Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
21001	Evaluate the Limit	limit as x approaches 0 of ( natural log of (x)^2)/(x-1)	$lim_{x \to 0} \frac{\ln ({(x)}^{2})}{x - 1}$
21002	Evaluate the Limit	limit as x approaches 0 of (e^(2x)-e^(-2x)-4x)/(x-sin(x))	$lim_{x \to 0} \frac{e^{2 x} - e^{- 2 x} - 4 x}{x - \sin (x)}$
21003	Evaluate the Limit	limit as x approaches infinity of (5x^3+1)/(10x^3-3x^2+7)	$lim_{x \to \infty} \frac{5 x^{3} + 1}{10 x^{3} - 3 x^{2} + 7}$
21004	Evaluate the Limit	limit as x approaches 0 of 9/(x^x)-(5^x)/x	$lim_{x \to 0} \frac{9}{x^{x}} - \frac{5^{x}}{x}$
21005	Evaluate the Limit	limit as x approaches 0 of (7^x-1)/x	$lim_{x \to 0} \frac{7^{x} - 1}{x}$
21006	Evaluate the Limit	limit as x approaches 0 of ( square root of 1-x-1)/x	$lim_{x \to 0} \frac{\sqrt{1 - x} - 1}{x}$
21007	Evaluate the Limit	limit as x approaches 0 of ( square root of x^2+1-1)/(x^2)	$lim_{x \to 0} \frac{\sqrt{x^{2} + 1} - 1}{x^{2}}$
21008	Evaluate the Limit	limit as x approaches 1 of (1- square root of x)/(1-x)	$lim_{x \to 1} \frac{1 - \sqrt{x}}{1 - x}$
21009	Evaluate the Limit	limit as x approaches infinity of ( square root of t+t^2)/(3t-t^2)	$lim_{x \to \infty} \frac{\sqrt{t} + t^{2}}{3 t - t^{2}}$
21010	Evaluate the Limit	limit as x approaches 0 of ( square root of 1+2x- square root of 1-4x)/x	$lim_{x \to 0} \frac{\sqrt{1 + 2 x} - \sqrt{1 - 4 x}}{x}$
21011	Evaluate the Integral	integral of log base 2 of x with respect to x	$\int \log_{2} (x) d x$
21012	Evaluate the Limit	limit as x approaches 0 of (x^(1/3))/x	$lim_{x \to 0} \frac{x^{\frac{1}{3}}}{x}$
21013	Evaluate the Limit	limit as x approaches 0 of (x^2)/(sin(3x)^2)	$lim_{x \to 0} \frac{x^{2}}{\sin^{2} (3 x)}$
21014	Evaluate the Limit	limit as x approaches 0 of (x^2)/(sin(8x)^2)	$lim_{x \to 0} \frac{x^{2}}{\sin^{2} (8 x)}$
21015	Evaluate the Limit	limit as x approaches 0 of (1-6x)^(1/x)	$lim_{x \to 0} {(1 - 6 x)}^{\frac{1}{x}}$
21016	Evaluate the Limit	limit as x approaches 0 of (1-cos(3x))^x	$lim_{x \to 0} {(1 - \cos (3 x))}^{x}$
21017	Evaluate the Limit	limit as x approaches 0 of (3x+2x^2)/(5x+6x^3)	$lim_{x \to 0} \frac{3 x + 2 x^{2}}{5 x + 6 x^{3}}$
21018	Evaluate the Limit	limit as x approaches 0 of (6sin(2x)-4x)/x	$lim_{x \to 0} \frac{6 \sin (2 x) - 4 x}{x}$
21019	Evaluate the Limit	limit as x approaches 0 of (1+2x)^(3/x)	$lim_{x \to 0} {(1 + 2 x)}^{\frac{3}{x}}$
21020	Evaluate the Limit	limit as x approaches 0 of (1+2x)^(1/(3x))	$lim_{x \to 0} {(1 + 2 x)}^{\frac{1}{3 x}}$
