Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
31301	Evaluate the Limit	( limit as x approaches 0 of -2x^2+3x-1)/(\|x\|)	$\frac{lim_{x \to 0} - 2 x^{2} + 3 x - 1}{\| x \|}$
31302	Evaluate the Limit	( limit as x approaches 0 of 2x^2-5x)/x	$\frac{lim_{x \to 0} 2 x^{2} - 5 x}{x}$
31303	Evaluate the Limit	( limit as x approaches 0 of 20x^2-13+5)/(5-4x^3)	$\frac{lim_{x \to 0} 20 x^{2} - 13 + 5}{5 - 4 x^{3}}$
31304	Evaluate the Limit	( limit as x approaches 0 of 2x)/(tan(3x))	$\frac{lim_{x \to 0} 2 x}{\tan (3 x)}$
31305	Evaluate the Limit	( limit as x approaches 0 of 2x+3arcsin(x))/(2x-arcsin(x))	$\frac{lim_{x \to 0} 2 x + 3 \arcsin (x)}{2 x - \arcsin (x)}$
31306	Evaluate	sec(pi/6)tan(pi/6)	$\sec (\frac{π}{6}) \tan (\frac{π}{6})$
31307	Evaluate	cos(4pi)	$\cos (4 π)$
31308	Evaluate the Limit	( limit as x approaches 0 of x^2+x^4)/(x^6-x^2)	$\frac{lim_{x \to 0} x^{2} + x^{4}}{x^{6} - x^{2}}$
31309	Evaluate the Limit	( limit as x approaches 0 of x^2+2x)/(x^3-3x)	$\frac{lim_{x \to 0} x^{2} + 2 x}{x^{3} - 3 x}$
31310	Evaluate the Limit	( limit as x approaches 0 of x^2-16)/(x-4)	$\frac{lim_{x \to 0} x^{2} - 16}{x - 4}$
31311	Evaluate	4cos(pi/2)	$4 \cos (\frac{π}{2})$
31312	Evaluate the Limit	( limit as x approaches 0 of square root of x+64-8)/x	$\frac{lim_{x \to 0} \sqrt{x + 64} - 8}{x}$
31313	Evaluate	-2sin(pi/2)	$- 2 \sin (\frac{π}{2})$
31314	Evaluate the Limit	( limit as x approaches 0 of cube root of x+1- cube root of 2)/(x-1)	$\frac{lim_{x \to 0} \sqrt[3]{x + 1} - \sqrt[3]{2}}{x - 1}$
31315	Evaluate the Limit	( limit as x approaches 0 of fourth root of x^4+1- square root of x^2+1)/(x^2)	$\frac{lim_{x \to 0} \sqrt[4]{x^{4} + 1} - \sqrt{x^{2} + 1}}{x^{2}}$
31316	Evaluate	1/((-2.1)^2-4)	$\frac{1}{{(- 2.1)}^{2} - 4}$
31317	Evaluate the Limit	( limit as x approaches 0 of square root of x+36-6)/x	$\frac{lim_{x \to 0} \sqrt{x + 36} - 6}{x}$
31318	Evaluate the Limit	( limit as x approaches 0 of sin(x)^3)/x	$\frac{lim_{x \to 0} \sin^{3} (x)}{x}$
31319	Evaluate the Limit	( limit as x approaches 1/3 of 3x^2+2x-1)/(9x^2-1)	$\frac{lim_{x \to \frac{1}{3}} 3 x^{2} + 2 x - 1}{9 x^{2} - 1}$
31320	Evaluate the Limit	limit as x approaches 1/6 of (6sin(pix)-1)^3	$lim_{x \to \frac{1}{6}} {(6 \sin (π x) - 1)}^{3}$
31321	Evaluate the Limit	( limit as x approaches 0 of square root of 0.001+2- square root of 2)/0.001	$\frac{lim_{x \to 0} \sqrt{0.001 + 2} - \sqrt{2}}{0.001}$
