Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
30601	Evaluate the Limit	limit as x approaches 0 of (tan(3x))/x	$lim_{x \to 0} \frac{\tan (3 x)}{x}$
30602	Evaluate the Limit	limit as x approaches 0 of (tan(4t))/(sin(2t))	$lim_{x \to 0} \frac{\tan (4 t)}{\sin (2 t)}$
30603	Evaluate the Limit	limit as x approaches 0 of (tan(4x))/(6x)	$lim_{x \to 0} \frac{\tan (4 x)}{6 x}$
30604	Find the Local Maxima and Minima	y=6x^4+8x^3	$y = 6 x^{4} + 8 x^{3}$
30605	Evaluate the Limit	limit as x approaches 0 of (tan(5x))/(3x)	$lim_{x \to 0} \frac{\tan (5 x)}{3 x}$
30606	Evaluate the Limit	limit as x approaches 0 of (sin(5x)sin(4x))/(sin(4x)sin(6x))	$lim_{x \to 0} \frac{\sin (5 x) \sin (4 x)}{\sin (4 x) \sin (6 x)}$
30607	Evaluate the Limit	limit as x approaches 0 of (sin(5x+10))/(4x+8)	$lim_{x \to 0} \frac{\sin (5 x + 10)}{4 x + 8}$
30608	Evaluate the Limit	limit as x approaches 0 of (sin(6x))/(6x)	$lim_{x \to 0} \frac{\sin (6 x)}{6 x}$
30609	Evaluate the Limit	limit as x approaches 0 of (sin(6x))/(tan(7x))	$lim_{x \to 0} \frac{\sin (6 x)}{\tan (7 x)}$
30610	Evaluate the Limit	limit as x approaches 0 of (sin(7x))/(sin(6x))	$lim_{x \to 0} \frac{\sin (7 x)}{\sin (6 x)}$
30611	Evaluate the Limit	limit as x approaches 0 of (sin(8x)-8xcos(8x))/(8x-sin(8x))	$lim_{x \to 0} \frac{\sin (8 x) - 8 x \cos (8 x)}{8 x - \sin (8 x)}$
30612	Evaluate the Limit	limit as x approaches 0 of (sin(9x))/(3x)	$lim_{x \to 0} \frac{\sin (9 x)}{3 x}$
30613	Evaluate the Limit	limit as x approaches 0 of (sin(a+x)-sin(a))/x	$lim_{x \to 0} \frac{\sin (a + x) - \sin (a)}{x}$
30614	Evaluate the Limit	limit as x approaches 0 of (sin(cx))/(3x)	$lim_{x \to 0} \frac{\sin (c x)}{3 x}$
30615	Evaluate the Limit	limit as x approaches 0 of (sin(x))/( square root of x)	$lim_{x \to 0} \frac{\sin (x)}{\sqrt{x}}$
30616	Evaluate the Limit	limit as x approaches 0 of (x^2)*2.71828^(sin(1/x))	$lim_{x \to 0} (x^{2}) \cdot {2.71828}^{\sin (\frac{1}{x})}$
30617	Evaluate the Limit	limit as x approaches 0 of (x^2)csc(1)^2x	$lim_{x \to 0} (x^{2}) \csc^{2} (1) x$
30618	Evaluate the Limit	limit as x approaches 0 of (x^2)e^(sin(1/x))	$lim_{x \to 0} (x^{2}) e^{\sin (\frac{1}{x})}$
30619	Evaluate the Limit	limit as x approaches 0 of (x^2) natural log of x	$lim_{x \to 0} (x^{2}) \ln (x)$
30620	Evaluate the Limit	limit as x approaches 0 of (x^2)cos(1/x)	$lim_{x \to 0} (x^{2}) \cos (\frac{1}{x})$
30621	Evaluate the Limit	limit as x approaches 0 of (x^2)cot(x^2)	$lim_{x \to 0} (x^{2}) \cot (x^{2})$
30622	Evaluate the Limit	limit as x approaches 0 of x/(arctan(2x))	$lim_{x \to 0} \frac{x}{\arctan (2 x)}$
30623	Evaluate the Limit	limit as x approaches 0 of cube root of x^2+16x+64	$lim_{x \to 0} \sqrt[3]{x^{2} + 16 x + 64}$
30624	Evaluate the Limit	limit as x approaches 0 of cube root of 4x	$lim_{x \to 0} \sqrt[3]{4 x}$
30625	Evaluate the Limit	limit as x approaches 0 of cube root of x	$lim_{x \to 0} \sqrt[3]{x}$
30626	Evaluate the Limit	limit as x approaches 0 of sixth root of x	$lim_{x \to 0} \sqrt[6]{x}$
