Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
32601	Evaluate the Limit	limit as x approaches (pi/4) of sin(x)	$lim_{x \to (\frac{π}{4})} \sin (x)$
32602	Evaluate the Limit	limit as t approaches 0 of (tan(t))/t	$lim_{t \to 0} \frac{\tan (t)}{t}$
32603	Evaluate the Limit	limit as t approaches 0 of (( square root of 1+t)-( square root of 1-t))/t	$lim_{t \to 0} \frac{(\sqrt{1 + t}) - (\sqrt{1 - t})}{t}$
32604	Evaluate the Limit	limit as t approaches 0 of (e^t-1)/(t^5)	$lim_{t \to 0} \frac{e^{t} - 1}{t^{5}}$
32605	Evaluate the Limit	limit as t approaches 0 of (sin(t/2)^2)/(sin(t))	$lim_{t \to 0} \frac{\sin^{2} (\frac{t}{2})}{\sin (t)}$
32606	Evaluate the Limit	limit as t approaches 0 of (e^(6t)-1)/t	$lim_{t \to 0} \frac{e^{6 t} - 1}{t}$
32607	Evaluate the Limit	limit as t approaches 0 of (e^(7t)-1)/(sin(t))	$lim_{t \to 0} \frac{e^{7 t} - 1}{\sin (t)}$
32608	Evaluate the Limit	limit as t approaches 0 of (t^2)/(1-cos(t)^2)	$lim_{t \to 0} \frac{t^{2}}{1 - \cos^{2} (t)}$
32609	Evaluate the Limit	limit as t approaches 0 of (t^2)/(1-cos(t))	$lim_{t \to 0} \frac{t^{2}}{1 - \cos (t)}$
32610	Evaluate the Limit	limit as t approaches 0 of (tan(3t)^2)/(2t)	$lim_{t \to 0} \frac{\tan^{2} (3 t)}{2 t}$
32611	Find the Derivative - d/dX	y=X^2-8X	$y = X^{2} - 8 X$
32612	Evaluate the Limit	limit as t approaches 0 of (1-cos(2t))/(sin(t))	$lim_{t \to 0} \frac{1 - \cos (2 t)}{\sin (t)}$
32613	Find the Derivative - d/dx	y=e^(-13x)	$y = e^{- 13 x}$
32614	Evaluate the Limit	limit as t approaches 0 from the left of (sin(1/t)^2)*3^(1/t)	$lim_{t \to 0} (\sin^{2} (\frac{1}{t})) \cdot 3^{\frac{1}{t}}$
32615	Evaluate the Limit	limit as t approaches 0 of (sin(4t))/(sin(5t))	$lim_{t \to 0} \frac{\sin (4 t)}{\sin (5 t)}$
32616	Evaluate the Limit	limit as t approaches 0 of (sin(5t))/(8t)	$lim_{t \to 0} \frac{\sin (5 t)}{8 t}$
32617	Evaluate the Limit	limit as t approaches 0 of t/(cot(5t))	$lim_{t \to 0} \frac{t}{\cot (5 t)}$
32618	Evaluate the Limit	limit as theta approaches 0 of theta/(sin(theta))	$lim_{θ \to 0} \frac{θ}{\sin (θ)}$
32619	Evaluate the Limit	limit as t approaches 0 of -2sin((mt+nt)/2)sin((mt-nt)/2)	$lim_{t \to 0} - 2 \sin (\frac{m t + n t}{2}) \sin (\frac{m t - n t}{2})$
32620	Evaluate the Limit	limit as t approaches 0 of arctan(t)	$lim_{t \to 0} \arctan (t)$
32621	Evaluate the Limit	limit as t approaches 0 of cos(pi/( square root of 17-cos(t)))	$lim_{t \to 0} \cos (\frac{π}{\sqrt{17 - \cos (t)}})$
