Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
33001	Evaluate the Limit	limit as x approaches 0 of (2x^6+6x^3)/(4x^5+3x^3)	$lim_{x \to 0} \frac{2 x^{6} + 6 x^{3}}{4 x^{5} + 3 x^{3}}$
33002	Evaluate the Limit	limit as x approaches 0 of 2/(x-5^6)	$lim_{x \to 0} \frac{2}{x - 5^{6}}$
33003	Evaluate the Limit	limit as x approaches 0 of (2sin(4x))/(5x)	$lim_{x \to 0} \frac{2 \sin (4 x)}{5 x}$
33004	Evaluate the Limit	limit as x approaches 0 of (2x(x+1))/(sin(3x))	$lim_{x \to 0} \frac{2 x (x + 1)}{\sin (3 x)}$
33005	Evaluate the Limit	limit as x approaches 0 of (2x)/(e^x-1)	$lim_{x \to 0} \frac{2 x}{e^{x} - 1}$
33006	Evaluate the Limit	limit as x approaches 0 of (2x)/( square root of x+3- square root of 3)	$lim_{x \to 0} \frac{2 x}{\sqrt{x + 3} - \sqrt{3}}$
33007	Evaluate	18e^(-0.2*1)	$18 e^{- 0.2 \cdot 1}$
33008	Evaluate the Limit	limit as x approaches 0 of ((x+h)^3-x^3)/h	$lim_{x \to 0} \frac{{(x + h)}^{3} - x^{3}}{h}$
33009	Evaluate the Limit	limit as x approaches 0 of (1-cos(2x)^2)/(x^2)	$lim_{x \to 0} \frac{1 - \cos^{2} (2 x)}{x^{2}}$
33010	Evaluate the Limit	limit as x approaches 0 of (1-e^(8(-0.01)))/(7(-0.01))	$lim_{x \to 0} \frac{1 - e^{8 (- 0.01)}}{7 (- 0.01)}$
33011	Evaluate the Limit	limit as x approaches 0 of (x^3-3x)/x	$lim_{x \to 0} \frac{x^{3} - 3 x}{x}$
33012	Evaluate the Limit	limit as x approaches 0 of (x^4)/(sin(x-x))	$lim_{x \to 0} \frac{x^{4}}{\sin (x - x)}$
33013	Evaluate the Limit	limit as x approaches 0 of (x^4-8x^2+1)/x	$lim_{x \to 0} \frac{x^{4} - 8 x^{2} + 1}{x}$
33014	Evaluate the Limit	limit as x approaches 0 of (x^5+7x)/x	$lim_{x \to 0} \frac{x^{5} + 7 x}{x}$
33015	Evaluate the Limit	limit as x approaches 0 of \|f(x)x\|	$lim_{x \to 0} \| f (x) x \|$
33016	Evaluate the Integral	integral of (z^-3)/3 with respect to z	$\int \frac{z^{- 3}}{3} d z$
33017	Evaluate the Limit	limit as x approaches 0 of ( square root of x+81-9)/x	$lim_{x \to 0} \frac{\sqrt{x + 81 - 9}}{x}$
33018	Evaluate the Limit	limit as x approaches 0 of ( cube root of 2x+1-1)/( square root of x+1-1)	$lim_{x \to 0} \frac{\sqrt[3]{2 x + 1} - 1}{\sqrt{x + 1} - 1}$
33019	Evaluate the Limit	limit as x approaches 0 of (x^2)/(tan(3x)^2)	$lim_{x \to 0} \frac{x^{2}}{\tan^{2} (3 x)}$
33020	Evaluate the Limit	limit as x approaches 0 of (x^2)/(1-cos(x)^2)	$lim_{x \to 0} \frac{x^{2}}{1 - \cos^{2} (x)}$
33021	Evaluate the Integral	integral of 5x-4 with respect to x	$\int 5 x - 4 d x$