30627	Evaluate the Limit	limit as x approaches 0 of (xe^x-x^2)/(x^4-2x^3-x^2)	$lim_{x \to 0} \frac{x e^{x} - x^{2}}{x^{4} - 2 x^{3} - x^{2}}$
30628	Evaluate the Limit	limit as x approaches 0 of (sin(2x)-2 square root of xsin(x)+4x^2)/x	$lim_{x \to 0} \frac{\sin (2 x) - 2 \sqrt{x} \sin (x) + 4 x^{2}}{x}$
30629	Evaluate the Limit	limit as x approaches 0 of 1/(3x)	$lim_{x \to 0} \frac{1}{3 x}$
30630	Evaluate the Limit	( limit as x approaches 0 of (0)( square root of 5x+5h- square root of 5x))/h	$\frac{lim_{x \to 0} (0) (\sqrt{5 x + 5 h} - \sqrt{5 x})}{h}$
30631	Evaluate the Limit	limit as x approaches 0 of x^2cos(1/(x^2))	$lim_{x \to 0} x^{2} \cos (\frac{1}{x^{2}})$
30632	Evaluate the Limit	limit as x approaches 0 of x^2cos(20piix)	$lim_{x \to 0} x^{2} \cos (20 π i x)$
30633	Evaluate the Limit	limit as x approaches 0 of x^2cos(x)	$lim_{x \to 0} x^{2} \cos (x)$
30634	Evaluate the Limit	limit as x approaches 0 from the left of (x+5)/(cot(x))	$lim_{x \to 0} \frac{x + 5}{\cot (x)}$
30635	Evaluate the Limit	limit as x approaches 0 from the left of (x+7)/(cot(x))	$lim_{x \to 0} \frac{x + 7}{\cot (x)}$
30636	Evaluate the Limit	limit as x approaches 0 of (x+xcos(x))/(sin(x)cos(x))	$lim_{x \to 0} \frac{x + x \cos (x)}{\sin (x) \cos (x)}$
30637	Evaluate the Limit	limit as x approaches 0 of (xcos(x))/(sin(2x))	$lim_{x \to 0} \frac{x \cos (x)}{\sin (2 x)}$
30638	Evaluate the Limit	limit as x approaches 0 of (xcot(x))/(cos(x))	$lim_{x \to 0} \frac{x \cot (x)}{\cos (x)}$
30639	Evaluate the Limit	limit as x approaches 0 of xe^(sin(pi/x))	$lim_{x \to 0} x e^{\sin (\frac{π}{x})}$
30640	Evaluate the Limit	limit as x approaches 0 of (x^3)sin(pi/x)=0	$lim_{x \to 0} (x^{3}) \sin (\frac{π}{x}) = 0$
30641	Evaluate the Limit	limit as x approaches 0 of x^4-1/(x-1)	$lim_{x \to 0} x^{4} - \frac{1}{x - 1}$
30642	Evaluate the Limit	limit as x approaches 0 of x^6 natural log of x	$lim_{x \to 0} x^{6} \ln (x)$
30643	Evaluate the Limit	limit as x approaches 0 of x^7sec(x)^7	$lim_{x \to 0} x^{7} \sec^{7} (x)$
30644	Evaluate the Limit	limit as x approaches 0 of x^e	$lim_{x \to 0} x^{e}$
30645	Evaluate the Limit	limit as x approaches 0 of x^( natural log of 1+x)	$lim_{x \to 0} x^{\ln (1 + x)}$
30646	Evaluate the Limit	limit as x approaches 0 of x/(x-1)-1/( natural log of x)	$lim_{x \to 0} \frac{x}{x - 1} - \frac{1}{\ln (x)}$
30647	Evaluate the Limit	limit as x approaches 1 of (x^3-2x^2-2x-3)/(x^4-2x^3-27)	$lim_{x \to 1} \frac{x^{3} - 2 x^{2} - 2 x - 3}{x^{4} - 2 x^{3} - 27}$
30648	Evaluate the Limit	limit as x approaches 1 of (x^3-4x^2+5x-2)/(x^3-x^2-x+1)	$lim_{x \to 1} \frac{x^{3} - 4 x^{2} + 5 x - 2}{x^{3} - x^{2} - x + 1}$
30649	Evaluate the Limit	limit as x approaches 1 of (x^49-1)/( square root of x-1)	$lim_{x \to 1} \frac{x^{49} - 1}{\sqrt{x} - 1}$
30650	Evaluate the Limit	limit as x approaches 1 of (x^5-1)/(x^2-x)	$lim_{x \to 1} \frac{x^{5} - 1}{x^{2} - x}$
30651	Evaluate the Limit	limit as x approaches 1 of (x^9-1)/(x^5-1)	$lim_{x \to 1} \frac{x^{9} - 1}{x^{5} - 1}$