32622	Evaluate the Limit	limit as t approaches 0 of cos(pi/( square root of 19-3sec(2t)))	$lim_{t \to 0} \cos (\frac{π}{\sqrt{19 - 3 \sec (2 t)}})$
32623	Evaluate the Limit	limit as t approaches 0 of sin(pi/2*cos(tan(t)))	$lim_{t \to 0} \sin (\frac{π}{2} \cdot \cos (\tan (t)))$
32624	Evaluate the Limit	limit as t approaches 0 of tan(((5pi)/4)-((pisin(t))/t))	$lim_{t \to 0} \tan ((\frac{5 π}{4}) - (\frac{π \sin (t)}{t}))$
32625	Evaluate the Limit	limit as t approaches 0 of tan(11/4*pi-(pisin(t))/t)	$lim_{t \to 0} \tan (\frac{11}{4} \cdot π - \frac{π \sin (t)}{t})$
32626	Evaluate the Limit	limit as t approaches 0 of tan(4pi-(pisin(t))/t)	$lim_{t \to 0} \tan (4 π - \frac{π \sin (t)}{t})$
32627	Evaluate the Limit	limit as t approaches 0 of tsin(1/t)	$lim_{t \to 0} t \sin (\frac{1}{t})$
32628	Evaluate the Limit	limit as t approaches 0 from the right of t natural log of t	$lim_{t \to 0} t \ln (t)$
32629	Evaluate the Limit	limit as t approaches 1 of (t^2+t-2)/(t^2-1)	$lim_{t \to 1} \frac{t^{2} + t - 2}{t^{2} - 1}$
32630	Evaluate the Limit	limit as t approaches 1 of (t^3-t)/(t^2-1)	$lim_{t \to 1} \frac{t^{3} - t}{t^{2} - 1}$
32631	Evaluate the Limit	limit as t approaches -1 of (t^2+1)^4(t+4)^5	$lim_{t \to - 1} {(t^{2} + 1)}^{4} {(t + 4)}^{5}$
32632	Evaluate the Limit	limit as t approaches 1 of (t^2+3t-4)/(t^2-1)	$lim_{t \to 1} \frac{t^{2} + 3 t - 4}{t^{2} - 1}$
32633	Evaluate the Limit	limit as t approaches -1 of (t^3+1)/(t^2-1)	$lim_{t \to - 1} \frac{t^{3} + 1}{t^{2} - 1}$
32634	Evaluate the Limit	limit as t approaches 1 of (t^3-1)/(3t^2-4t+1)	$lim_{t \to 1} \frac{t^{3} - 1}{3 t^{2} - 4 t + 1}$
32635	Evaluate the Limit	limit as t approaches 1 of (t^3-2t^2+1)/(t^3-1)	$lim_{t \to 1} \frac{t^{3} - 2 t^{2} + 1}{t^{3} - 1}$
32636	Evaluate the Limit	limit as t approaches 1 of 3(t-1)(t-6)	$lim_{t \to 1} 3 (t - 1) (t - 6)$
32637	Evaluate the Limit	limit as t approaches 1 of sin(pit)	$lim_{t \to 1} \sin (π t)$
32638	Evaluate the Limit	limit as t approaches 10 of 250(0.90)^t	$lim_{t \to 10} 250 {(0.9)}^{t}$
32639	Evaluate the Limit	limit as t approaches 10 of 500(0.80)	$lim_{t \to 10} 500 (0.8)$
32640	Evaluate the Limit	limit as t approaches 100 of ( square root of t-10)/(t-100)	$lim_{t \to 100} \frac{\sqrt{t - 10}}{t - 100}$
32641	Evaluate the Limit	limit as t approaches 12 of (t^2+3t-180)/(t^2-144)	$lim_{t \to 12} \frac{t^{2} + 3 t - 180}{t^{2} - 144}$
