Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
32801	Evaluate the Limit	limit as x approaches pi/2 of (cos(3x))/(1+cos(2x))	$lim_{x \to \frac{π}{2}} \frac{\cos (3 x)}{1 + \cos (2 x)}$
32802	Evaluate the Limit	limit as x approaches -pi/2 of (cos(8x))/(2x-sin(cos(x)))	$lim_{x \to - \frac{π}{2}} \frac{\cos (8 x)}{2 x - \sin (\cos (x))}$
32803	Evaluate the Limit	limit as x approaches pi/2 of (cos(x))/x	$lim_{x \to \frac{π}{2}} \frac{\cos (x)}{x}$
32804	Evaluate the Limit	limit as x approaches pi/2 of (csc(x)-1)/(2cot(x))	$lim_{x \to \frac{π}{2}} \frac{\csc (x) - 1}{2 \cot (x)}$
32805	Evaluate the Limit	limit as x approaches pi/2 of (sin(x))/(1+cos(2x))	$lim_{x \to \frac{π}{2}} \frac{\sin (x)}{1 + \cos (2 x)}$
32806	Evaluate the Limit	limit as x approaches pi/2 of (tan(2pi))/(x-pi/2)	$lim_{x \to \frac{π}{2}} \frac{\tan (2 π)}{x - \frac{π}{2}}$
32807	Evaluate the Limit	limit as x approaches pi/2 of (tan(4x))/(tan(5x))	$lim_{x \to \frac{π}{2}} \frac{\tan (4 x)}{\tan (5 x)}$
32808	Evaluate the Limit	limit as x approaches pi/2 of (tan(x-(pi/2)))/(2x-pi)	$lim_{x \to \frac{π}{2}} \frac{\tan (x - (\frac{π}{2}))}{2 x - π}$
32809	Evaluate the Limit	limit as x approaches pi/2 of (tan(x))/(21(2x-pi))	$lim_{x \to \frac{π}{2}} \frac{\tan (x)}{21 (2 x - π)}$
32810	Evaluate the Limit	limit as x approaches pi/2 of (tan(x))/x	$lim_{x \to \frac{π}{2}} \frac{\tan (x)}{x}$
32811	Evaluate the Limit	limit as x approaches pi/2 of tan(x)-sec(x)	$lim_{x \to \frac{π}{2}} \tan (x) - \sec (x)$
32812	Evaluate the Limit	limit as x approaches pi/3 of (cos(x)-0.5)/(x-pi/3)	$lim_{x \to \frac{π}{3}} \frac{\cos (x) - 0.5}{x - \frac{π}{3}}$
32813	Evaluate the Limit	limit as x approaches pi/3 of (sin(3x))/(1-2cos(x))	$lim_{x \to \frac{π}{3}} \frac{\sin (3 x)}{1 - 2 \cos (x)}$
32814	Evaluate the Limit	limit as x approaches pi/3 of (sin(x)-( square root of 3)/2)/(x-pi/3)	$lim_{x \to \frac{π}{3}} \frac{\sin (x) - \frac{\sqrt{3}}{2}}{x - \frac{π}{3}}$
32815	Evaluate the Limit	limit as x approaches pi/3 of (tan(x)- square root of 3)/(x-pi/3)	$lim_{x \to \frac{π}{3}} \frac{\tan (x) - \sqrt{3}}{x - \frac{π}{3}}$
32816	Evaluate the Limit	limit as x approaches pi/4 of 1/(tan(x-1))-2/(tan(x)^2-1)	$lim_{x \to \frac{π}{4}} \frac{1}{\tan (x - 1)} - \frac{2}{\tan^{2} (x) - 1}$
32817	Evaluate the Limit	limit as x approaches pi/4 of 3cos(x)	$lim_{x \to \frac{π}{4}} 3 \cos (x)$
32818	Evaluate the Limit	limit as x approaches pi/4 of (tan(x)-1)*sec(2x)	$lim_{x \to \frac{π}{4}} (\tan (x) - 1) \cdot \sec (2 x)$