30652	Evaluate the Limit	limit as x approaches 1 of (1/(1-x))-(1/(1-x^3))	$lim_{x \to 1} (\frac{1}{1 - x}) - (\frac{1}{1 - x^{3}})$
30653	Evaluate the Limit	limit as h approaches 0 of (f(4+h)-f*4)/h	$lim_{h \to 0} \frac{f (4 + h) - f \cdot 4}{h}$
30654	Evaluate the Limit	limit as x approaches 1 of 1/x-1/(e^x-1)	$lim_{x \to 1} \frac{1}{x} - \frac{1}{e^{x} - 1}$
30655	Evaluate the Limit	limit as x approaches 1 of (12x^2-5x)/x	$lim_{x \to 1} \frac{12 x^{2} - 5 x}{x}$
30656	Evaluate the Limit	limit as x approaches 1 of (1-x+ natural log of x)/(1+cos(7pix))	$lim_{x \to 1} \frac{1 - x + \ln (x)}{1 + \cos (7 π x)}$
30657	Evaluate the Limit	limit as x approaches 1 of (2x^3-54)/(x^2-9)	$lim_{x \to 1} \frac{2 x^{3} - 54}{x^{2} - 9}$
30658	Evaluate the Limit	limit as x approaches -1 of (x^2-1)/(\|x\|-1)	$lim_{x \to - 1} \frac{x^{2} - 1}{\| x \| - 1}$
30659	Evaluate the Limit	limit as x approaches 1 of (arctan(x))/(arcsin(x+1))	$lim_{x \to 1} \frac{\arctan (x)}{\arcsin (x + 1)}$
30660	Evaluate the Limit	limit as x approaches 1 of (g(x)h(x))/(f(x))	$lim_{x \to 1} \frac{g (x) h (x)}{f (x)}$
30661	Evaluate the Limit	limit as x approaches 1 of ( natural log of 6x^2+5x-10)/(2x^2-2)	$lim_{x \to 1} \frac{\ln (6 x^{2} + 5 x - 10)}{2 x^{2} - 2}$
30662	Evaluate the Limit	limit as x approaches 1 of ( natural log of x)/(4x-x^2-3)	$lim_{x \to 1} \frac{\ln (x)}{4 x - x^{2} - 3}$
30663	Evaluate the Limit	limit as x approaches 1 of (x-x^3)/(x-1)	$lim_{x \to 1} \frac{x - x^{3}}{x - 1}$
30664	Evaluate the Limit	limit as x approaches -1 of (\|t+1\|)/(t+1)	$lim_{x \to - 1} \frac{\| t + 1 \|}{t + 1}$
30665	Evaluate the Limit	limit as x approaches 1 of (2x^2-x+1)/(3x-2)	$lim_{x \to 1} \frac{2 x^{2} - x + 1}{3 x - 2}$
30666	Evaluate the Limit	limit as x approaches 1 of (tan(2x-2)^2)/(x^2-2x+1)	$lim_{x \to 1} \frac{\tan^{2} (2 x - 2)}{x^{2} - 2 x + 1}$
30667	Evaluate the Limit	limit as x approaches 1 of ( square root of 5-x-2)/( square root of 10-x-3)	$lim_{x \to 1} \frac{\sqrt{5 - x} - 2}{\sqrt{10 - x} - 3}$
30668	Evaluate the Limit	limit as h approaches 0 of ( square root of 5h+1-1)/h	$lim_{h \to 0} \frac{\sqrt{5 h + 1} - 1}{h}$
30669	Evaluate the Limit	limit as x approaches -1 of (x^13+1)/(x+1)	$lim_{x \to - 1} \frac{x^{13} + 1}{x + 1}$
30670	Evaluate the Limit	limit as h approaches 0 of ( square root of 7h+1-1)/h	$lim_{h \to 0} \frac{\sqrt{7 h + 1} - 1}{h}$
30671	Evaluate the Limit	limit as x approaches 1 of (2-t)/((t-1)^2)	$lim_{x \to 1} \frac{2 - t}{{(t - 1)}^{2}}$
30672	Evaluate the Limit	limit as x approaches 0 from the right of x^( square root of x)	$lim_{x \to 0} x^{\sqrt{x}}$
30673	Evaluate the Limit	limit as x approaches 0 from the right of x^(x^2)	$lim_{x \to 0} x^{x^{2}}$
30674	Evaluate the Limit	limit as x approaches 0 from the right of x^1.4* natural log of x	$lim_{x \to 0} x^{1.4} \cdot \ln (x)$
30675	Evaluate the Limit	limit as x approaches 0 from the right of x^2+4	$lim_{x \to 0} x^{2} + 4$
30676	Evaluate the Limit	limit as x approaches 0 from the right of x^(2x)	$lim_{x \to 0} x^{2 x}$
