Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
32501	Evaluate the Limit	limit as h approaches 0 of (e^h-1)/(2h)	$lim_{h \to 0} \frac{e^{h} - 1}{2 h}$
32502	Evaluate the Limit	limit as h approaches 0 of ( square root of 4h+1-1)/h	$lim_{h \to 0} \frac{\sqrt{4 h + 1} - 1}{h}$
32503	Evaluate the Limit	limit as h approaches 0 of (( square root of 7+h- square root of 7)( square root of 7+h+ square root of 7))/(h( square root of 7+h+7))	$lim_{h \to 0} \frac{(\sqrt{7 + h} - \sqrt{7}) (\sqrt{7 + h} + \sqrt{7})}{h (\sqrt{7 + h} + 7)}$
32504	Evaluate the Limit	limit as h approaches 0 of (2(x+h)^3-2x^3)/h	$lim_{h \to 0} \frac{2 {(x + h)}^{3} - 2 x^{3}}{h}$
32505	Evaluate the Limit	limit as x approaches 0 of (cos(3x-1))/(sin(5x))	$lim_{x \to 0} \frac{\cos (3 x - 1)}{\sin (5 x)}$
32506	Evaluate the Limit	limit as x approaches 0 of (cos(9x)-1)/(sin(8x))	$lim_{x \to 0} \frac{\cos (9 x) - 1}{\sin (8 x)}$
32507	Evaluate the Limit	limit as x approaches 0 of (cos(pi+x)+1)/x	$lim_{x \to 0} \frac{\cos (π + x) + 1}{x}$
32508	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(6x+tan(x))	$lim_{x \to 0} \frac{\sin (x)}{6 x + \tan (x)}$
32509	Find the Derivative - d/dx	y=4	$y = 4$
32510	Evaluate the Limit	limit as x approaches 0 of (sin(4x))/(x+tan(9x))	$lim_{x \to 0} \frac{\sin (4 x)}{x + \tan (9 x)}$
32511	Evaluate the Limit	limit as x approaches 0 of (sin(5x))/(x+tan(8x))	$lim_{x \to 0} \frac{\sin (5 x)}{x + \tan (8 x)}$
32512	Evaluate the Limit	limit as x approaches 0 of (tan(x))/(sin(x)^2)	$lim_{x \to 0} \frac{\tan (x)}{\sin^{2} (x)}$
32513	Evaluate the Limit	limit as x approaches 0 of (tan(x))/(sin(2x))	$lim_{x \to 0} \frac{\tan (x)}{\sin (2 x)}$
32514	Evaluate the Limit	limit as x approaches 0 of (tan(Ax))/(Bx)	$lim_{x \to 0} \frac{\tan (A x)}{B x}$
32515	Evaluate the Limit	limit as x approaches 0 of (sin(x))cot(2x)	$lim_{x \to 0} (\sin (x)) \cot (2 x)$
32516	Evaluate the Limit	limit as x approaches 0 from the right of (sin(x))/(x^2)	$lim_{x \to 0} \frac{\sin (x)}{x^{2}}$
32517	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(theta+tan(theta))	$lim_{x \to 0} \frac{\sin (x)}{θ + \tan (θ)}$
32518	Evaluate the Limit	limit as x approaches 0 of (sin(x/2))/x	$lim_{x \to 0} \frac{\sin (\frac{x}{2})}{x}$
32519	Evaluate the Limit	limit as x approaches 0 of 3+2csc(x)	$lim_{x \to 0} 3 + 2 \csc (x)$
32520	Evaluate the Limit	limit as x approaches 0 of (1-cos(mx))/(1-cos(nx))	$lim_{x \to 0} \frac{1 - \cos (m x)}{1 - \cos (n x)}$