31322	Evaluate the Limit	( limit as x approaches 0 of square root of -0.01+2- square root of 2)/-0.01	$\frac{lim_{x \to 0} \sqrt{- 0.01 + 2} - \sqrt{2}}{- 0.01}$
31323	Evaluate the Limit	( limit as x approaches 0 of 1-e^x)/(x^2+2x)	$\frac{lim_{x \to 0} 1 - e^{x}}{x^{2} + 2 x}$
31324	Evaluate the Limit	( limit as x approaches 0 of 1+3x-1)/x	$\frac{lim_{x \to 0} 1 + 3 x - 1}{x}$
31325	Evaluate the Limit	( limit as x approaches 0 of 1+xsin(x)-cos(2x))/(sin(x)^2)	$\frac{lim_{x \to 0} 1 + x \sin (x) - \cos (2 x)}{\sin^{2} (x)}$
31326	Evaluate the Limit	( limit as x approaches 0 of 1-cos(2x))/(x^2)	$\frac{lim_{x \to 0} 1 - \cos (2 x)}{x^{2}}$
31327	Evaluate the Limit	( limit as x approaches 0 of 1-cos(2x))/(cos(7x)-cos(3x))	$\frac{lim_{x \to 0} 1 - \cos (2 x)}{\cos (7 x) - \cos (3 x)}$
31328	Evaluate the Limit	( limit as x approaches 0 of 1-cos(4x))/(16x^2)	$\frac{lim_{x \to 0} 1 - \cos (4 x)}{16 x^{2}}$
31329	Evaluate the Limit	( limit as x approaches 0 of 1)/(x square root of 1+x)-1/x	$\frac{lim_{x \to 0} 1}{x \sqrt{1 + x}} - \frac{1}{x}$
31330	Evaluate the Limit	( limit as x approaches 0 of 1)/x-1/(sin(x))	$\frac{lim_{x \to 0} 1}{x} - \frac{1}{\sin (x)}$
31331	Evaluate the Limit	( limit as x approaches 0 of x^3+15x)/x	$\frac{lim_{x \to 0} x^{3} + 15 x}{x}$
31332	Evaluate the Limit	( limit as x approaches 0 of x^3+5x)/x	$\frac{lim_{x \to 0} x^{3} + 5 x}{x}$
31333	Evaluate the Limit	( limit as x approaches 0 of x^3-7x-3)/(x^2-5)	$\frac{lim_{x \to 0} x^{3} - 7 x - 3}{x^{2} - 5}$
31334	Evaluate the Limit	( limit as x approaches 0 of x^4-5x^2)/(x^2)	$\frac{lim_{x \to 0} x^{4} - 5 x^{2}}{x^{2}}$
31335	Evaluate the Limit	( limit as x approaches 0 of x^50-1)/(x-1)	$\frac{lim_{x \to 0} x^{50} - 1}{x - 1}$
31336	Evaluate the Limit	( limit as x approaches 0 of (1)\|x\|)/x	$\frac{lim_{x \to 0} (1) \| x \|}{x}$
31337	Evaluate the Limit	( limit as x approaches 0 of x^2-5x)/(3x)	$\frac{lim_{x \to 0} x^{2} - 5 x}{3 x}$
31338	Evaluate the Limit	( limit as x approaches 0 of square root of x^2+100-10)/(x^2)	$\frac{lim_{x \to 0} \sqrt{x^{2} + 100} - 10}{x^{2}}$
31339	Evaluate the Limit	( limit as x approaches 0 of ( square root of x^2+9)-3)/(x^2)	$\frac{lim_{x \to 0} (\sqrt{x^{2} + 9}) - 3}{x^{2}}$
31340	Evaluate the Limit	( limit as x approaches 0 of square root of x^2+x)/( square root of x^3+2)	$\frac{lim_{x \to 0} \sqrt{x^{2} + x}}{\sqrt{x^{3} + 2}}$
31341	Evaluate the Limit	( limit as x approaches 0 of square root of 1+sin(x)- square root of 1-sin(x))/x	$\frac{lim_{x \to 0} \sqrt{1 + \sin (x)} - \sqrt{1 - \sin (x)}}{x}$