33022	Evaluate the Limit	limit as x approaches 0 of (x^2+11x+24)/(x^2-x-12)	$lim_{x \to 0} \frac{x^{2} + 11 x + 24}{x^{2} - x - 12}$
33023	Evaluate the Limit	limit as x approaches 0 of (x^2+3x)/(e^x-1)	$lim_{x \to 0} \frac{x^{2} + 3 x}{e^{x} - 1}$
33024	Evaluate the Integral	integral of (e^(1/z))/(z^2) with respect to z	$\int \frac{e^{\frac{1}{z}}}{z^{2}} d z$
33025	Evaluate the Limit	limit as x approaches 0 of (x^2-2x)/(x^3-3x)	$lim_{x \to 0} \frac{x^{2} - 2 x}{x^{3} - 3 x}$
33026	Evaluate the Limit	limit as x approaches 0 of (x^2-5x+2)/(x^2+3x-3)	$lim_{x \to 0} \frac{x^{2} - 5 x + 2}{x^{2} + 3 x - 3}$
33027	Evaluate the Summation	sum from k=1 to 5 of (-1)^k(2+5k)	$\sum_{k = 1}^{5} {(- 1)}^{k} (2 + 5 k)$
33028	Evaluate the Limit	limit as x approaches 0 of -(x^2-x-6)/(x^2-9)	$lim_{x \to 0} - \frac{x^{2} - x - 6}{x^{2} - 9}$
33029	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (1+3/x)^(4x)	$lim_{x \to \infty} {(1 + \frac{3}{x})}^{4 x}$
33030	Evaluate the Integral	integral of x/( square root of x+5) with respect to x	$\int \frac{x}{\sqrt{x + 5}} d x$
33031	Evaluate the Limit	limit as x approaches 0 of ((x+c)^2-c^2)/x	$lim_{x \to 0} \frac{{(x + c)}^{2} - c^{2}}{x}$
33032	Evaluate the Limit	limit as x approaches 0 of ((x+h)^2-x^2)/h	$lim_{x \to 0} \frac{{(x + h)}^{2} - x^{2}}{h}$
33033	Evaluate the Limit	limit as x approaches 0 of (tan(7x))/(sin(2x))	$lim_{x \to 0} \frac{\tan (7 x)}{\sin (2 x)}$
33034	Evaluate the Limit	limit as x approaches 0 of (e^x-e^(-x))/x	$lim_{x \to 0} \frac{e^{x} - e^{- x}}{x}$
33035	Evaluate the Limit	limit as x approaches 0 of (e^x-e^(-x)-2x)/(x-sin(x))	$lim_{x \to 0} \frac{e^{x} - e^{- x} - 2 x}{x - \sin (x)}$
33036	Evaluate the Limit	limit as x approaches 0 of (e^x)/(x^2-x)	$lim_{x \to 0} \frac{e^{x}}{x^{2} - x}$
33037	Evaluate the Limit	limit as x approaches 0 of (e^x)/(x-2 natural log of x)	$lim_{x \to 0} \frac{e^{x}}{x - 2 \ln (x)}$
33038	Evaluate the Limit	limit as x approaches 0 of (e^x-1)/(sin(7x))	$lim_{x \to 0} \frac{e^{x} - 1}{\sin (7 x)}$
33039	Evaluate the Limit	limit as x approaches 0 of (\|x\|)/(x+2)	$lim_{x \to 0} \frac{\| x \|}{x + 2}$
33040	Evaluate the Limit	limit as x approaches 0 of (\|x-1\|)/(x-1)	$lim_{x \to 0} \frac{\| x - 1 \|}{x - 1}$
33041	Evaluate the Limit	limit as x approaches 0 of (1/(x+5)-1/5)/x	$lim_{x \to 0} \frac{\frac{1}{x + 5} - \frac{1}{5}}{x}$
33042	Evaluate the Limit	limit as x approaches 0 of (2e^(7x)-2)/(7x)	$lim_{x \to 0} \frac{2 e^{7 x} - 2}{7 x}$