32521	Evaluate the Limit	limit as x approaches 0 of (sin(8x))/(x+tan(9x))	$lim_{x \to 0} \frac{\sin (8 x)}{x + \tan (9 x)}$
32522	Evaluate the Limit	( limit as x approaches 9 of 81-x^2)/(3- square root of x)	$\frac{lim_{x \to 9} 81 - x^{2}}{3 - \sqrt{x}}$
32523	Evaluate the Limit	( limit as x approaches 9 of 9x sixth root of 6x+10-2)/(9-x)	$\frac{lim_{x \to 9} 9 x \sqrt[6]{6 x + 10} - 2}{9 - x}$
32524	Evaluate the Limit	f(x) = limit as x approaches 0.6 of (2640)+400	$f (x) = lim_{x \to 0.6} (2640) + 400$
32525	Evaluate the Limit	f(x) = limit as x approaches 1 of x-1	$f (x) = lim_{x \to 1} x - 1$
32526	Evaluate the Limit	f(x) = limit as x approaches 2.5 of x^3-3x^2+1	$f (x) = lim_{x \to 2.5} x^{3} - 3 x^{2} + 1$
32527	Evaluate the Limit	f(x) = limit as x approaches 3 of 4x^2+5x+3	$f (x) = lim_{x \to 3} 4 x^{2} + 5 x + 3$
32528	Evaluate the Limit	f(x) = limit as x approaches 454 of x^2	$f (x) = lim_{x \to 454} x^{2}$
32529	Evaluate the Limit	limit as x approaches -8 of (7- square root of x^2-15)/(x+8)	$lim_{x \to - 8} \frac{7 - \sqrt{x^{2} - 15}}{x + 8}$
32530	Evaluate the Limit	f(x) limit as h approaches 0 of square root of x+1	$f (x) lim_{h \to 0} \sqrt{x + 1}$
32531	Evaluate the Limit	limit as x approaches 1 of (x^3+x^2-5x+3)/(x^3-3x+2)	$lim_{x \to 1} \frac{x^{3} + x^{2} - 5 x + 3}{x^{3} - 3 x + 2}$
32532	Evaluate the Limit	f(x) limit as x approaches 15 of 1/x	$f (x) lim_{x \to 15} \frac{1}{x}$
32533	Evaluate the Limit	(f(x^2-3x-10))/((x+2) limit as x approaches -2 of f(x))	$\frac{f (x^{2} - 3 x - 10)}{(x + 2) lim_{x \to - 2} f (x)}$
32534	Evaluate the Limit	f limit as x approaches 0 of arctan( natural log of x)	$f lim_{x \to 0} \arctan (\ln (x))$
32535	Evaluate the Limit	g(x)=(\|x-2\|)/((x-2) limit as x approaches 2 from the right of g(x))	$g (x) = \frac{\| x - 2 \|}{(x - 2) lim_{x \to 2} g (x)}$
32536	Evaluate the Limit	g(x)=x^2-6 limit as x approaches 3 of g(x)	$g (x) = x^{2} - 6 lim_{x \to 3} g (x)$
32537	Evaluate the Limit	L = limit as x approaches 8 of ( square root of 4x^2-8)/(x-2)	$L = lim_{x \to 8} \frac{\sqrt{4 x^{2} - 8}}{x - 2}$
32538	Evaluate the Limit	li limit as x approaches 0 of (3)m	$l i lim_{x \to 0} (3) m$
32539	Evaluate the Limit	li limit as x approaches 0 of (sin(3x)cot(4x))/(cot(5x))	$l i lim_{x \to 0} \frac{\sin (3 x) \cot (4 x)}{\cot (5 x)}$
32540	Evaluate the Limit	limit as x approaches 0 of (3cot(2x))/(csc(x))	$lim_{x \to 0} \frac{3 \cot (2 x)}{\csc (x)}$
32541	Evaluate the Limit	limit as x approaches (pi/2) of (1-sin(x))/(cos(x))	$lim_{x \to (\frac{π}{2})} \frac{1 - \sin (x)}{\cos (x)}$