21021	Evaluate the Limit	limit as x approaches 0 of (1-4x)^(1/x)	$lim_{x \to 0} {(1 - 4 x)}^{\frac{1}{x}}$
21022	Evaluate the Limit	limit as x approaches 0 of (1+sin(3x))^(cot(5x))	$lim_{x \to 0} {(1 + \sin (3 x))}^{\cot (5 x)}$
21023	Evaluate the Limit	limit as x approaches negative infinity of (x-2)/(x^2+2x+1)	$lim_{x \to - \infty} \frac{x - 2}{x^{2} + 2 x + 1}$
21024	Evaluate the Limit	limit as x approaches 3 of (x^2-8x+15)/(x-3)	$lim_{x \to 3} \frac{x^{2} - 8 x + 15}{x - 3}$
21025	Evaluate the Limit	limit as x approaches infinity of square root of x^2+ax- square root of x^2+bx	$lim_{x \to \infty} \sqrt{x^{2} + a x} - \sqrt{x^{2} + b x}$
21026	Evaluate the Limit	limit as x approaches 1 of (3x^2-5)/(x^2-3x-4)	$lim_{x \to 1} \frac{3 x^{2} - 5}{x^{2} - 3 x - 4}$
21027	Evaluate the Limit	limit as x approaches 0 of (cos(x)-3cos(3x))/(x^2)	$lim_{x \to 0} \frac{\cos (x) - 3 \cos (3 x)}{x^{2}}$
21028	Evaluate the Limit	limit as x approaches 0 of (sin(4x))/(5x)	$lim_{x \to 0} \frac{\sin (4 x)}{5 x}$
21029	Evaluate the Limit	limit as x approaches infinity of cos(1/x)	$lim_{x \to \infty} \cos (\frac{1}{x})$
21030	Evaluate the Limit	limit as x approaches 0 of cos(x)^(1/x)	$lim_{x \to 0} {\cos (x)}^{\frac{1}{x}}$
21031	Evaluate the Limit	limit as x approaches 0 of (3x+\|x\|)/x	$lim_{x \to 0} \frac{3 x + \| x \|}{x}$
21032	Evaluate the Limit	limit as x approaches 0 of (cos(x)+sin(x))^(1/x)	$lim_{x \to 0} {(\cos (x) + \sin (x))}^{\frac{1}{x}}$
21033	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(2x)	$lim_{x \to 0} \frac{\sin (x)}{2 x}$
21034	Evaluate the Limit	limit as x approaches 0 of ((1+2x)^(1/3)-1)/x	$lim_{x \to 0} \frac{{(1 + 2 x)}^{\frac{1}{3}} - 1}{x}$
21035	Evaluate the Limit	limit as x approaches 0 of ((-8+x)^2-64)/x	$lim_{x \to 0} \frac{{(- 8 + x)}^{2} - 64}{x}$
21036	Evaluate the Limit	limit as x approaches 0 of sin(x)^(tan(x))	$lim_{x \to 0} {\sin (x)}^{\tan (x)}$
21037	Evaluate the Limit	limit as x approaches 0 of (1/(x+6)-1/6)/x	$lim_{x \to 0} \frac{\frac{1}{x + 6} - \frac{1}{6}}{x}$
21038	Evaluate the Limit	limit as x approaches 0 of (13^x-1)/x	$lim_{x \to 0} \frac{13^{x} - 1}{x}$
21039	Evaluate the Limit	limit as x approaches 0 of (14^x-1)/x	$lim_{x \to 0} \frac{14^{x} - 1}{x}$
21040	Evaluate the Limit	limit as x approaches 0 of (3^x-1)/x	$lim_{x \to 0} \frac{3^{x} - 1}{x}$
21041	Evaluate the Limit	( limit as x approaches 8 of 5x-1)/(2x+5)	$\frac{lim_{x \to 8} 5 x - 1}{2 x + 5}$
21042	Evaluate the Limit	( limit as x approaches 8 of 5x^3+2x)/(-3x^4+3x^3+6)	$\frac{lim_{x \to 8} 5 x^{3} + 2 x}{- 3 x^{4} + 3 x^{3} + 6}$