30677	Evaluate the Limit	limit as x approaches 0 from the right of 12sin(x)^(14x)	$lim_{x \to 0} 12 {\sin (x)}^{14 x}$
30678	Evaluate the Limit	limit as x approaches 0 from the right of 6sin(x) natural log of x	$lim_{x \to 0} 6 \sin (x) \ln (x)$
30679	Evaluate the Limit	limit as x approaches 0 from the right of sin(x)* natural log of x	$lim_{x \to 0} \sin (x) \cdot \ln (x)$
30680	Evaluate the Limit	limit as x approaches 0 from the right of sin(x) natural log of 4x	$lim_{x \to 0} \sin (x) \ln (4 x)$
30681	Evaluate the Limit	limit as x approaches 0 from the right of tan(x) natural log of x	$lim_{x \to 0} \tan (x) \ln (x)$
30682	Evaluate the Limit	limit as x approaches 1 of (8/(1-x))-(16/(1-x^2))	$lim_{x \to 1} (\frac{8}{1 - x}) - (\frac{16}{1 - x^{2}})$
30683	Evaluate the Limit	limit as x approaches 1 of ( natural log of (x)^2)/(x-1)	$lim_{x \to 1} \frac{\ln ({(x)}^{2})}{x - 1}$
30684	Evaluate the Limit	limit as x approaches -1 of (x^2-3)/(x^2+1)	$lim_{x \to - 1} \frac{x^{2} - 3}{x^{2} + 1}$
30685	Evaluate the Limit	limit as x approaches 1 of (x^2-9)/(x^2+2x-3)	$lim_{x \to 1} \frac{x^{2} - 9}{x^{2} + 2 x - 3}$
30686	Evaluate the Limit	limit as x approaches 1 of (x^5-1)/(x-1)	$lim_{x \to 1} \frac{x^{5} - 1}{x - 1}$
30687	Evaluate the Limit	limit as x approaches 0 from the right of 7/x-7/(\|x\|)	$lim_{x \to 0} \frac{7}{x} - \frac{7}{\| x \|}$
30688	Evaluate the Limit	limit as x approaches 0 from the right of (9sin(x))/(6\|x\|)	$lim_{x \to 0} \frac{9 \sin (x)}{6 \| x \|}$
30689	Evaluate the Limit	limit as x approaches 0 from the right of (sin(x))tan(x)	$lim_{x \to 0} (\sin (x)) \tan (x)$
30690	Evaluate the Limit	limit as x approaches 0 from the right of (3-2e^x)^(5/x)	$lim_{x \to 0} {(3 - 2 e^{x})}^{\frac{5}{x}}$
30691	Evaluate the Limit	limit as x approaches 0 from the right of tan(3x)^x	$lim_{x \to 0} {\tan (3 x)}^{x}$
30692	Evaluate the Limit	limit as x approaches 0 from the right of (x-3)/(x^2)	$lim_{x \to 0} \frac{x - 3}{x^{2}}$
30693	Evaluate the Limit	limit as x approaches 0 from the right of ( square root of h^2+4h+5- square root of 5)/h	$lim_{x \to 0} \frac{\sqrt{h^{2} + 4 h + 5} - \sqrt{5}}{h}$
30694	Evaluate the Limit	limit as x approaches 0 from the right of ( square root of x)/( natural log of x+1)	$lim_{x \to 0} \frac{\sqrt{x}}{\ln (x + 1)}$
30695	Evaluate the Limit	limit as x approaches 0 from the right of 1/(t square root of 1+t)-1/t	$lim_{x \to 0} \frac{1}{t \sqrt{1 + t}} - \frac{1}{t}$
30696	Evaluate the Limit	limit as x approaches -3 of square root of 9x+89	$lim_{x \to - 3} \sqrt{9 x + 89}$
30697	Evaluate the Limit	limit as x approaches 0 from the right of (6sin(x))/(9\|x\|)	$lim_{x \to 0} \frac{6 \sin (x)}{9 \| x \|}$
30698	Evaluate the Limit	limit as x approaches 0 from the right of (cos(x))/x	$lim_{x \to 0} \frac{\cos (x)}{x}$
30699	Evaluate the Limit	limit as x approaches 0 from the right of cos(x)^(7/(x^2))	$lim_{x \to 0} {\cos (x)}^{\frac{7}{x^{2}}}$
30700	Evaluate the Limit	limit as x approaches 0 from the right of e^(2x)	$lim_{x \to 0} e^{2 x}$