Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
33101	Evaluate the Limit	limit as x approaches 0 of (((3+x)^-1)/x)-(3^-1)/x	$lim_{x \to 0} (\frac{{(3 + x)}^{- 1}}{x}) - \frac{3^{- 1}}{x}$
33102	Evaluate the Limit	limit as x approaches 0 of (1-4x)^(5/x)	$lim_{x \to 0} {(1 - 4 x)}^{\frac{5}{x}}$
33103	Evaluate the Limit	limit as x approaches 0 of (16cos(16x))/(26cos(26x))	$lim_{x \to 0} \frac{16 \cos (16 x)}{26 \cos (26 x)}$
33104	Evaluate the Limit	limit as x approaches 0 of (17x)/( natural log of (x^2-2x+1)^3)	$lim_{x \to 0} \frac{17 x}{\ln ({(x^{2} - 2 x + 1)}^{3})}$
33105	Evaluate the Limit	limit as x approaches 0 of (1-7x)^(1/x)	$lim_{x \to 0} {(1 - 7 x)}^{\frac{1}{x}}$
33106	Evaluate the Limit	limit as x approaches 0 of (1-cos(3x))/(x^2)	$lim_{x \to 0} \frac{1 - \cos (3 x)}{x^{2}}$
33107	Evaluate the Limit	limit as x approaches 0 of (1-cos(3x))/(2x)	$lim_{x \to 0} \frac{1 - \cos (3 x)}{2 x}$
33108	Evaluate the Limit	limit as x approaches 0 of (1-cos(9x))/(2x^2)	$lim_{x \to 0} \frac{1 - \cos (9 x)}{2 x^{2}}$
33109	Evaluate the Limit	limit as x approaches 0 of (1-cos(x))/(xtan(x))	$lim_{x \to 0} \frac{1 - \cos (x)}{x \tan (x)}$
33110	Evaluate the Limit	limit as x approaches 0 of (1-cos(x)cos(2x)cos(3x))/(1-cos(x))	$lim_{x \to 0} \frac{1 - \cos (x) \cdot \cos (2 x) \cdot \cos (3 x)}{1 - \cos (x)}$
33111	Evaluate the Limit	limit as x approaches 0 of (1-sec(4x))/((6x)^2)	$lim_{x \to 0} \frac{1 - \sec (4 x)}{{(6 x)}^{2}}$
33112	Evaluate the Limit	limit as x approaches 0 of (2(6+x)^2-72)/x	$lim_{x \to 0} \frac{2 {(6 + x)}^{2} - 72}{x}$
33113	Evaluate the Limit	limit as x approaches 0 of (2x^3+4x-1)/(3x^4+100x^2+15)	$lim_{x \to 0} \frac{2 x^{3} + 4 x - 1}{3 x^{4} + 100 x^{2} + 15}$
33114	Evaluate the Limit	limit as x approaches 0 of (3sin(4x))/(5x)	$lim_{x \to 0} \frac{3 \sin (4 x)}{5 x}$
33115	Evaluate the Limit	limit as x approaches 0 of (3x-tan(3x))/(tan(3x)*sin(x^2))	$lim_{x \to 0} \frac{3 x - \tan (3 x)}{\tan (3 x) \cdot \sin (x^{2})}$
33116	Evaluate the Limit	limit as x approaches 0 of (4(y+x)^2-4y^2)/x	$lim_{x \to 0} \frac{4 {(y + x)}^{2} - 4 y^{2}}{x}$
33117	Evaluate the Limit	limit as x approaches 0 of (4x)/(tan(5x))	$lim_{x \to 0} \frac{4 x}{\tan (5 x)}$
33118	Evaluate the Limit	limit as x approaches 0 of (5x^3+8y^2)/(3y^4-16y^2)	$lim_{x \to 0} \frac{5 x^{3} + 8 y^{2}}{3 y^{4} - 16 y^{2}}$
33119	Evaluate the Limit	limit as x approaches 0 of (6e^(4x)-6)/(4x)	$lim_{x \to 0} \frac{6 e^{4 x} - 6}{4 x}$