32542	Evaluate the Limit	limit as x approaches (9pi)/4 of (sin(x-1/( square root of 2)))/(x-(9pi)/4)	$lim_{x \to \frac{9 π}{4}} \frac{\sin (x - \frac{1}{\sqrt{2}})}{x - \frac{9 π}{4}}$
32543	Evaluate the Limit	limit as x approaches 1/2*pi of (cos(2x))/(tan(x))	$lim_{x \to \frac{1}{2} \cdot π} \frac{\cos (2 x)}{\tan (x)}$
32544	Evaluate the Limit	limit as x approaches -pi/2 of (5)(sec(x+tan(x)))	$lim_{x \to - \frac{π}{2}} (5) (\sec (x + \tan (x)))$
32545	Evaluate the Limit	limit as x approaches pi/2 of 6xsin(x)	$lim_{x \to \frac{π}{2}} 6 x \sin (x)$
32546	Evaluate the Limit	limit as x approaches pi/2 of 9xsin(x)	$lim_{x \to \frac{π}{2}} 9 x \sin (x)$
32547	Evaluate the Limit	limit as x approaches pi/4 of (cos(x)-1/( square root of 2))/(x-pi/4)	$lim_{x \to \frac{π}{4}} \frac{\cos (x) - \frac{1}{\sqrt{2}}}{x - \frac{π}{4}}$
32548	Evaluate the Limit	limit as x approaches pi/6 of ((cos(x) square root of 3)/2)/(x-pi/6)	$lim_{x \to \frac{π}{6}} \frac{\frac{\cos (x) \sqrt{3}}{2}}{x - \frac{π}{6}}$
32549	Evaluate the Limit	limit as x approaches infinity of (x^2-3x+8)/(x^3+2x^2+5)	$lim_{x \to \infty} \frac{x^{2} - 3 x + 8}{x^{3} + 2 x^{2} + 5}$
32550	Evaluate the Limit	limit as x approaches 0 of (sin(4x)sin(-x))/(xsin(3x))	$lim_{x \to 0} \frac{\sin (4 x) \sin (- x)}{x \sin (3 x)}$
32551	Evaluate the Limit	limit as x approaches 0 of (1/(2+sin(x))-1/2)/(sin(x))	$lim_{x \to 0} \frac{\frac{1}{2 + \sin (x)} - \frac{1}{2}}{\sin (x)}$
32552	Evaluate the Limit	limit as x approaches 0 of (2sin(x))/(cos(x)sin(x))	$lim_{x \to 0} \frac{2 \sin (x)}{\cos (x) \sin (x)}$
32553	Evaluate the Limit	limit as x approaches 0 of (3tan(x))/x	$lim_{x \to 0} \frac{3 \tan (x)}{x}$
32554	Evaluate the Limit	limit as x approaches 0 of ((4sin(4x))/(4x))((7x)/(7sin(7x)))	$lim_{x \to 0} (\frac{4 \sin (4 x)}{4 x}) (\frac{7 x}{7 \sin (7 x)})$
32555	Evaluate the Limit	limit as x approaches 0 of (sec(x)-1)/x	$lim_{x \to 0} \frac{\sec (x) - 1}{x}$
32556	Find the Derivative - d/dx	y=cos((1-e^(2x))/(1+e^(2x)))	$y = \cos (\frac{1 - e^{2 x}}{1 + e^{2 x}})$
32557	Evaluate the Limit	( limit as x approaches 8 of x)/((8x)/( square root of 9x^2+6))	$\frac{lim_{x \to 8} x}{\frac{8 x}{\sqrt{9 x^{2} + 6}}}$
32558	Find the Derivative - d/dx	y=sin((pix)^4)	$y = \sin ({(π x)}^{4})$
32559	Evaluate the Limit	( limit as x approaches 8 of x)/( cube root of x^2-1)	$\frac{lim_{x \to 8} x}{\sqrt[3]{x^{2} - 1}}$