33043	Evaluate the Limit	limit as x approaches 0 of ((4cos(4x))/(sin(4x)))/(tan(x))	$lim_{x \to 0} \frac{\frac{4 \cos (4 x)}{\sin (4 x)}}{\tan (x)}$
33044	Evaluate the Limit	limit as x approaches 0 of (6^x-2^x)/x	$lim_{x \to 0} \frac{6^{x} - 2^{x}}{x}$
33045	Evaluate the Limit	limit as x approaches 0 of (6^x-1)/x	$lim_{x \to 0} \frac{6^{x} - 1}{x}$
33046	Evaluate the Limit	limit as x approaches 0 of (e^(x^2)-1)/(cos(x)-1)	$lim_{x \to 0} \frac{e^{x^{2}} - 1}{\cos (x) - 1}$
33047	Evaluate the Limit	limit as x approaches 0 of (e^(2x))/x	$lim_{x \to 0} \frac{e^{2 x}}{x}$
33048	Evaluate the Limit	limit as x approaches 0 of (e^(3x)-1)/x	$lim_{x \to 0} \frac{e^{3 x} - 1}{x}$
33049	Evaluate the Limit	limit as x approaches 0 of (e^(4x)-1)/x	$lim_{x \to 0} \frac{e^{4 x} - 1}{x}$
33050	Evaluate the Limit	limit as x approaches 0 of (e^(4x)-1-4x)/(x^2)	$lim_{x \to 0} \frac{e^{4 x} - 1 - 4 x}{x^{2}}$
33051	Evaluate the Limit	limit as x approaches 0 of (arctan(x))/(arcsin(x))	$lim_{x \to 0} \frac{\arctan (x)}{\arcsin (x)}$
33052	Evaluate the Limit	limit as x approaches 0 of ( square root of -0.01+2- square root of 2)/-0.01	$lim_{x \to 0} \frac{\sqrt{- 0.01 + 2} - \sqrt{2}}{- 0.01}$
33053	Evaluate the Limit	limit as x approaches 0 of ( square root of x^2+x+25-5)/(x^2+x)	$lim_{x \to 0} \frac{\sqrt{x^{2} + x + 25} - 5}{x^{2} + x}$
33054	Evaluate the Integral	integral from -pi/2 to pi of 11cos(x) with respect to x	$\int_{- \frac{π}{2}}^{π} 11 \cos (x) d x$
33055	Evaluate the Limit	limit as x approaches 0 of ( square root of 13x+1-1)/x	$lim_{x \to 0} \frac{\sqrt{13 x + 1} - 1}{x}$
33056	Evaluate the Limit	limit as x approaches 0 of ( square root of 1-x- square root of 1)/x	$lim_{x \to 0} \frac{\sqrt{1 - x} - \sqrt{1}}{x}$
33057	Evaluate the Limit	limit as x approaches 0 of ( square root of 3-x- square root of 3)/x	$lim_{x \to 0} \frac{\sqrt{3 - x} - \sqrt{3}}{x}$
33058	Evaluate the Integral	integral of e^(r^2) with respect to r	$\int e^{r^{2}} d r$
33059	Evaluate the Integral	integral from 0 to 1 of (e^( square root of x))/( square root of x) with respect to x	$\int_{0}^{1} \frac{e^{\sqrt{x}}}{\sqrt{x}} d x$
33060	Evaluate the Limit	limit as x approaches 0 of ( square root of 5+x- square root of 5)/x	$lim_{x \to 0} \frac{\sqrt{5 + x} - \sqrt{5}}{x}$
33061	Evaluate the Limit	limit as x approaches 0 of ((sin(3x))/(cos(3x)))/(sin(-x))	$lim_{x \to 0} \frac{\frac{\sin (3 x)}{\cos (3 x)}}{\sin (- x)}$
33062	Evaluate the Integral	integral from -2 to 4 of \|2x-3\| with respect to x	$\int_{- 2}^{4} \| 2 x - 3 \| d x$
