Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
31001	Evaluate the Limit	limit as x approaches 6 of (x^2-36)/(x-6)	$lim_{x \to 6} \frac{x^{2} - 36}{x - 6}$
31002	Evaluate the Limit	limit as x approaches -pi of square root of x+8cos(x+pi)	$lim_{x \to - π} \sqrt{x + 8} \cos (x + π)$
31003	Evaluate the Limit	limit as x approaches -pi of square root of x+9cos(x+pi)	$lim_{x \to - π} \sqrt{x + 9} \cos (x + π)$
31004	Evaluate the Limit	limit as x approaches -pi of square root of x-8cos(x-pi)	$lim_{x \to - π} \sqrt{x - 8} \cos (x - π)$
31005	Evaluate the Limit	limit as x approaches pi of sin(x)^(csc(x))	$lim_{x \to π} {\sin (x)}^{\csc (x)}$
31006	Evaluate the Limit	limit as x approaches pi of (tan(sin(x)))/(sin(x))	$lim_{x \to π} \frac{\tan (\sin (x))}{\sin (x)}$
31007	Evaluate the Limit	limit as x approaches pi of square root of (pi+1-(cos(x-pi))+x)/(tan(x-pi)sin(x-pi))	$lim_{x \to π} \sqrt{\frac{π + 1 - (\cos (x - π)) + x}{\tan (x - π) \sin (x - π)}}$
31008	Evaluate the Limit	limit as x approaches -pi of square root of x+15cos(x+pi)	$lim_{x \to - π} \sqrt{x + 15} \cos (x + π)$
31009	Evaluate the Limit	limit as a approaches pi of 5sin(a)	$lim_{a \to π} 5 \sin (a)$
31010	Evaluate the Limit	limit as x approaches pi of (3)cot(x)	$lim_{x \to π} (3) \cot (x)$
31011	Find the Derivative - d/dx	(4-5x-x^2)/(x^2-6)	$\frac{4 - 5 x - x^{2}}{x^{2} - 6}$
31012	Evaluate the Limit	limit as x approaches pi of (4)cot(x)	$lim_{x \to π} (4) \cot (x)$
31013	Evaluate the Limit	limit as x approaches pi of x/(sin(x))	$lim_{x \to π} \frac{x}{\sin (x)}$
31014	Evaluate the Limit	limit as x approaches pi of cos(6pi)	$lim_{x \to π} \cos (6 π)$
31015	Evaluate the Limit	limit as x approaches pi of csc(7x)	$lim_{x \to π} \csc (7 x)$
31016	Evaluate the Limit	limit as x approaches pi of natural log of 1+cos(x)	$lim_{x \to π} \ln (1 + \cos (x))$
31017	Evaluate the Limit	limit as x approaches pi of natural log of sin(pi/2)	$lim_{x \to π} \ln (\sin (\frac{π}{2}))$
31018	Evaluate the Limit	limit as x approaches pi of tan((5x)/6)	$lim_{x \to π} \tan (\frac{5 x}{6})$
31019	Evaluate the Limit	limit as x approaches pi of tan((2x)/3)	$lim_{x \to π} \tan (\frac{2 x}{3})$
31020	Evaluate the Limit	limit as x approaches pi of tan(pi/3)	$lim_{x \to π} \tan (\frac{π}{3})$
31021	Evaluate the Limit	limit as x approaches 10 of (x^2-100)/(x-10)	$lim_{x \to 10} \frac{x^{2} - 100}{x - 10}$
31022	Evaluate the Limit	limit as x approaches pi of 7sin(x+sin(x))	$lim_{x \to π} 7 \sin (x + \sin (x))$
31023	Evaluate the Limit	limit as x approaches pi of (8)sin(x+sin(x))	$lim_{x \to π} (8) \sin (x + \sin (x))$
31024	Evaluate the Limit	limit as x approaches pi of 9tan(x)	$lim_{x \to π} 9 \tan (x)$
31025	Evaluate the Limit	limit as x approaches pi of cos((2x)/3)	$lim_{x \to π} \cos (\frac{2 x}{3})$
31026	Evaluate the Limit	limit as x approaches pi of cos(x/2+e^(sin(x)))	$lim_{x \to π} \cos (\frac{x}{2} + e^{\sin (x)})$