33120	Evaluate the Limit	limit as x approaches 0 of (8x^2-6x)/x	$lim_{x \to 0} \frac{8 x^{2} - 6 x}{x}$
33121	Evaluate the Limit	limit as x approaches 0 of (8sin( square root of 2x))/( square root of 2x)	$lim_{x \to 0} \frac{8 \sin (\sqrt{2} x)}{\sqrt{2} x}$
33122	Evaluate the Limit	limit as x approaches 0 of (8sin(x))/(11x)	$lim_{x \to 0} \frac{8 \sin (x)}{11 x}$
33123	Evaluate the Limit	limit as x approaches 0 of (9sec(x)-9)/(x^2)	$lim_{x \to 0} \frac{9 \sec (x) - 9}{x^{2}}$
33124	Evaluate the Limit	limit as x approaches 0 of (cos(x))/(cot(x))	$lim_{x \to 0} \frac{\cos (x)}{\cot (x)}$
33125	Evaluate the Limit	limit as x approaches 0 of cos(x)^(7/(x^2))	$lim_{x \to 0} {\cos (x)}^{\frac{7}{x^{2}}}$
33126	Evaluate the Limit	limit as x approaches 0 of 1/(2x)-1/(sin(2x))	$lim_{x \to 0} \frac{1}{2 x} - \frac{1}{\sin (2 x)}$
33127	Evaluate the Limit	limit as x approaches 0 of e^x- natural log of x+1	$lim_{x \to 0} e^{x} - \ln (x + 1)$
33128	Evaluate the Limit	limit as x approaches 0 of (cos(5x)-cos(3x))/(x^2)	$lim_{x \to 0} \frac{\cos (5 x) - \cos (3 x)}{x^{2}}$
33129	Evaluate the Limit	limit as x approaches 0 of ((cos(x))(cos(x))+6cos(x)-7)/(cos(x)-1)	$lim_{x \to 0} \frac{(\cos (x)) (\cos (x)) + 6 \cos (x) - 7}{\cos (x) - 1}$
33130	Evaluate the Limit	limit as x approaches 0 of (((x+h)^2-6)/(3(x+h)^2)-(x^2-6)/(3x^3))/h	$lim_{x \to 0} \frac{\frac{{(x + h)}^{2} - 6}{3 {(x + h)}^{2}} - \frac{x^{2} - 6}{3 x^{3}}}{h}$
33131	Evaluate the Limit	limit as x approaches 0 of ((-5-x)^2-25)/x	$lim_{x \to 0} \frac{{(- 5 - x)}^{2} - 25}{x}$
33132	Evaluate the Limit	limit as x approaches 0 of (\|2x-1\|-\|2x+1\|)/x	$lim_{x \to 0} \frac{\| 2 x - 1 \| - \| 2 x + 1 \|}{x}$
33133	Evaluate the Limit	limit as x approaches 0 of (\|2x-1\|-1)/(3x)	$lim_{x \to 0} \frac{\| 2 x - 1 \| - 1}{3 x}$
33134	Evaluate the Limit	limit as x approaches 0 of (\|x+1\|-\|x-1\|)/x	$lim_{x \to 0} \frac{\| x + 1 \| - \| x - 1 \|}{x}$
33135	Evaluate the Limit	limit as x approaches 0 of (1/(5+x)-1/5)/x	$lim_{x \to 0} \frac{\frac{1}{5 + x} - \frac{1}{5}}{x}$
33136	Evaluate the Limit	limit as x approaches 0 of (a^(mx)-1)/(a^(nx)-1)	$lim_{x \to 0} \frac{a^{m x} - 1}{a^{n x} - 1}$
33137	Evaluate the Limit	limit as x approaches 0 of (e^(3x)-x^2-3x-1)/(1-cos(2x))	$lim_{x \to 0} \frac{e^{3 x} - x^{2} - 3 x - 1}{1 - \cos (2 x)}$
33138	Evaluate the Limit	limit as x approaches 0 of (e^x-e^(-x))/(e^x+e^(-x))	$lim_{x \to 0} \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}}$