32642	Evaluate the Limit	limit as t approaches 2 of (t^2-4)/(2t^2-2t-12)	$lim_{t \to 2} \frac{t^{2} - 4}{2 t^{2} - 2 t - 12}$
32643	Evaluate the Limit	limit as x approaches -2 of (x^4-2)/(2x^2-3x+2)	$lim_{x \to - 2} \frac{x^{4} - 2}{2 x^{2} - 3 x + 2}$
32644	Evaluate the Limit	limit as t approaches 2 of (t^3-8)/(t-2)	$lim_{t \to 2} \frac{t^{3} - 8}{t - 2}$
32645	Find the Derivative - d/dx	(8x^7)/(5y^4)	$\frac{8 x^{7}}{5 y^{4}}$
32646	Evaluate the Limit	limit as t approaches 2 of ((t^2-2)/(t^3-3t+5))^2	$lim_{t \to 2} {(\frac{t^{2} - 2}{t^{3} - 3 t + 5})}^{2}$
32647	Evaluate the Limit	limit as t approaches 2 of (t^2+3t-10)/(t^2-4)	$lim_{t \to 2} \frac{t^{2} + 3 t - 10}{t^{2} - 4}$
32648	Evaluate the Limit	limit as t approaches 2 of (t^2-3t+2)/(t^2-4)	$lim_{t \to 2} \frac{t^{2} - 3 t + 2}{t^{2} - 4}$
32649	Evaluate the Limit	limit as t approaches 2 of (t^2-t-2)/(t^2+3t-10)	$lim_{t \to 2} \frac{t^{2} - t - 2}{t^{2} + 3 t - 10}$
32650	Evaluate the Limit	limit as t approaches 2 of ( square root of t- square root of 2)/(t-2)	$lim_{t \to 2} \frac{\sqrt{t} - \sqrt{2}}{t - 2}$
32651	Evaluate the Limit	limit as t approaches 2 of t^-1	$lim_{t \to 2} t^{- 1}$
32652	Evaluate the Limit	limit as t approaches 2 of t^2-4	$lim_{t \to 2} t^{2} - 4$
32653	Evaluate the Limit	limit as t approaches 2 of 12t^2-6t	$lim_{t \to 2} 12 t^{2} - 6 t$
32654	Evaluate the Limit	limit as t approaches 2 of 2t^3-3t^2	$lim_{t \to 2} 2 t^{3} - 3 t^{2}$
32655	Evaluate the Limit	limit as t approaches -2 of 7t^4-4t	$lim_{t \to - 2} 7 t^{4} - 4 t$
32656	Evaluate the Limit	limit as x approaches 0/0 of fifth root of x^5-3x^4+17-x	$lim_{x \to \frac{0}{0}} \sqrt[5]{x^{5} - 3 x^{4} + 17} - x$
32657	Evaluate the Limit	limit as x approaches 2.5 of (sin(x-2))/(x^2-4)	$lim_{x \to 2.5} \frac{\sin (x - 2)}{x^{2} - 4}$
32658	Evaluate the Limit	limit as x approaches -4 of ( square root of 12-x-4)/(x+4)	$lim_{x \to - 4} \frac{\sqrt{12 - x} - 4}{x + 4}$
32659	Evaluate the Limit	limit as h approaches 0 of (x+h-x)/h	$lim_{h \to 0} \frac{x + h - x}{h}$
32660	Evaluate the Limit	limit as x approaches pi/2 of (9cos(x))/(cot(x))	$lim_{x \to \frac{π}{2}} \frac{9 \cos (x)}{\cot (x)}$
32661	Evaluate the Limit	limit as x approaches 0 of (-10+x)/(x^4)	$lim_{x \to 0} \frac{- 10 + x}{x^{4}}$
32662	Evaluate the Limit	limit as x approaches 1/0 of (3x-x^3)/(x^3+x+1)	$lim_{x \to \frac{1}{0}} \frac{3 x - x^{3}}{x^{3} + x + 1}$