21043	Evaluate the Limit	( limit as x approaches 8 of 2x^5)/(e^(4x))	$\frac{lim_{x \to 8} 2 x^{5}}{e^{4 x}}$
21044	Evaluate the Limit	( limit as x approaches 8 of 2x^2-3x-6)/( square root of x^4+1)	$\frac{lim_{x \to 8} 2 x^{2} - 3 x - 6}{\sqrt{x^{4} + 1}}$
21045	Evaluate the Limit	( limit as x approaches 8 of 3 square root of x^3+3x)/( square root of 2x^3)	$\frac{lim_{x \to 8} 3 \sqrt{x^{3}} + 3 x}{\sqrt{2 x^{3}}}$
21046	Evaluate the Limit	( limit as x approaches pi of 5 square root of x)/(csc(x))	$\frac{lim_{x \to π} 5 \sqrt{x}}{\csc (x)}$
21047	Evaluate the Limit	limit as x approaches 0 of (1-e^(-x))/(e^x-1)	$lim_{x \to 0} \frac{1 - e^{- x}}{e^{x} - 1}$
21048	Evaluate the Limit	( limit as x approaches pi of sin(x))/(x-pi)	$\frac{lim_{x \to π} \sin (x)}{x - π}$
21049	Evaluate the Limit	( limit as x approaches infinity of square root of 2x^2+1)/(3x-5)	$\frac{lim_{x \to \infty} \sqrt{2 x^{2} + 1}}{3 x - 5}$
21050	Evaluate the Limit	( limit as x approaches 9 of x-9)/( square root of x-3)	$\frac{lim_{x \to 9} x - 9}{\sqrt{x - 3}}$
21051	Evaluate the Limit	( limit as x approaches pi of sin(x))/(1-cos(x))	$\frac{lim_{x \to π} \sin (x)}{1 - \cos (x)}$
21052	Evaluate the Limit	( limit as x approaches pi of sin(x))/(pi-x)	$\frac{lim_{x \to π} \sin (x)}{π - x}$
21053	Evaluate the Limit	( limit as y approaches 2 of 3- square root of 4x+1)/(x^2-2x)	$\frac{lim_{y \to 2} 3 - \sqrt{4 x + 1}}{x^{2} - 2 x}$
21054	Evaluate the Limit	( limit as y approaches 2 of y+2)/(y^2+5y+6)	$\frac{lim_{y \to 2} y + 2}{y^{2} + 5 y + 6}$
21055	Evaluate the Limit	( limit as y approaches -3 of y^2+4y+3)/(y^2-3)	$\frac{lim_{y \to - 3} y^{2} + 4 y + 3}{y^{2} - 3}$
21056	Evaluate the Limit	( limit as z approaches 8 of (-8z^3-5z)+2)/(z^3+2z^2-5z+3)	$\frac{lim_{z \to 8} (- 8 z^{3} - 5 z) + 2}{z^{3} + 2 z^{2} - 5 z + 3}$
21057	Evaluate the Limit	( limit as x approaches 9 of x^2-7x-18)/(x-9)	$\frac{lim_{x \to 9} x^{2} - 7 x - 18}{x - 9}$
21058	Evaluate the Limit	( limit as x approaches 9 of x^2-81)/( square root of x-3)	$\frac{lim_{x \to 9} x^{2} - 81}{\sqrt{x} - 3}$
21059	Evaluate the Summation	sum from n=1 to 12 of 2n+5	$\sum_{n = 1}^{12} 2 n + 5$
21060	Evaluate the Limit	( limit as x approaches -9 of x^2+6x-27)/(x+9)	$\frac{lim_{x \to - 9} x^{2} + 6 x - 27}{x + 9}$
21061	Evaluate the Limit	( limit as x approaches 8 of (-6x^2)+6x-2)/(-5x^2+6)	$\frac{lim_{x \to 8} (- 6 x^{2}) + 6 x - 2}{- 5 x^{2} + 6}$
21062	Evaluate the Limit	( limit as x approaches 8 of 2x+3)/( square root of x^2-5)	$\frac{lim_{x \to 8} 2 x + 3}{\sqrt{x^{2} - 5}}$