32819	Find the Derivative - d/dx	1/(6x^(5/6))	$\frac{1}{6 x^{\frac{5}{6}}}$
32820	Evaluate the Limit	limit as x approaches pi/4 of (cos(x)(sin(x)-1))/(cos(x)-sin(x))	$lim_{x \to \frac{π}{4}} \frac{\cos (x) (\sin (x) - 1)}{\cos (x) - \sin (x)}$
32821	Evaluate the Limit	limit as x approaches pi/4 of (tan(x)-1)/(x-pi/4)	$lim_{x \to \frac{π}{4}} \frac{\tan (x) - 1}{x - \frac{π}{4}}$
32822	Evaluate the Limit	limit as x approaches pi/4 of (1-tan(x))/(cos(x)-sin(x))	$lim_{x \to \frac{π}{4}} \frac{1 - \tan (x)}{\cos (x) - \sin (x)}$
32823	Evaluate the Limit	limit as x approaches pi/4 of (1-tan(x))/(cot(2x))	$lim_{x \to \frac{π}{4}} \frac{1 - \tan (x)}{\cot (2 x)}$
32824	Evaluate the Limit	limit as x approaches pi/4 of (1-tan(x))/(sin(x)+cos(x))	$lim_{x \to \frac{π}{4}} \frac{1 - \tan (x)}{\sin (x) + \cos (x)}$
32825	Evaluate the Limit	limit as x approaches pi/4 of (cot(x)-1)/(x-pi/4)	$lim_{x \to \frac{π}{4}} \frac{\cot (x) - 1}{x - \frac{π}{4}}$
32826	Evaluate the Limit	limit as x approaches pi/4 of (sin(t))/t	$lim_{x \to \frac{π}{4}} \frac{\sin (t)}{t}$
32827	Evaluate the Limit	limit as x approaches pi/2 of x^2cos(x)	$lim_{x \to \frac{π}{2}} x^{2} \cos (x)$
32828	Evaluate the Limit	limit as x approaches pi/2 of 1-(sin(x))/(1+cos(2x))	$lim_{x \to \frac{π}{2}} 1 - \frac{\sin (x)}{1 + \cos (2 x)}$
32829	Evaluate the Limit	limit as x approaches -pi/2 of 2sec(2x)	$lim_{x \to - \frac{π}{2}} 2 \sec (2 x)$
32830	Find the Derivative - d/d@VAR	f(x)=(4x-7)^(1/2)	$f (x) = {(4 x - 7)}^{\frac{1}{2}}$
32831	Evaluate the Limit	limit as x approaches pi/2 of (cos(pi/8x)pi)/8	$lim_{x \to \frac{π}{2}} \frac{\cos (\frac{π}{8} x) π}{8}$
32832	Evaluate the Limit	limit as x approaches pi/2 from the left of natural log of cos(x)	$lim_{x \to \frac{π}{2}} \ln (\cos (x))$
32833	Evaluate the Limit	limit as x approaches pi/2 of natural log of sin(x)	$lim_{x \to \frac{π}{2}} \ln (\sin (x))$
32834	Evaluate the Limit	limit as x approaches pi/2 of sec(x)-(tan(x))/(pi-2x)	$lim_{x \to \frac{π}{2}} \sec (x) - \frac{\tan (x)}{π - 2 x}$
32835	Evaluate the Limit	limit as x approaches 1/4 of 4/( square root of x)	$lim_{x \to \frac{1}{4}} \frac{4}{\sqrt{x}}$
32836	Evaluate the Limit	limit as x approaches 1/5 of (-2-15x)/(50x^2+4)	$lim_{x \to \frac{1}{5}} \frac{- 2 - 15 x}{50 x^{2} + 4}$
32837	Evaluate the Limit	limit as x approaches infinity of (-x^7-6x^2+12)/(x^3+5x^2+1)	$lim_{x \to \infty} \frac{- x^{7} - 6 x^{2} + 12}{x^{3} + 5 x^{2} + 1}$
32838	Evaluate the Limit	limit as x approaches e^2 of ( log of x)/( log of e)	$lim_{x \to e^{2}} \frac{\log (x)}{\log (e)}$