32663	Evaluate the Limit	limit as x approaches 1/0 of 2-x	$lim_{x \to \frac{1}{0}} 2 - x$
32664	Evaluate the Limit	limit as x approaches 1/2 of 3xsec(pix)	$lim_{x \to \frac{1}{2}} 3 x \sec (π x)$
32665	Evaluate the Limit	limit as x approaches 1/2 of (2x+1)/(6x^2+3x)	$lim_{x \to \frac{1}{2}} \frac{2 x + 1}{6 x^{2} + 3 x}$
32666	Evaluate the Limit	limit as x approaches 1/2 of ((x-1/2)(6x^2+x-2))/(4x^2-4x+1)	$lim_{x \to \frac{1}{2}} \frac{(x - \frac{1}{2}) (6 x^{2} + x - 2)}{4 x^{2} - 4 x + 1}$
32667	Evaluate the Limit	limit as x approaches 1/2 of (x^2-5x+2)/(x^2+3x-3)	$lim_{x \to \frac{1}{2}} \frac{x^{2} - 5 x + 2}{x^{2} + 3 x - 3}$
32668	Evaluate the Limit	limit as x approaches 1/2 of (2x^2-3x-2)/(x-1/2)	$lim_{x \to \frac{1}{2}} \frac{2 x^{2} - 3 x - 2}{x - \frac{1}{2}}$
32669	Evaluate the Limit	limit as x approaches 1/2 of (2x-1)/(2x^2+9x-5)	$lim_{x \to \frac{1}{2}} \frac{2 x - 1}{2 x^{2} + 9 x - 5}$
32670	Evaluate the Limit	limit as x approaches 1/2 of (4x^2-1)/(x-1/2)	$lim_{x \to \frac{1}{2}} \frac{4 x^{2} - 1}{x - \frac{1}{2}}$
32671	Evaluate the Limit	limit as x approaches -1/2 of (4x-2)/(4x^2+1)	$lim_{x \to - \frac{1}{2}} \frac{4 x - 2}{4 x^{2} + 1}$
32672	Evaluate the Limit	limit as x approaches 1/2 of (4x-2)/(6x^2+x-2)	$lim_{x \to \frac{1}{2}} \frac{4 x - 2}{6 x^{2} + x - 2}$
32673	Evaluate the Limit	limit as x approaches -1/2 of (3x^2)(2x-1)	$lim_{x \to \frac{- 1}{2}} (3 x^{2}) (2 x - 1)$
32674	Evaluate the Limit	limit as x approaches 1/2 of xsin(1/x)	$lim_{x \to \frac{1}{2}} x \sin (\frac{1}{x})$
32675	Evaluate the Limit	limit as x approaches 1/2pi of (x-1/2pi)tan(3x)	$lim_{x \to \frac{1}{2} \cdot π} (x - \frac{1}{2} \cdot π) \tan (3 x)$
32676	Evaluate the Limit	limit as x approaches 1/25 of (2/( square root of x)-10)/(x-1/25)	$lim_{x \to \frac{1}{25}} \frac{\frac{2}{\sqrt{x}} - 10}{x - \frac{1}{25}}$
32677	Evaluate the Limit	limit as x approaches -1/3 of (9x^2-1)/(3x+1)	$lim_{x \to - \frac{1}{3}} \frac{9 x^{2} - 1}{3 x + 1}$
32678	Evaluate the Limit	limit as x approaches 1/3 of square root of (27x^3-1)/(3x-1)	$lim_{x \to \frac{1}{3}} \sqrt{\frac{27 x^{3} - 1}{3 x - 1}}$
32679	Evaluate the Limit	limit as x approaches infinity of ( square root of 11x^2+1)/(x-11)	$lim_{x \to \infty} \frac{\sqrt{11 x^{2} + 1}}{x - 11}$
32680	Evaluate the Limit	limit as x approaches 0 of (sin(6x))/(5x)	$lim_{x \to 0} \frac{\sin (6 x)}{5 x}$
32681	Evaluate the Limit	limit as x approaches 0 of (2x)/(cot(6x))	$lim_{x \to 0} \frac{2 x}{\cot (6 x)}$