32560	Evaluate the Limit	( limit as x approaches 8 of x)/(2x+1)	$\frac{lim_{x \to 8} x}{2 x + 1}$
32561	Evaluate the Limit	( limit as x approaches 8 of 5x^5+3x^3-7)/(4+2x+11x^5)	$\frac{lim_{x \to 8} 5 x^{5} + 3 x^{3} - 7}{4 + 2 x + 11 x^{5}}$
32562	Evaluate the Limit	( limit as x approaches 9 of sixth root of 7x+1-2)/(1/x-1/9)	$\frac{lim_{x \to 9} \sqrt[6]{7 x + 1} - 2}{\frac{1}{x} - \frac{1}{9}}$
32563	Evaluate the Limit	( limit as x approaches 9 of -x^2+23x-126)/(x-9)	$\frac{lim_{x \to 9} - x^{2} + 23 x - 126}{x - 9}$
32564	Find the Derivative - d/dx	natural log of natural log of 3x	$\ln (\ln (3 x))$
32565	Evaluate the Limit	limit as t approaches 8 of square root of (25t^2+1)/((t+1)^2)	$lim_{t \to 8} \sqrt{\frac{25 t^{2} + 1}{{(t + 1)}^{2}}}$
32566	Evaluate the Limit	limit as t approaches 8 of (12+2.8)sin((2pi)/365(t-80))	$lim_{t \to 8} (12 + 2.8) \cdot \sin (\frac{2 π}{365} \cdot (t - 80))$
32567	Evaluate the Limit	limit as t approaches 8 of 283+3(1-e^(-0.03t))	$lim_{t \to 8} 283 + 3 (1 - e^{- 0.03 t})$
32568	Evaluate the Limit	limit as t approaches 8 of natural log of \|3-4t\|	$lim_{t \to 8} \ln (\| 3 - 4 t \|)$
32569	Evaluate the Limit	limit as x approaches 7 of tan((pix)/4)	$lim_{x \to 7} \tan (\frac{π x}{4})$
32570	Evaluate the Limit	limit as t approaches 9 of 6t^2-14t+1	$lim_{t \to 9} 6 t^{2} - 14 t + 1$
32571	Evaluate the Limit	limit as t approaches a of a^2	$lim_{t \to a} a^{2}$
32572	Evaluate the Limit	limit as t approaches a of (s(a)-st)/(5-t)	$lim_{t \to a} \frac{s (a) - s t}{5 - t}$
32573	Evaluate the Limit	limit as t approaches x of (t^2-x^2)/(t^5-x^5)	$lim_{t \to x} \frac{t^{2} - x^{2}}{t^{5} - x^{5}}$
32574	Evaluate the Limit	limit as h approaches 0 of 3/( square root of 3h+1+1)	$lim_{h \to 0} \frac{3}{\sqrt{3 h + 1} + 1}$
32575	Find the Derivative - d/dx	cos(2x^4-6)	$\cos (2 x^{4} - 6)$
32576	Evaluate the Limit	limit as u approaches 2 of ( square root of 4u+1-3)/(u-2)	$lim_{u \to 2} \frac{\sqrt{4 u + 1} - 3}{u - 2}$
32577	Evaluate the Limit	limit as u approaches 3 from the left of (2-3)/(u-3)	$lim_{u \to 3} \frac{2 - 3}{u - 3}$
32578	Evaluate the Limit	limit as u approaches 3 of (2-3)/(u-3)	$lim_{u \to 3} \frac{2 - 3}{u - 3}$
32579	Evaluate the Limit	limit as u approaches 3 of (u^4-81)/(u^3-23)	$lim_{u \to 3} \frac{u^{4} - 81}{u^{3} - 23}$
32580	Evaluate the Limit	limit as u approaches 3 of (u^(3-27))/(u^4-81)	$lim_{u \to 3} \frac{u^{3 - 27}}{u^{4} - 81}$
32581	Evaluate the Limit	limit as u approaches -5 of square root of u^4+5u+25	$lim_{u \to - 5} \sqrt{u^{4} + 5 u + 25}$
