scientific_journal-761	120	20	.	.	PUNCT
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american_scientific_journal-761	121	2	8	8	NUM
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american_scientific_journal-761	121	5	,	,	PUNCT
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american_scientific_journal-761	121	7	&	&	CCONJ
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american_scientific_journal-761	121	9	,	,	PUNCT
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american_scientific_journal-761	121	23	-	-	PUNCT
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american_scientific_journal-761	122	13	,	,	PUNCT
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american_scientific_journal-761	123	14	,	,	PUNCT
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