33063	Evaluate the Limit	limit as x approaches 0 of (sin(3x)^2)/(x^2)	$lim_{x \to 0} \frac{\sin^{2} (3 x)}{x^{2}}$
33064	Evaluate the Limit	limit as x approaches 0 of natural log of (x^4+8x+1)^(x-1)	$lim_{x \to 0} \ln ({(x^{4} + 8 x + 1)}^{x - 1})$
33065	Evaluate the Limit	limit as x approaches 0 of (cot(9x))/(csc(9x))	$lim_{x \to 0} \frac{\cot (9 x)}{\csc (9 x)}$
33066	Evaluate the Limit	limit as x approaches 0 of (f(2+h)-f*2)/h	$lim_{x \to 0} \frac{f (2 + h) - f \cdot 2}{h}$
33067	Evaluate the Limit	limit as x approaches 0 of ( natural log of 1+2x)/x	$lim_{x \to 0} \frac{\ln (1 + 2 x)}{x}$
33068	Evaluate the Limit	limit as x approaches 0 of ( natural log of x)^(sin(2x))	$lim_{x \to 0} {(\ln (x))}^{\sin (2 x)}$
33069	Evaluate the Limit	limit as x approaches 0 of (sin(x/3))/(sin(x))	$lim_{x \to 0} \frac{\sin (\frac{x}{3})}{\sin (x)}$
33070	Evaluate the Limit	limit as x approaches 0 of (sin(x^2))/(5x^2+x^3)	$lim_{x \to 0} \frac{\sin (x^{2})}{5 x^{2} + x^{3}}$
33071	Evaluate the Limit	limit as x approaches 0 of (sin(3x)sec(3x))/(2x)	$lim_{x \to 0} \frac{\sin (3 x) \sec (3 x)}{2 x}$
33072	Evaluate the Limit	limit as x approaches 0 of (sin(3x)sin(5x))/(x^2)	$lim_{x \to 0} \frac{\sin (3 x) \sin (5 x)}{x^{2}}$
33073	Evaluate the Limit	limit as x approaches 0 of (sin(5x))/(cos(3x))	$lim_{x \to 0} \frac{\sin (5 x)}{\cos (3 x)}$
33074	Evaluate the Limit	limit as x approaches 0 of (sin(8)x)/x	$lim_{x \to 0} \frac{\sin (8) x}{x}$
33075	Evaluate the Limit	limit as x approaches 0 of (sin(8x))/(x^2+7x)	$lim_{x \to 0} \frac{\sin (8 x)}{x^{2} + 7 x}$
33076	Evaluate the Limit	limit as x approaches 0 of (tan(1x)+sin(9x))/1	$lim_{x \to 0} \frac{\tan (1 x) + \sin (9 x)}{1}$
33077	Evaluate the Limit	limit as x approaches 0 of (tan(5x))/(2x)	$lim_{x \to 0} \frac{\tan (5 x)}{2 x}$
33078	Evaluate the Limit	limit as x approaches 0 of (tan(6x))/x	$lim_{x \to 0} \frac{\tan (6 x)}{x}$
33079	Evaluate the Limit	limit as x approaches 0 of tan(x)^(cos(x))	$lim_{x \to 0} {\tan (x)}^{\cos (x)}$
33080	Evaluate the Limit	limit as x approaches 0 of (tan(x)-arctan(x)-2/3x^3)/(e^(x^3)sin(x)-x-5/6x^3)	$lim_{x \to 0} \frac{\tan (x) - \arctan (x) - \frac{2}{3} x^{3}}{e^{x^{3}} \sin (x) - x - \frac{5}{6} x^{3}}$
33081	Evaluate the Limit	limit as x approaches 0 of ((x+h+2)/((x+h-4)/h))-(x-2)/((x-4)/h)	$lim_{x \to 0} (\frac{x + h + 2}{\frac{x + h - 4}{h}}) - \frac{x - 2}{\frac{x - 4}{h}}$