32582	Evaluate the Limit	limit as u approaches -8 of (8u^4+4)/((u^2-5)(2u^2-1))	$lim_{u \to - 8} \frac{8 u^{4} + 4}{(u^{2} - 5) (2 u^{2} - 1)}$
32583	Evaluate the Limit	limit as u approaches 8 of arcsec(u+1)	$lim_{u \to 8} arcsec (u + 1)$
32584	Evaluate the Limit	limit as x approaches infinity of (9-e^x)/(9+8e^x)	$lim_{x \to \infty} \frac{9 - e^{x}}{9 + 8 e^{x}}$
32585	Evaluate the Limit	limit as v approaches 4 of (1/v-1/4)/(v-4)	$lim_{v \to 4} \frac{\frac{1}{v} - \frac{1}{4}}{v - 4}$
32586	Evaluate the Limit	limit as w approaches 0 of ((w+1)sin(2w))/(sin(3w))	$lim_{w \to 0} \frac{(w + 1) \sin (2 w)}{\sin (3 w)}$
32587	Evaluate the Limit	limit as w approaches 0 of (cos(w)-1)/(sin(w))	$lim_{w \to 0} \frac{\cos (w) - 1}{\sin (w)}$
32588	Evaluate the Limit	limit as w approaches 7 of ( square root of w+2+1)/( square root of w-3-1)	$lim_{w \to 7} \frac{\sqrt{w + 2} + 1}{\sqrt{w - 3} - 1}$
32589	Evaluate the Limit	limit as w approaches k of (w^2+9kw+8k^2)/(w^2+kw)	$lim_{w \to k} \frac{w^{2} + 9 k w + 8 k^{2}}{w^{2} + k w}$
32590	Evaluate the Limit	limit as w approaches -k of (w^2+12kw+11k^2)/(w^2+kw)	$lim_{w \to - k} \frac{w^{2} + 12 k w + 11 k^{2}}{w^{2} + k w}$
32591	Evaluate the Limit	limit as w approaches x of (w^2-x^w)/(w-x)	$lim_{w \to x} \frac{w^{2} - x^{w}}{w - x}$
32592	Evaluate the Limit	limit as x approaches (2/3) of (2x+4)/(\|3x-2\|)	$lim_{x \to (\frac{2}{3})} \frac{2 x + 4}{\| 3 x - 2 \|}$
32593	Evaluate the Limit	limit as x approaches (-3/2) of (7x-5)/((4x^2-6x+9)(2x-3)(4x^2+6x+9))	$lim_{x \to (- \frac{3}{2})} \frac{7 x - 5}{(4 x^{2} - 6 x + 9) (2 x - 3) (4 x^{2} + 6 x + 9)}$
32594	Evaluate the Limit	limit as x approaches (9/8) of (17x)/(9-8x)	$lim_{x \to (\frac{9}{8})} \frac{17 x}{9 - 8 x}$
32595	Evaluate the Limit	limit as x approaches pi/2 from the left of 2/(1+e^(tan(x)))	$lim_{x \to \frac{π}{2}} \frac{2}{1 + e^{\tan (x)}}$
32596	Evaluate the Limit	limit as x approaches (pi/2) of 3^(etan(x))	$lim_{x \to (\frac{π}{2})} 3^{e \tan (x)}$
32597	Evaluate the Limit	limit as x approaches pi/2 from the left of sec(x)	$lim_{x \to \frac{π}{2}} \sec (x)$
32598	Evaluate the Limit	limit as x approaches (pi/2) of tan(x)-sec(x)	$lim_{x \to (\frac{π}{2})} \tan (x) - \sec (x)$
32599	Evaluate the Limit	limit as x approaches (pi/4) of (1+sin(4x))^(cot(4x))	$lim_{x \to (\frac{π}{4})} {(1 + \sin (4 x))}^{\cot (4 x)}$
32600	Evaluate the Limit	limit as x approaches (pi/4) of tan(x)^(tan(2x))	$lim_{x \to (\frac{π}{4})} {\tan (x)}^{\tan (2 x)}$