31342	Evaluate the Limit	( limit as x approaches 0 of square root of 1+tan(x)- square root of 1sin(x))/(x^3)	$\frac{lim_{x \to 0} \sqrt{1 + \tan (x)} - \sqrt{1 \sin (x)}}{x^{3}}$
31343	Evaluate the Integral	integral of 1/(x^2-9) with respect to x	$\int \frac{1}{x^{2} - 9} d x$
31344	Evaluate the Limit	( limit as x approaches 0 of square root of 1+x-1-x/2)/(x^2)	$\frac{lim_{x \to 0} \sqrt{1 + x} - 1 - \frac{x}{2}}{x^{2}}$
31345	Evaluate the Limit	( limit as x approaches 0 of square root of 2-x^2- square root of 2+x^2)/(5x^2)	$\frac{lim_{x \to 0} \sqrt{2 - x^{2}} - \sqrt{2 + x^{2}}}{5 x^{2}}$
31346	Evaluate the Limit	( limit as x approaches 0 of square root of 2- square root of 1+cos(x))/(sin(x)^2)	$\frac{lim_{x \to 0} \sqrt{2} - \sqrt{1 + \cos (x)}}{\sin^{2} (x)}$
31347	Evaluate the Limit	( limit as x approaches 0 of 1/(2+x))/x-(1/2)/x	$\frac{lim_{x \to 0} \frac{1}{2 + x}}{x} - \frac{\frac{1}{2}}{x}$
31348	Evaluate the Limit	( limit as x approaches 0 of 3^x-1)/(2^x-1)	$\frac{lim_{x \to 0} 3^{x} - 1}{2^{x} - 1}$
31349	Evaluate the Limit	( limit as x approaches 0 of 5^x-1)/x	$\frac{lim_{x \to 0} 5^{x} - 1}{x}$
31350	Evaluate the Limit	( limit as x approaches 0 of cos(x)^2)/(cos(x^2))	$\frac{lim_{x \to 0} \cos^{2} (x)}{\cos (x^{2})}$
31351	Evaluate the Limit	( limit as x approaches 0 of (e^(2x))-1)/(5x)	$\frac{lim_{x \to 0} (e^{2 x}) - 1}{5 x}$
31352	Evaluate the Limit	( limit as x approaches 0 of (e^(2x))-2)/(5x)	$\frac{lim_{x \to 0} (e^{2 x}) - 2}{5 x}$
31353	Evaluate the Limit	( limit as x approaches 0 of e^(-2x)-1)/(-13x)	$\frac{lim_{x \to 0} e^{- 2 x} - 1}{- 13 x}$
31354	Evaluate the Limit	( limit as x approaches 0 of e^(2x)-1)/(tan(x))	$\frac{lim_{x \to 0} e^{2 x} - 1}{\tan (x)}$
31355	Find the 2nd Derivative	f(x)=-x^3-12x^2-45x+2	$f (x) = - x^{3} - 12 x^{2} - 45 x + 2$
31356	Evaluate the Limit	( limit as x approaches 0 of e^x-1)/(2x)	$\frac{lim_{x \to 0} e^{x} - 1}{2 x}$
31357	Evaluate the Limit	( limit as x approaches 0 of e^x-x-1)/(x^2)	$\frac{lim_{x \to 0} e^{x} - x - 1}{x^{2}}$
31358	Evaluate the Summation	sum from n=1 to 8 of 2^n	$\sum_{n = 1}^{8} 2^{n}$
31359	Evaluate the Limit	( limit as x approaches 0 of arcsin(x))/(sin(x))	$\frac{lim_{x \to 0} \arcsin (x)}{\sin (x)}$
31360	Evaluate the Summation	sum from k=1 to 4 of (-1)^k(k+11)	$\sum_{k = 1}^{4} {(- 1)}^{k} (k + 11)$