32682	Evaluate the Limit	limit as x approaches infinity of 4x- square root of 16x^2-5x+6	$lim_{x \to \infty} 4 x - \sqrt{16 x^{2} - 5 x + 6}$
32683	Evaluate the Limit	limit as x approaches negative infinity of natural log of x	$lim_{x \to - \infty} \ln (x)$
32684	Evaluate the Limit	limit as x approaches negative infinity of (6x-5)/( square root of 4x^2+2)	$lim_{x \to - \infty} \frac{6 x - 5}{\sqrt{4 x^{2} + 2}}$
32685	Evaluate the Limit	limit as x approaches infinity of (x-cos(x))/x	$lim_{x \to \infty} \frac{x - \cos (x)}{x}$
32686	Evaluate the Limit	limit as x approaches 1 of (3x)/(x-1)-3/( natural log of x)	$lim_{x \to 1} \frac{3 x}{x - 1} - \frac{3}{\ln (x)}$
32687	Evaluate the Limit	limit as x approaches -1 of (x^2+8x+7)/(x^2-5x-6)	$lim_{x \to - 1} \frac{x^{2} + 8 x + 7}{x^{2} - 5 x - 6}$
32688	Find the Derivative - d/dx	x^2sin(8x)	$x^{2} \sin (8 x)$
32689	Evaluate the Limit	limit as x approaches (0.5) of (int^2)x-int^2x	$lim_{x \to (0.5)} (i n t^{2}) x - i n t^{2} x$
32690	Evaluate the Limit	limit as x approaches (-1) of (x^2+3x)/(2tan(x))	$lim_{x \to (- 1)} \frac{x^{2} + 3 x}{2 \tan (x)}$
32691	Evaluate the Limit	limit as x approaches (2) of (x^6-24x-16)/(x^3+2x-12)	$lim_{x \to (2)} \frac{x^{6} - 24 x - 16}{x^{3} + 2 x - 12}$
32692	Evaluate the Limit	limit as x approaches (-2) of (2x+6)/(x^2+x-6)	$lim_{x \to (- 2)} \frac{2 x + 6}{x^{2} + x - 6}$
32693	Evaluate the Limit	limit as x approaches (-4) of (12x^2-x-6)/(12x^2+23x-24)	$lim_{x \to (- 4)} \frac{12 x^{2} - x - 6}{12 x^{2} + 23 x - 24}$
32694	Evaluate the Limit	limit as x approaches (5) of 3	$lim_{x \to (5)} 3$
32695	Evaluate the Limit	limit as x approaches (-8) of (4+6e^(2x))/(5-9e^(3x))	$lim_{x \to (- 8)} \frac{4 + 6 e^{2 x}}{5 - 9 e^{3 x}}$
32696	Evaluate the Limit	limit as x approaches (8) of 5/(2+e^(-7x))	$lim_{x \to (8)} \frac{5}{2 + e^{- 7 x}}$
32697	Evaluate the Limit	limit as x approaches -0.1 of ( square root of x+2- square root of 2)/x	$lim_{x \to - 0.1} \frac{\sqrt{x + 2} - \sqrt{2}}{x}$
32698	Evaluate the Limit	limit as x approaches -0.2 from the right of square root of (x+5)/(x+1)	$lim_{x \to - 0.2} \sqrt{\frac{x + 5}{x + 1}}$
32699	Evaluate the Limit	limit as x approaches -0.6 of (-12x-12)/(-4x+5)	$lim_{x \to - 0.6} \frac{- 12 x - 12}{- 4 x + 5}$
32700	Evaluate the Limit	limit as x approaches -0.99 of 1/(3-2^(1/x))	$lim_{x \to - 0.99} \frac{1}{3 - 2^{\frac{1}{x}}}$