32839	Evaluate the Limit	limit as x approaches 4 of ( square root of x-2)/(x^3-64)	$lim_{x \to 4} \frac{\sqrt{x} - 2}{x^{3} - 64}$
32840	Find the Derivative - d/d@VAR	B(y)=cy^-5	$B (y) = c y^{- 5}$
32841	Evaluate the Limit	limit as x approaches 0 of (1-tan(x))/(sin(x)-cos(x))	$lim_{x \to 0} \frac{1 - \tan (x)}{\sin (x) - \cos (x)}$
32842	Evaluate the Limit	limit as x approaches 0 of (2x)/(x^2+5)	$lim_{x \to 0} \frac{2 x}{x^{2} + 5}$
32843	Evaluate the Limit	limit as x approaches 0 of (2x+sin(3x))/(x-tan(6x))	$lim_{x \to 0} \frac{2 x + \sin (3 x)}{x - \tan (6 x)}$
32844	Evaluate the Limit	limit as x approaches 0 of (2x-3)/(3x+4)	$lim_{x \to 0} \frac{2 x - 3}{3 x + 4}$
32845	Evaluate the Limit	limit as x approaches 0 of (3sin(x))/(4x)	$lim_{x \to 0} \frac{3 \sin (x)}{4 x}$
32846	Evaluate the Limit	limit as x approaches 0 of (3tan(x)-2x-2+4x^2)/(2x^4)	$lim_{x \to 0} \frac{3 \tan (x) - 2 x - 2 + 4 x^{2}}{2 x^{4}}$
32847	Evaluate the Limit	limit as x approaches 0 of (4(e^(2x)-1))/(e^x-1)	$lim_{x \to 0} \frac{4 (e^{2 x} - 1)}{e^{x} - 1}$
32848	Evaluate the Limit	limit as x approaches 0 of (5(1-cos(x)))/x	$lim_{x \to 0} \frac{5 (1 - \cos (x))}{x}$
32849	Evaluate the Limit	limit as x approaches 0 of (5/x)tan(x)	$lim_{x \to 0} (\frac{5}{x}) \tan (x)$
32850	Evaluate the Limit	limit as x approaches 0 of (5sin(x))/3+2/(1-cos(x))	$lim_{x \to 0} \frac{5 \sin (x)}{3} + \frac{2}{1 - \cos (x)}$
32851	Evaluate the Limit	limit as x approaches 0 of (5x)/(sin(2x))+(tan(6x))/(4x)	$lim_{x \to 0} \frac{5 x}{\sin (2 x)} + \frac{\tan (6 x)}{4 x}$
32852	Evaluate the Limit	limit as x approaches 0 of (5x+6)/x	$lim_{x \to 0} \frac{5 x + 6}{x}$
32853	Evaluate the Limit	limit as x approaches 0 of (6x)/(4- square root of x+16)	$lim_{x \to 0} \frac{6 x}{4 - \sqrt{x + 16}}$
32854	Evaluate the Limit	limit as x approaches 0 of (x^2+4x)/x	$lim_{x \to 0} \frac{x^{2} + 4 x}{x}$
32855	Evaluate the Limit	limit as x approaches 0 of (x^2-3x)/x	$lim_{x \to 0} \frac{x^{2} - 3 x}{x}$
32856	Evaluate the Limit	limit as x approaches 0 of (x^4+3x+2)/(5-9x^2-12x^3)	$lim_{x \to 0} \frac{x^{4} + 3 x + 2}{5 - 9 x^{2} - 12 x^{3}}$
32857	Evaluate the Limit	limit as x approaches 0 of (1- square root of 1-x^2)/(x^2)	$lim_{x \to 0} \frac{1 - \sqrt{1 - x^{2}}}{x^{2}}$
32858	Evaluate the Limit	limit as x approaches 0 of 1/( square root of 1-cos(x))- square root of 3/(1-cos(x)^3)	$lim_{x \to 0} \frac{1}{\sqrt{1 - \cos (x)}} - \sqrt{\frac{3}{1 - \cos^{3} (x)}}$