33139	Evaluate the Limit	limit as x approaches 0 of (e^x-x^(-x))/x	$lim_{x \to 0} \frac{e^{x} - x^{- x}}{x}$
33140	Evaluate the Limit	limit as x approaches 0 of (e^x+5x)^(2/x)	$lim_{x \to 0} {(e^{x} + 5 x)}^{\frac{2}{x}}$
33141	Evaluate the Limit	limit as x approaches 0 of (e^x+x)^(2/x)	$lim_{x \to 0} {(e^{x} + x)}^{\frac{2}{x}}$
33142	Evaluate the Limit	limit as x approaches 0 of (e^x-1)/(sin(5x))	$lim_{x \to 0} \frac{e^{x} - 1}{\sin (5 x)}$
33143	Evaluate the Limit	limit as x approaches 0 of (sin(3+x)^2-sin(9))/x	$lim_{x \to 0} \frac{\sin^{2} (3 + x) - \sin (9)}{x}$
33144	Evaluate the Limit	limit as x approaches 0 of ((sin(3x))/(cos(3x)))/(5x)	$lim_{x \to 0} \frac{\frac{\sin (3 x)}{\cos (3 x)}}{5 x}$
33145	Evaluate the Limit	limit as x approaches 0 of (-(arcsin(x-1)))/(x^2)	$lim_{x \to 0} \frac{- (\arcsin (x - 1))}{x^{2}}$
33146	Evaluate the Limit	limit as x approaches 0 of (arctan(x))/((1/x)-7)	$lim_{x \to 0} \frac{\arctan (x)}{(\frac{1}{x}) - 7}$
33147	Evaluate the Limit	limit as x approaches 0 of ( square root of 1+tan(x)- square root of 1+sin(x))/(x^3)	$lim_{x \to 0} \frac{\sqrt{1 + \tan (x)} - \sqrt{1 + \sin (x)}}{x^{3}}$
33148	Find the Critical Points	4x^3+x^2+4x	$4 x^{3} + x^{2} + 4 x$
33149	Evaluate the Limit	limit as x approaches 0 of ( square root of 3x+49-7)/x	$lim_{x \to 0} \frac{\sqrt{3 x + 49} - 7}{x}$
33150	Evaluate the Limit	limit as x approaches 0 of ( square root of 4x^2+6)/(2x^2)	$lim_{x \to 0} \frac{\sqrt{4 x^{2} + 6}}{2 x^{2}}$
33151	Evaluate the Limit	limit as x approaches 0 of (arcsin(4x))/(arccos(5x))	$lim_{x \to 0} \frac{\arcsin (4 x)}{\arccos (5 x)}$
33152	Evaluate the Limit	limit as x approaches 0 of ((tan(2x))/(x^3))+1/(x^2)+(sin(x))/x	$lim_{x \to 0} (\frac{\tan (2 x)}{x^{3}}) + \frac{1}{x^{2}} + \frac{\sin (x)}{x}$
33153	Evaluate the Limit	limit as x approaches 0 of ((tan(2x))/(x^3))+2/(x^2)+(sin(x))/x	$lim_{x \to 0} (\frac{\tan (2 x)}{x^{3}}) + \frac{2}{x^{2}} + \frac{\sin (x)}{x}$
33154	Evaluate the Limit	limit as x approaches 0 of (tan(2x))/(sin(3x))	$lim_{x \to 0} \frac{\tan (2 x)}{\sin (3 x)}$
33155	Evaluate the Limit	limit as x approaches 0 of (tan(2x))/(tan(x))	$lim_{x \to 0} \frac{\tan (2 x)}{\tan (x)}$
33156	Evaluate the Limit	limit as x approaches 0 of (tan(3x)+3x)/(sin(5x))	$lim_{x \to 0} \frac{\tan (3 x) + 3 x}{\sin (5 x)}$
33157	Evaluate the Limit	limit as x approaches 0 of (tan(4x))/(tan(5x))	$lim_{x \to 0} \frac{\tan (4 x)}{\tan (5 x)}$