31361	Evaluate the Limit	( limit as x approaches 0 of sin(x)^2)/(1-cos(x))	$\frac{lim_{x \to 0} \sin^{2} (x)}{1 - \cos (x)}$
31362	Evaluate the Limit	( limit as x approaches 0 of 2sec(3x)-2)/(3xsec(3x))	$\frac{lim_{x \to 0} 2 \sec (3 x) - 2}{3 x \sec (3 x)}$
31363	Evaluate the Limit	( limit as x approaches 0 of 3cos(2x)-3)/(2xcos(2x))	$\frac{lim_{x \to 0} 3 \cos (2 x) - 3}{2 x \cos (2 x)}$
31364	Evaluate the Limit	( limit as x approaches 0 of 3x)/(cot(4x))	$\frac{lim_{x \to 0} 3 x}{\cot (4 x)}$
31365	Evaluate the Limit	( limit as x approaches 0 of 5x^3-2x^2)/(sin(x))	$\frac{lim_{x \to 0} 5 x^{3} - 2 x^{2}}{\sin (x)}$
31366	Evaluate the Limit	( limit as x approaches 0 of 5cos(0.01)-5)/0.01	$\frac{lim_{x \to 0} 5 \cos (0.01) - 5}{0.01}$
31367	Evaluate the Limit	( limit as x approaches 0 of 5x)/(tan(3x))	$\frac{lim_{x \to 0} 5 x}{\tan (3 x)}$
31368	Evaluate the Limit	( limit as x approaches 0 of (5x-5sin(x))*2)/(x^2)	$\frac{lim_{x \to 0} (5 x - 5 \sin (x)) \cdot 2}{x^{2}}$
31369	Evaluate the Limit	( limit as x approaches 0 of 6x^2-2x)/(3x)	$\frac{lim_{x \to 0} 6 x^{2} - 2 x}{3 x}$
31370	Evaluate the Limit	( limit as x approaches 0 of cos(2x)-cos(x))/(2^2)	$\frac{lim_{x \to 0} \cos (2 x) - \cos (x)}{2^{2}}$
31371	Evaluate the Limit	( limit as x approaches 0 of cos(6x)-1)/(sin(7x))	$\frac{lim_{x \to 0} \cos (6 x) - 1}{\sin (7 x)}$
31372	Evaluate the Summation	sum from k=1 to 550 of 2k+50	$\sum_{k = 1}^{550} 2 k + 50$
31373	Evaluate the Limit	( limit as x approaches 0 of sec(9x)-1)/(xsin(6x))	$\frac{lim_{x \to 0} \sec (9 x) - 1}{x \sin (6 x)}$
31374	Evaluate the Limit	( limit as x approaches 0 of sin(2x))/(sin(5x))	$\frac{lim_{x \to 0} \sin (2 x)}{\sin (5 x)}$
31375	Evaluate the Limit	( limit as x approaches 0 of sin(3)x)/x	$\frac{lim_{x \to 0} \sin (3) x}{x}$
31376	Evaluate the Limit	( limit as x approaches 0 of sin(3x)+tan(5x))/x	$\frac{lim_{x \to 0} \sin (3 x) + \tan (5 x)}{x}$
31377	Evaluate the Limit	( limit as x approaches 0 of sin(3x)cot(5x))/(xcot(4x))	$\frac{lim_{x \to 0} \sin (3 x) \cot (5 x)}{x \cot (4 x)}$
31378	Evaluate the Limit	( limit as x approaches 0 of sin(4x)sec(2x))/(7x)	$\frac{lim_{x \to 0} \sin (4 x) \sec (2 x)}{7 x}$
31379	Evaluate the Limit	( limit as x approaches 0 of sin(6x))/(4x)	$\frac{lim_{x \to 0} \sin (6 x)}{4 x}$
31380	Evaluate the Limit	( limit as x approaches 0 of sin(9x))/x	$\frac{lim_{x \to 0} \sin (9 x)}{x}$
31381	Evaluate the Limit	limit as x approaches 0 of (tan(x/x))^(1/(x^2))