21063	Evaluate the Limit	( limit as x approaches 8 of tan(12x^2))/( natural log of 1+4x^2)	$\frac{lim_{x \to 8} \tan (12 x^{2})}{\ln (1 + 4 x^{2})}$
21064	Evaluate the Limit	( limit as x approaches 8 of x)/(6x-10)	$\frac{lim_{x \to 8} x}{6 x - 10}$
21065	Evaluate the Limit	( limit as x approaches 8 of \|x-8\|)/(x-8)	$\frac{lim_{x \to 8} \| x - 8 \|}{x - 8}$
21066	Evaluate the Limit	( limit as x approaches -8 of t^2-64)/(2t^2+17t+8)	$\frac{lim_{x \to - 8} t^{2} - 64}{2 t^{2} + 17 t + 8}$
21067	Evaluate the Limit	( limit as x approaches 8 of square root of x^2+7)/( square root of 7x^2+1)	$\frac{lim_{x \to 8} \sqrt{x^{2} + 7}}{\sqrt{7 x^{2} + 1}}$
21068	Evaluate the Limit	( limit as x approaches 8 of 10^8x^5+10^6x^4+10^4x^2)/(10^9x^6+10^7x^5+10^5x^3)	$\frac{lim_{x \to 8} 10^{8} x^{5} + 10^{6} x^{4} + 10^{4} x^{2}}{10^{9} x^{6} + 10^{7} x^{5} + 10^{5} x^{3}}$
21069	Evaluate the Limit	( limit as x approaches -8 of fifth root of x- ninth root of x)/( fifth root of x+ ninth root of x)	$\frac{lim_{x \to - 8} \sqrt[5]{x} - \sqrt[9]{x}}{\sqrt[5]{x} + \sqrt[9]{x}}$
21070	Evaluate the Limit	( limit as x approaches 5 of x^3-125)/(x^2-25)	$\frac{lim_{x \to 5} x^{3} - 125}{x^{2} - 25}$
21071	Evaluate the Limit	( limit as x approaches 8 of square root of 3x^12-16)/(x^6-3)	$\frac{lim_{x \to 8} \sqrt{3 x^{12} - 16}}{x^{6} - 3}$
21072	Evaluate the Limit	( limit as x approaches -8 of square root of x^6-1)/(x^5-1)	$\frac{lim_{x \to - 8} \sqrt{x^{6} - 1}}{x^{5} - 1}$
21073	Evaluate the Limit	( limit as x approaches 8 of square root of 7+8x^2)/(10+7x)	$\frac{lim_{x \to 8} \sqrt{7 + 8 x^{2}}}{10 + 7 x}$
21074	Evaluate the Limit	( limit as x approaches 8 of x^3-8)/(x^2-4)	$\frac{lim_{x \to 8} x^{3} - 8}{x^{2} - 4}$
21075	Evaluate the Limit	( limit as x approaches 8 of x^2-3x-28)/(2x^3-98x)	$\frac{lim_{x \to 8} x^{2} - 3 x - 28}{2 x^{3} - 98 x}$
21076	Evaluate the Limit	( limit as x approaches 8 of 12e^x)/(2x^2)	$\frac{lim_{x \to 8} 12 e^{x}}{2 x^{2}}$
21077	Evaluate the Limit	( limit as x approaches 8 of x^2-2x-48)/(x-8)	$\frac{lim_{x \to 8} x^{2} - 2 x - 48}{x - 8}$
21078	Evaluate the Limit	( limit as x approaches 8 of x^2+2x-5)/(3x^2+2)	$\frac{lim_{x \to 8} x^{2} + 2 x - 5}{3 x^{2} + 2}$
21079	Evaluate the Limit	( limit as x approaches -8 of x^2+9x+8)/(x^2+7x-8)	$\frac{lim_{x \to - 8} x^{2} + 9 x + 8}{x^{2} + 7 x - 8}$
21080	Evaluate the Limit	( limit as x approaches 49 of 49-x)/(7- square root of x)	$\frac{lim_{x \to 49} 49 - x}{7 - \sqrt{x}}$