33158	Evaluate the Limit	limit as x approaches 0 of (tan(7x))/(sin(x))	$lim_{x \to 0} \frac{\tan (7 x)}{\sin (x)}$
33159	Evaluate the Limit	limit as x approaches 0 of (tan(9x))/(tan(4x))	$lim_{x \to 0} \frac{\tan (9 x)}{\tan (4 x)}$
33160	Evaluate the Limit	limit as x approaches 0 of (tan(x))/(3x)	$lim_{x \to 0} \frac{\tan (x)}{3 x}$
33161	Evaluate the Limit	limit as x approaches 0 of ( square root of 16h+1-1)(h)^-1	$lim_{x \to 0} (\sqrt{16 h + 1} - 1) {(h)}^{- 1}$
33162	Evaluate the Limit	limit as x approaches 0 of fifth root of x^5-3x^4+17-x	$lim_{x \to 0} \sqrt[5]{x^{5} - 3 x^{4} + 17} - x$
33163	Evaluate the Limit	limit as x approaches 0 of x/(4^x-2^x)	$lim_{x \to 0} \frac{x}{4^{x} - 2^{x}}$
33164	Evaluate the Limit	limit as x approaches 0 of x/(x^2-7x)	$lim_{x \to 0} \frac{x}{x^{2} - 7 x}$
33165	Evaluate the Limit	limit as x approaches 0 of (sin(5x))/(sin(8x))	$lim_{x \to 0} \frac{\sin (5 x)}{\sin (8 x)}$
33166	Find the Critical Points	-3x^4+24x^3-30x^2	$- 3 x^{4} + 24 x^{3} - 30 x^{2}$
33167	Evaluate the Limit	limit as x approaches 0 of (sin(-7x))/(-3x)	$lim_{x \to 0} \frac{\sin (- 7 x)}{- 3 x}$
33168	Evaluate the Limit	limit as x approaches 0 of (sin(h))/(2h)	$lim_{x \to 0} \frac{\sin (h)}{2 h}$
33169	Evaluate the Limit	limit as x approaches 0 of (sin(h))/h	$lim_{x \to 0} \frac{\sin (h)}{h}$
33170	Evaluate the Limit	limit as x approaches 0 of (sin(picos(x)))/(xsin(x))	$lim_{x \to 0} \frac{\sin (π \cos (x))}{x \sin (x)}$
33171	Evaluate the Limit	limit as x approaches 0 of (9x^2-4x)/x	$lim_{x \to 0} \frac{9 x^{2} - 4 x}{x}$
33172	Evaluate the Limit	limit as x approaches 0 of (9x^5+3x^4-17x^3)/(7x^8-13x^7-8x^3)	$lim_{x \to 0} \frac{9 x^{5} + 3 x^{4} - 17 x^{3}}{7 x^{8} - 13 x^{7} - 8 x^{3}}$
33173	Evaluate the Limit	limit as x approaches 0 of (cos(-0.1)-1)/-0.1	$lim_{x \to 0} \frac{\cos (- 0.1) - 1}{- 0.1}$
33174	Evaluate the Limit	limit as x approaches 0 of cos(2x)^(1/x)	$lim_{x \to 0} {\cos (2 x)}^{\frac{1}{x}}$
33175	Evaluate the Limit	limit as x approaches 0 of (cos(3x)-1)/(5x)	$lim_{x \to 0} \frac{\cos (3 x) - 1}{5 x}$
33176	Evaluate the Limit	limit as x approaches 0 of (cos(x))/(3x)	$lim_{x \to 0} \frac{\cos (x)}{3 x}$
33177	Evaluate the Limit	limit as x approaches 0 of ( natural log of cos(4x))/(3x^2)	$lim_{x \to 0} \frac{\ln (\cos (4 x))}{3 x^{2}}$
33178	Evaluate the Limit	limit as x approaches 0 of ( natural log of sin(x))/(x-pi/2)	$lim_{x \to 0} \frac{\ln (\sin (x))}{x - \frac{π}{2}}$