31027	Evaluate the Limit	limit as x approaches pi of cos(x/6)	$lim_{x \to π} \cos (\frac{x}{6})$
31028	Evaluate the Limit	limit as x approaches pi of cos(3(x))	$lim_{x \to π} \cos (3 (x))$
31029	Evaluate the Limit	limit as x approaches pi of cos(9x)	$lim_{x \to π} \cos (9 x)$
31030	Evaluate the Limit	limit as x approaches pi of cos(pi)	$lim_{x \to π} \cos (π)$
31031	Evaluate the Limit	limit as x approaches pi of cos(x)	$lim_{x \to π} \cos (x)$
31032	Evaluate the Limit	limit as x approaches pi of cos(x+2)	$lim_{x \to π} \cos (x + 2)$
31033	Evaluate the Limit	limit as x approaches pi of (9)cot(x)	$lim_{x \to π} (9) \cot (x)$
31034	Evaluate the Limit	limit as x approaches pi of (9)sin(x+sin(x))	$lim_{x \to π} (9) \sin (x + \sin (x))$
31035	Evaluate the Limit	limit as x approaches -pi of natural log of tan(x)	$lim_{x \to - π} \ln (\tan (x))$
31036	Evaluate the Limit	limit as x approaches pi of sec(2x)	$lim_{x \to π} \sec (2 x)$
31037	Evaluate the Limit	limit as x approaches pi of sec(x)	$lim_{x \to π} \sec (x)$
31038	Evaluate the Limit	limit as x approaches -pi of sec(x)tan(x)	$lim_{x \to - π} \sec (x) \tan (x)$
31039	Evaluate the Limit	limit as x approaches pi of sin((2pi)/2)	$lim_{x \to π} \sin (\frac{2 π}{2})$
31040	Evaluate the Limit	limit as x approaches pi of sin((2pi)/3)	$lim_{x \to π} \sin (\frac{2 π}{3})$
31041	Evaluate the Limit	limit as x approaches pi of sin(pi/2)	$lim_{x \to π} \sin (\frac{π}{2})$
31042	Evaluate the Limit	limit as x approaches pi of sin(x/2-pi)	$lim_{x \to π} \sin (\frac{x}{2} - π)$
31043	Evaluate the Limit	limit as x approaches pi of sin(x/3)	$lim_{x \to π} \sin (\frac{x}{3})$
31044	Evaluate the Limit	limit as x approaches pi of sin(x/6)	$lim_{x \to π} \sin (\frac{x}{6})$
31045	Evaluate the Limit	limit as x approaches pi of sin(-2x+sin(3x))	$lim_{x \to π} \sin (- 2 x + \sin (3 x))$
31046	Evaluate the Limit	limit as x approaches pi of sin(3x-(sin(7x)))	$lim_{x \to π} \sin (3 x - (\sin (7 x)))$
31047	Evaluate the Limit	limit as x approaches pi of sin(4x-sin(5x))	$lim_{x \to π} \sin (4 x - \sin (5 x))$
31048	Evaluate the Limit	limit as x approaches pi of sin(-6x+sin(3x))	$lim_{x \to π} \sin (- 6 x + \sin (3 x))$
31049	Evaluate the Limit	limit as x approaches pi of sin(6x+sin(5x))	$lim_{x \to π} \sin (6 x + \sin (5 x))$
31050	Evaluate the Limit	limit as x approaches negative infinity of (3-e^x)/(1+e^x)	$lim_{x \to - \infty} \frac{3 - e^{x}}{1 + e^{x}}$
31051	Evaluate the Limit	limit as x approaches infinity of (2x-3)/(4x+10)	$lim_{x \to \infty} \frac{2 x - 3}{4 x + 10}$
31052	Find the Derivative - d/dx	(3x-2)/(2x+1)	$\frac{3 x - 2}{2 x + 1}$
31053	Evaluate the Limit	limit as x approaches negative infinity of x	$lim_{x \to - \infty} x$
31054	Evaluate the Limit	limit as x approaches 6 of (x^2-10x+24)/(x^2-10x+24)	$lim_{x \to 6} \frac{x^{2} - 10 x + 24}{x^{2} - 10 x + 24}$