32859	Evaluate the Limit	limit as x approaches 0 of 1/(x^(1/3))-1/((x-1)^(1/3))	$lim_{x \to 0} \frac{1}{x^{\frac{1}{3}}} - \frac{1}{{(x - 1)}^{\frac{1}{3}}}$
32860	Evaluate the Limit	limit as x approaches 0 of (-1/2)(1/2)	$lim_{x \to 0} (- \frac{1}{2}) (\frac{1}{2})$
32861	Evaluate the Limit	limit as x approaches 0 of 1/(3-2^(1/x))	$lim_{x \to 0} \frac{1}{3 - 2^{\frac{1}{x}}}$
32862	Evaluate the Limit	limit as x approaches 0 of (1/(3x))-(1/(x(x+3)))	$lim_{x \to 0} (\frac{1}{3 x}) - (\frac{1}{x (x + 3)})$
32863	Evaluate the Limit	limit as x approaches 0 of 1/( natural log of x+1)-1/x	$lim_{x \to 0} \frac{1}{\ln (x + 1)} - \frac{1}{x}$
32864	Evaluate the Limit	limit as x approaches 0 of 1/(sin(x))-1/(e^x-1)	$lim_{x \to 0} \frac{1}{\sin (x)} - \frac{1}{e^{x} - 1}$
32865	Evaluate the Limit	limit as x approaches 0 of (1/(t square root of 1+t))-(1/t)	$lim_{x \to 0} (\frac{1}{t \sqrt{1 + t}}) - (\frac{1}{t})$
32866	Evaluate the Limit	limit as x approaches 0 of (1/t)-(1/(t^2+t))	$lim_{x \to 0} (\frac{1}{t}) - (\frac{1}{t^{2} + t})$
32867	Evaluate the Limit	limit as x approaches 8 of (cos(1))/x	$lim_{x \to 8} \frac{\cos (1)}{x}$
32868	Evaluate the Limit	limit as x approaches 8 of (x)sin(pi/x)	$lim_{x \to 8} (x) \sin (\frac{π}{x})$
32869	Evaluate the Limit	limit as x approaches infinity of (t^2+3.3t+50)/(0.1t^2-1.5t+13)	$lim_{x \to \infty} \frac{t^{2} + 3.3 t + 50}{0.1 t^{2} - 1.5 t + 13}$
32870	Evaluate the Limit	limit as x approaches x of square root of (3s^7-4s^5)/(2s^7+1)	$lim_{x \to x} \sqrt{\frac{3 s^{7} - 4 s^{5}}{2 s^{7} + 1}}$
32871	Evaluate the Limit	limit as x approaches 0 of (sin(7x)^2)/(sin(11x)^2)	$lim_{x \to 0} \frac{\sin^{2} (7 x)}{\sin^{2} (11 x)}$
32872	Evaluate the Limit	limit as x approaches 0 of (1/x)( natural log of (2+x)/2)	$lim_{x \to 0} (\frac{1}{x}) (\ln (\frac{2 + x}{2}))$
32873	Evaluate the Limit	limit as x approaches 0 of (sin(7x))/(x-3pi)	$lim_{x \to 0} \frac{\sin (7 x)}{x - 3 π}$
32874	Evaluate the Limit	limit as x approaches 0 of (1/(x-4)+1/4)/x	$lim_{x \to 0} \frac{\frac{1}{x - 4} + \frac{1}{4}}{x}$
32875	Evaluate the Limit	limit as x approaches 0 of ((3+h)^-1-3^-1)/h	$lim_{x \to 0} \frac{{(3 + h)}^{- 1} - 3^{- 1}}{h}$
32876	Evaluate the Limit	limit as x approaches 0 of (1/(tan(x)))/(1/(sin(x)))	$lim_{x \to 0} \frac{\frac{1}{\tan (x)}}{\frac{1}{\sin (x)}}$
32877	Evaluate the Limit	limit as x approaches 0 of ( square root of 2-x+ square root of 2)/x	$lim_{x \to 0} \frac{\sqrt{2 - x} + \sqrt{2}}{x}$
32878	Evaluate the Limit	limit as x approaches 0 of (1-cos(x)^2)/(x^2)	$lim_{x \to 0} \frac{1 - \cos^{2} (x)}{x^{2}}$