31382	Evaluate the Limit	( limit as x approaches 0 of tan(x)-sin(x))/(sin(x)^3)	$\frac{lim_{x \to 0} \tan (x) - \sin (x)}{\sin^{3} (x)}$
31383	Evaluate the Limit	( limit as x approaches 0 of tan(x)-sin(x))/(x^3)	$\frac{lim_{x \to 0} \tan (x) - \sin (x)}{x^{3}}$
31384	Evaluate the Limit	( limit as x approaches 0 of x+sin(x))/(tan(x))	$\frac{lim_{x \to 0} x + \sin (x)}{\tan (x)}$
31385	Evaluate the Limit	( limit as x approaches 0 of xcsc(x)+1)/(xcsc(x))	$\frac{lim_{x \to 0} x \csc (x) + 1}{x \csc (x)}$
31386	Evaluate the Limit	( limit as x approaches 0 of xsin(x))/(2-2cos(x))	$\frac{lim_{x \to 0} x \sin (x)}{2 - 2 \cos (x)}$
31387	Evaluate the Limit	( limit as x approaches 0 of (1/(x+4))-1/4)/x	$\frac{lim_{x \to 0} (\frac{1}{x + 4}) - \frac{1}{4}}{x}$
31388	Evaluate the Limit	( limit as x approaches 0 of (0.001)^3+15(0.001)^2)/((0.001)^2)	$\frac{lim_{x \to 0} {(0.001)}^{3} + 15 {(0.001)}^{2}}{{(0.001)}^{2}}$
31389	Evaluate the Limit	( limit as x approaches 0 of (0.001)^3+4(0.001)^2)/((0.001)^2)	$\frac{lim_{x \to 0} {(0.001)}^{3} + 4 {(0.001)}^{2}}{{(0.001)}^{2}}$
31390	Evaluate the Limit	( limit as x approaches 0 of (-0.01)^2+4(-0.01))/-0.01	$\frac{lim_{x \to 0} {(- 0.01)}^{2} + 4 (- 0.01)}{- 0.01}$
31391	Evaluate the Limit	( limit as x approaches 0 of (-0.01)^2+9(-0.01))/-0.01	$\frac{lim_{x \to 0} {(- 0.01)}^{2} + 9 (- 0.01)}{- 0.01}$
31392	Evaluate the Limit	( limit as x approaches 0 of (-0.1)^2+4(-0.1))/-0.1	$\frac{lim_{x \to 0} {(- 0.1)}^{2} + 4 (- 0.1)}{- 0.1}$
31393	Evaluate the Limit	( limit as x approaches 0 of (-0.1)^3+4(-0.1)^2)/((-0.1)^2)	$\frac{lim_{x \to 0} {(- 0.1)}^{3} + 4 {(- 0.1)}^{2}}{{(- 0.1)}^{2}}$
31394	Evaluate the Limit	( limit as x approaches 0 of (13+x)^2-169)/x	$\frac{lim_{x \to 0} {(13 + x)}^{2} - 169}{x}$
31395	Evaluate the Limit	( limit as x approaches 0 of (4+x)^3-64)/x	$\frac{lim_{x \to 0} {(4 + x)}^{3} - 64}{x}$
31396	Evaluate the Limit	( limit as x approaches 0 of (6+7x)^3-216)/x	$\frac{lim_{x \to 0} {(6 + 7 x)}^{3} - 216}{x}$
31397	Evaluate the Limit	( limit as x approaches 0 of sin(7x)^2)/(sin(11x)^2)	$\frac{lim_{x \to 0} \sin^{2} (7 x)}{\sin^{2} (11 x)}$
31398	Evaluate the Limit	( limit as x approaches 0 of sin(8x)^2)/(t^2)	$\frac{lim_{x \to 0} \sin^{2} (8 x)}{t^{2}}$
31399	Evaluate the Summation	sum from i=1 to infinity of 0.5^i	$\sum_{i = 1}^{\infty} {(0.5)}^{i}$
31400	Evaluate the Limit	( limit as x approaches 0 of (x-t)^2-x^2)/t	$\frac{lim_{x \to 0} {(x - t)}^{2} - x^{2}}{t}$