31055	Evaluate the Limit	limit as x approaches 1 of ( natural log of x)/((x-1)^3)	$lim_{x \to 1} \frac{\ln (x)}{{(x - 1)}^{3}}$
31056	Evaluate the Limit	limit as x approaches negative infinity of x^4-x^5	$lim_{x \to - \infty} x^{4} - x^{5}$
31057	Evaluate the Limit	limit as x approaches infinity of (x^2-36)/(x(x-6))	$lim_{x \to \infty} \frac{x^{2} - 36}{x (x - 6)}$
31058	Evaluate the Limit	limit as x approaches infinity of ( square root of 3x^2-2)/(5x+1)	$lim_{x \to \infty} \frac{\sqrt{3 x^{2} - 2}}{5 x + 1}$
31059	Evaluate the Limit	limit as x approaches 7 of (x-7)/( square root of 7x-7)	$lim_{x \to 7} \frac{x - 7}{\sqrt{7 x - 7}}$
31060	Evaluate the Limit	limit as x approaches 0 of 5xcot(2x)	$lim_{x \to 0} 5 x \cot (2 x)$
31061	Evaluate the Limit	limit as x approaches 0 of ( square root of x^2+25-5)/x	$lim_{x \to 0} \frac{\sqrt{x^{2} + 25} - 5}{x}$
31062	Evaluate the Limit	limit as y approaches 3/2 of square root of (8y^3-27)/(4y^2-9)	$lim_{y \to \frac{3}{2}} \sqrt{\frac{8 y^{3} - 27}{4 y^{2} - 9}}$
31063	Evaluate the Limit	limit as y approaches pi/2 of (y-pi/2)tan(y)	$lim_{y \to \frac{π}{2}} (y - \frac{π}{2}) \tan (y)$
31064	Evaluate the Limit	limit as y approaches pi/2 of (sin(y-1))/(y-pi/2)	$lim_{y \to \frac{π}{2}} \frac{\sin (y - 1)}{y - \frac{π}{2}}$
31065	Evaluate the Limit	limit as y approaches 0 of ( square root of 7x+y- square root of 7x)/y	$lim_{y \to 0} \frac{\sqrt{7 x + y} - \sqrt{7 x}}{y}$
31066	Evaluate the Limit	limit as y approaches 0 of 1/(sin(y)^2)-1/(y^2)	$lim_{y \to 0} \frac{1}{\sin^{2} (y)} - \frac{1}{y^{2}}$
31067	Evaluate the Limit	limit as y approaches 0 of 4/(y^2+y)-4/y	$lim_{y \to 0} \frac{4}{y^{2} + y} - \frac{4}{y}$
31068	Evaluate the Limit	limit as y approaches 0 of (5y^3+8y^2)/(3y^4-16y^2)	$lim_{y \to 0} \frac{5 y^{3} + 8 y^{2}}{3 y^{4} - 16 y^{2}}$
31069	Evaluate the Limit	limit as y approaches 0 of (6(x+y)^2-6(x-y)-28-6x^2-6x-28)/y	$lim_{y \to 0} \frac{6 {(x + y)}^{2} - 6 (x - y) - 28 - 6 x^{2} - 6 x - 28}{y}$
31070	Evaluate the Limit	limit as y approaches 0 of (e-y^2)/(y^2)-(sec(y))/(y^2)	$lim_{y \to 0} \frac{e - y^{2}}{y^{2}} - \frac{\sec (y)}{y^{2}}$
31071	Evaluate the Limit	limit as y approaches 0 of (sin(2y))/(sin(3y))	$lim_{y \to 0} \frac{\sin (2 y)}{\sin (3 y)}$
31072	Evaluate the Limit	limit as y approaches 0 of (sin(3y))/y	$lim_{y \to 0} \frac{\sin (3 y)}{y}$
31073	Evaluate the Limit	limit as y approaches 0 of (sin(3y)cot(5y))/(y*cot(4y))	$lim_{y \to 0} \frac{\sin (3 y) \cot (5 y)}{y \cdot \cot (4 y)}$
31074	Evaluate the Limit	limit as y approaches 0 of (sin(4y))/y	$lim_{y \to 0} \frac{\sin (4 y)}{y}$
31075	Evaluate the Limit	limit as y approaches 0 of ((x+y)^2-2(x+y)-(x^2-2x))/y	$lim_{y \to 0} \frac{{(x + y)}^{2} - 2 (x + y) - (x^{2} - 2 x)}{y}$
31076	Evaluate the Limit	limit as x approaches 0 of (sin(2x)^2)/(5x)	$lim_{x \to 0} \frac{\sin^{2} (2 x)}{5 x}$