32879	Evaluate the Limit	limit as x approaches 0 of ((2+h^3)-8)/h	$lim_{x \to 0} \frac{(2 + h^{3}) - 8}{h}$
32880	Evaluate the Limit	limit as x approaches 0 of (23e^(3x)-23)/(e^x-1)	$lim_{x \to 0} \frac{23 e^{3 x} - 23}{e^{x} - 1}$
32881	Evaluate the Limit	limit as x approaches 0 of 3/(x^2-15x+2)	$lim_{x \to 0} \frac{3}{x^{2} - 15 x + 2}$
32882	Evaluate the Limit	limit as x approaches 0 of (6x)/(cot(7x))	$lim_{x \to 0} \frac{6 x}{\cot (7 x)}$
32883	Evaluate the Limit	limit as x approaches 0 of (sin(13x))/x	$lim_{x \to 0} \frac{\sin (13 x)}{x}$
32884	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(x+tan(x))	$lim_{x \to 0} \frac{\sin (x)}{x + \tan (x)}$
32885	Evaluate the Limit	limit as x approaches 0 of (xcot(x))/(sec(2x))	$lim_{x \to 0} \frac{x \cot (x)}{\sec (2 x)}$
32886	Evaluate the Limit	limit as a approaches 0 of (0.01-sin(0.01))/0.01	$lim_{a \to 0} \frac{0.01 - \sin (0.01)}{0.01}$
32887	Evaluate the Limit	limit as x approaches 0 of (0.01-sin(0.01))/(0.01^2)	$lim_{x \to 0} \frac{0.01 - \sin (0.01)}{{0.01}^{2}}$
32888	Evaluate the Limit	limit as x approaches 0 of (sin(x)^9)/x	$lim_{x \to 0} \frac{\sin^{9} (x)}{x}$
32889	Evaluate the Limit	limit as x approaches 0 of (e^(5x)-1-5x)/(x^2)	$lim_{x \to 0} \frac{e^{5 x} - 1 - 5 x}{x^{2}}$
32890	Evaluate the Limit	limit as x approaches 0 of (e^x-e^(-x))/(4sin(x))	$lim_{x \to 0} \frac{e^{x} - e^{- x}}{4 \sin (x)}$
32891	Evaluate the Limit	limit as x approaches 0 of (sin(4x)^2)/(xsin(x))	$lim_{x \to 0} \frac{\sin^{2} (4 x)}{x \sin (x)}$
32892	Evaluate the Limit	limit as x approaches 0 of (arctan(x)-x)/(x^3)	$lim_{x \to 0} \frac{\arctan (x) - x}{x^{3}}$
32893	Evaluate the Limit	limit as x approaches 0 of (8(1-cos(x)))/(x^2)	$lim_{x \to 0} \frac{8 (1 - \cos (x))}{x^{2}}$
32894	Find the Derivative - d/d@VAR	f(x)=\|x-5\|	$f (x) = \| x - 5 \|$
32895	Evaluate the Limit	limit as x approaches 0 of (1/x-1/3)/(x-3)	$lim_{x \to 0} \frac{\frac{1}{x} - \frac{1}{3}}{x - 3}$
32896	Evaluate the Limit	limit as x approaches 0 of ((1/(x+5))/x)-((1/5)/x)	$lim_{x \to 0} (\frac{\frac{1}{x + 5}}{x}) - (\frac{\frac{1}{5}}{x})$
32897	Evaluate the Limit	limit as x approaches 0 of (e^(2x)-1)/(4x)	$lim_{x \to 0} \frac{e^{2 x} - 1}{4 x}$
32898	Evaluate the Limit	limit as x approaches 8 of 4xe^(-9x)	$lim_{x \to 8} 4 x e^{- 9 x}$
32899	Find the Derivative - d/d@VAR	f(x)=4x^3-3x^2+2x-pi	$f (x) = 4 x^{3} - 3 x^{2} + 2 x - π$
32900	Evaluate the Limit	limit as x approaches 0 of (sin(3x)tan(5x))/(x^2cos(7x))	$lim_{x \to 0} \frac{\sin (3 x) \tan (5 x)}{x^{2} \cos (7 x)}$