33082	Evaluate the Limit	limit as x approaches 0 of (x-13)/( square root of x- square root of 26-x)	$lim_{x \to 0} \frac{x - 13}{\sqrt{x} - \sqrt{26 - x}}$
33083	Evaluate the Limit	limit as x approaches 0 of (xcos(8x))/(cos(10x))	$lim_{x \to 0} \frac{x \cos (8 x)}{\cos (10 x)}$
33084	Evaluate the Limit	limit as a approaches 0 of (0.1-sin(0.1))/(0.1^2)	$lim_{a \to 0} \frac{0.1 - \sin (0.1)}{{0.1}^{2}}$
33085	Evaluate the Limit	limit as a approaches 0 of (0.5-sin(0.5))/(0.5^3)	$lim_{a \to 0} \frac{0.5 - \sin (0.5)}{{0.5}^{3}}$
33086	Evaluate the Limit	limit as x approaches 0 of (cos(pi/2-x)-cos(pi/2))/x	$lim_{x \to 0} \frac{\cos (\frac{π}{2} - x) - \cos (\frac{π}{2})}{x}$
33087	Evaluate the Limit	limit as x approaches 0 of ( cube root of 8+x-2)/x	$lim_{x \to 0} \frac{\sqrt[3]{8 + x} - 2}{x}$
33088	Evaluate the Limit	limit as x approaches 0 of ( cube root of x+1-1)/x	$lim_{x \to 0} \frac{\sqrt[3]{x + 1} - 1}{x}$
33089	Evaluate the Limit	limit as x approaches 0 of ( cube root of x+4-2)/x	$lim_{x \to 0} \frac{\sqrt[3]{x + 4} - 2}{x}$
33090	Evaluate the Limit	limit as x approaches 0 of ( fourth root of x+1- cube root of x+1)/x	$lim_{x \to 0} \frac{\sqrt[4]{x + 1} - \sqrt[3]{x + 1}}{x}$
33091	Evaluate the Limit	limit as x approaches 0 of (x^100-2x^80-1)^20	$lim_{x \to 0} {(x^{100} - 2 x^{80} - 1)}^{20}$
33092	Evaluate the Limit	limit as x approaches 0 of (x^2-9)/(x^2-3x)	$lim_{x \to 0} \frac{x^{2} - 9}{x^{2} - 3 x}$
33093	Evaluate the Limit	limit as x approaches 0 of (x^3-8)/(x^4-16)	$lim_{x \to 0} \frac{x^{3} - 8}{x^{4} - 16}$
33094	Evaluate the Limit	limit as x approaches 0 of (1- square root of 1-x^2)/x	$lim_{x \to 0} \frac{1 - \sqrt{1 - x^{2}}}{x}$
33095	Evaluate the Integral	integral from negative infinity to infinity of xe^(-x^2) with respect to x	$\int_{- \infty}^{\infty} x e^{- x^{2}} d x$
33096	Evaluate the Integral	integral of 8xe^(7x) with respect to x	$\int 8 x e^{7 x} d x$
33097	Evaluate the Limit	limit as x approaches pi/4 of (sin(x)-cos(x))/(tan(x-1))	$lim_{x \to \frac{π}{4}} \frac{\sin (x) - \cos (x)}{\tan (x - 1)}$
33098	Evaluate the Limit	limit as x approaches pi/4 of (sin(x-pi/4))/(x-pi/4)	$lim_{x \to \frac{π}{4}} \frac{\sin (x - \frac{π}{4})}{x - \frac{π}{4}}$
33099	Evaluate the Limit	limit as x approaches 0 of ((1+4x)^(1/3)-1)/((1+3x)^(1/5)-1)	$lim_{x \to 0} \frac{{(1 + 4 x)}^{\frac{1}{3}} - 1}{{(1 + 3 x)}^{\frac{1}{5}} - 1}$
33100	Evaluate the Limit	limit as x approaches 0 of ((1+h)^3-1)/h	$lim_{x \to 0} \frac{{(1 + h)}^{3} - 1}{h}$