31077	Evaluate the Limit	limit as y approaches 0 of (cos(x-y)-cos(x+y))/y	$lim_{y \to 0} \frac{\cos (x - y) - \cos (x + y)}{y}$
31078	Evaluate the Limit	limit as y approaches 0 of ((t+y)^2-7(t+y)+5-(t^2-7t+5))/y	$lim_{y \to 0} \frac{{(t + y)}^{2} - 7 (t + y) + 5 - (t^{2} - 7 t + 5)}{y}$
31079	Evaluate the Limit	limit as y approaches 0 of ((x+y)^100-x^100)/y	$lim_{y \to 0} \frac{{(x + y)}^{100} - x^{100}}{y}$
31080	Evaluate the Limit	( limit as h approaches 0 of e^(x+h)+e^x)/h	$\frac{lim_{h \to 0} e^{x + h} + e^{x}}{h}$
31081	Evaluate the Limit	( limit as h approaches 0 of h^2+8h+87-15)/h	$\frac{lim_{h \to 0} h^{2} + 8 h + 87 - 15}{h}$
31082	Evaluate the Limit	( limit as h approaches 0 of square root of 144+h-12)/h	$\frac{lim_{h \to 0} \sqrt{144 + h} - 12}{h}$
31083	Evaluate the Limit	( limit as h approaches 0 of square root of 36+h-6)/h	$\frac{lim_{h \to 0} \sqrt{36 + h} - 6}{h}$
31084	Evaluate the Limit	( limit as h approaches 0 of square root of 4+h- square root of 4)/h	$\frac{lim_{h \to 0} \sqrt{4 + h} - \sqrt{4}}{h}$
31085	Evaluate the Limit	( limit as h approaches 0 of square root of 8h+1-1)/h	$\frac{lim_{h \to 0} \sqrt{8 h + 1} - 1}{h}$
31086	Evaluate the Limit	( limit as h approaches 0 of ( square root of 9+h)-3)/h	$\frac{lim_{h \to 0} (\sqrt{9 + h}) - 3}{h}$
31087	Evaluate the Limit	( limit as h approaches 0 of 1-cos(h)^2)/h	$\frac{lim_{h \to 0} 1 - \cos^{2} (h)}{h}$
31088	Evaluate the Limit	( limit as h approaches 0 of 1+6h)/h	$\frac{lim_{h \to 0} 1 + 6 h}{h}$
31089	Evaluate the Limit	( limit as h approaches 0 of (11+h)-121)/h	$\frac{lim_{h \to 0} (11 + h) - 121}{h}$
31090	Evaluate the Limit	( limit as h approaches 0 of 2h^3+h)/(3h^3-h)	$\frac{lim_{h \to 0} 2 h^{3} + h}{3 h^{3} - h}$
31091	Evaluate the Limit	( limit as h approaches 0 of (-8+h^2)(-64))/h	$\frac{lim_{h \to 0} (- 8 + h^{2}) (- 64)}{h}$
31092	Evaluate the Limit	( limit as h approaches 0 of 8hx+4h^2+7h)/h	$\frac{lim_{h \to 0} 8 h x + 4 h^{2} + 7 h}{h}$
31093	Evaluate the Limit	limit as h approaches 0 of (h+10)^2-100	$lim_{h \to 0} {(h + 10)}^{2} - 100$
31094	Evaluate the Limit	( limit as h approaches 0 of natural log of cos(x+h)- natural log of cos(x))/h	$\frac{lim_{h \to 0} \ln (\cos (x + h)) - \ln (\cos (x))}{h}$
31095	Evaluate the Limit	( limit as h approaches 0 of natural log of e+h-1)/h	$\frac{lim_{h \to 0} \ln (e + h) - 1}{h}$
31096	Evaluate the Limit	( limit as h approaches 0 of sin(pi+h)-sin(pi))/h	$\frac{lim_{h \to 0} \sin (π + h) - \sin (π)}{h}$
31097	Evaluate the Limit	( limit as h approaches 0 of (x+h)-x)/h	$\frac{lim_{h \to 0} (x + h) - x}{h}$
31098	Evaluate the Limit	( limit as h approaches 0 of x+h+9/(x+h)-x-9/x)/h	$\frac{lim_{h \to 0} x + h + \frac{9}{x + h} - x - \frac{9}{x}}{h}$
31099	Find the Derivative - d/dx	2^20	$2^{20}$
31100	Find the Derivative - d/dx	-14/(x^3)	$- \frac{14}{x^{3}}$