21081	Evaluate the Limit	( limit as x approaches 5 of x^2-2x-15)/(x+3)	$\frac{lim_{x \to 5} x^{2} - 2 x - 15}{x + 3}$
21082	Evaluate the Limit	( limit as x approaches 5 of x^2-3x-10)/(x^2-10x+25)	$\frac{lim_{x \to 5} x^{2} - 3 x - 10}{x^{2} - 10 x + 25}$
21083	Evaluate the Limit	( limit as x approaches 49 of square root of x-7)/(x-49)	$\frac{lim_{x \to 49} \sqrt{x - 7}}{x - 49}$
21084	Evaluate the Limit	( limit as x approaches 5 of \|5-x\|)/(5-x)	$\frac{lim_{x \to 5} \| 5 - x \|}{5 - x}$
21085	Evaluate the Limit	( limit as x approaches 5 of square root of x^2+11-6)/(x-5)	$\frac{lim_{x \to 5} \sqrt{x^{2} + 11} - 6}{x - 5}$
21086	Evaluate the Integral	integral of (sin(2x))/(cos(x)) with respect to x	$\int \frac{\sin (2 x)}{\cos (x)} d x$
21087	Evaluate the Limit	( limit as x approaches 5 of 4-x)/((x-5)^2)	$\frac{lim_{x \to 5} 4 - x}{{(x - 5)}^{2}}$
21088	Evaluate the Limit	( limit as x approaches 6 of x^2-3x-18)/(x-6)	$\frac{lim_{x \to 6} x^{2} - 3 x - 18}{x - 6}$
21089	Evaluate the Limit	( limit as x approaches 6 of x^2-4x-12)/(x-6)	$\frac{lim_{x \to 6} x^{2} - 4 x - 12}{x - 6}$
21090	Evaluate the Limit	( limit as x approaches 5 of x-5)/( square root of x- square root of 5)	$\frac{lim_{x \to 5} x - 5}{\sqrt{x} - \sqrt{5}}$
21091	Evaluate the Limit	( limit as x approaches 5 of x-5)/(x^2-10x+25)	$\frac{lim_{x \to 5} x - 5}{x^{2} - 10 x + 25}$
21092	Evaluate the Limit	( limit as x approaches 6 of x^2+3x-54)/(x^2-36)	$\frac{lim_{x \to 6} x^{2} + 3 x - 54}{x^{2} - 36}$
21093	Evaluate the Limit	limit as x approaches negative infinity of (1-x-x^2)/(2x^2-7)	$lim_{x \to - \infty} \frac{1 - x - x^{2}}{2 x^{2} - 7}$
21094	Evaluate the Limit	( limit as x approaches 7 of x^2-5x-14)/(x-7)	$\frac{lim_{x \to 7} x^{2} - 5 x - 14}{x - 7}$
21095	Evaluate the Limit	limit as x approaches negative infinity of ( square root of 5x^2-2)/(x+3)	$lim_{x \to - \infty} \frac{\sqrt{5 x^{2} - 2}}{x + 3}$
21096	Evaluate the Limit	( limit as x approaches 7 of x-7)/( square root of 7x-7)	$\frac{lim_{x \to 7} x - 7}{\sqrt{7 x} - 7}$
21097	Evaluate the Limit	( limit as x approaches 76 of square root of x+5-9)/(x-76)	$\frac{lim_{x \to 76} \sqrt{x + 5} - 9}{x - 76}$
21098	Evaluate the Limit	limit as x approaches -8 of ((x-7)/(x-5))^2	$lim_{x \to - 8} {(\frac{x - 7}{x - 5})}^{2}$
21099	Evaluate the Limit	limit as x approaches 8 of (1/x)^n	$lim_{x \to 8} {(\frac{1}{x})}^{n}$
21100	Evaluate the Limit	( limit as x approaches 8 of (2x-1)(3-x))/((x-1)(x+3))	$\frac{lim_{x \to 8} (2 x - 1) (3 - x)}{(x - 1) (x + 3)}$