33179	Evaluate the Limit	limit as x approaches 0 of ( natural log of tan(45+ax))/(sin(bx))	$lim_{x \to 0} \frac{\ln (\tan (45 + a x))}{\sin (b x)}$
33180	Evaluate the Limit	limit as x approaches 0 of (sec(x)-1)/(tan(x)^2)	$lim_{x \to 0} \frac{\sec (x) - 1}{\tan^{2} (x)}$
33181	Evaluate the Limit	limit as x approaches 0 of (sec(x-1))/(tan(x)^2)	$lim_{x \to 0} \frac{\sec (x - 1)}{\tan^{2} (x)}$
33182	Evaluate the Limit	limit as x approaches 0 of (sin(x^2))/(1-cos(2x))	$lim_{x \to 0} \frac{\sin (x^{2})}{1 - \cos (2 x)}$
33183	Evaluate the Limit	limit as x approaches 0 of (sin(1))/x	$lim_{x \to 0} \frac{\sin (1)}{x}$
33184	Find the Inflection Points	x^3+30x^2	$x^{3} + 30 x^{2}$
33185	Evaluate the Limit	limit as x approaches 0 of (sin(3cos(x)))/(4sec(x))	$lim_{x \to 0} \frac{\sin (3 \cos (x))}{4 \sec (x)}$
33186	Evaluate the Limit	limit as x approaches 0 of (sin(3x))/(2x)-(3x)/(sin(4x))	$lim_{x \to 0} \frac{\sin (3 x)}{2 x} - \frac{3 x}{\sin (4 x)}$
33187	Determine if Continuous	f(x) = square root of x^2+25	$f (x) = \sqrt{x^{2} + 25}$
33188	Determine if Continuous	f(x) = square root of x-10	$f (x) = \sqrt{x - 10}$
33189	Evaluate the Limit	limit as x approaches 0 of (sin(3x)cot(5x))/(xcot(4x))	$lim_{x \to 0} \frac{\sin (3 x) \cot (5 x)}{x \cot (4 x)}$
33190	Evaluate the Limit	limit as x approaches 0 of (sin(4x))/(tan(5x))	$lim_{x \to 0} \frac{\sin (4 x)}{\tan (5 x)}$
33191	Evaluate the Limit	limit as x approaches 0 of (sin(5x))/(4x)	$lim_{x \to 0} \frac{\sin (5 x)}{4 x}$
33192	Graph	f(x)=(1-cos(x))/x	$f (x) = \frac{1 - \cos (x)}{x}$
33193	Evaluate the Limit	limit as x approaches 0 of 1/x+(7x-1)/x	$lim_{x \to 0} \frac{1}{x} + \frac{7 x - 1}{x}$
33194	Evaluate the Limit	limit as x approaches 0 of (1+x+sin(x))/(3cos(x))	$lim_{x \to 0} \frac{1 + x + \sin (x)}{3 \cos (x)}$
33195	Evaluate the Limit	limit as x approaches 0 of 12/(x^2)	$lim_{x \to 0} \frac{12}{x^{2}}$
33196	Evaluate the Limit	limit as x approaches 0 of (1-cos(12x))/(144x^2)	$lim_{x \to 0} \frac{1 - \cos (12 x)}{144 x^{2}}$
33197	Evaluate the Limit	limit as x approaches 0 of ( square root of 16h+1-1)/h	$lim_{x \to 0} \frac{\sqrt{16 h + 1} - 1}{h}$
33198	Evaluate the Limit	limit as x approaches 0 from the left of 1/x	$lim_{x \to 0} \frac{1}{x}$
33199	Graph	f(x)=3x^3-9x	$f (x) = 3 x^{3} - 9 x$
33200	Evaluate the Limit	limit as x approaches 0 of 1-2x^3	$lim_{x \to 0} 1 - 2 x^{3}$