Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
84001	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (3x^2+x)/(4sin(2x)-3x)	$lim_{x \to 0} \frac{3 x^{2} + x}{4 \sin (2 x) - 3 x}$
84002	Find the Derivative - d/dx	(x+y)^2(x-y)^2=x^4+y^4	${(x + y)}^{2} {(x - y)}^{2} = x^{4} + y^{4}$
84003	Evaluate the Integral	integral of sin(x/2)cos(x/2) with respect to x	$\int \sin (\frac{x}{2}) \cos (\frac{x}{2}) d x$
84004	Evaluate the Integral	integral from -a to a of f(x) with respect to x	$\int_{- a}^{a} f (x) d x$
84005	Evaluate the Integral	integral from 1 to 4 of (3 square root of x-2/x) with respect to x	$\int_{1}^{4} (3 \sqrt{x} - \frac{2}{x}) d x$
84006	Integrate By Parts	integral from 1 to e of x^3 natural log of x with respect to x	$\int_{1}^{e} x^{3} \ln (x) d x$
84007	Find the Derivative - d/dx	(-10+9x^-3+x^2)(7-10x^2)	$(- 10 + 9 x^{- 3} + x^{2}) (7 - 10 x^{2})$
84008	Find the Derivative of the Integral	h(x) = integral from -2 to sin(x) of (cos(t^4)+t) with respect to t	$h (x) = \int_{- 2}^{\sin (x)} (\cos (t^{4}) + t) d t$
84009	Find the Derivative - d/dx	3^(4-11x)	$3^{4 - 11 x}$
84010	Find the Derivative - d/dx	(1-2x)/(x^2)	$\frac{1 - 2 x}{x^{2}}$
84011	Find the Antiderivative	f(x)=3/x+4/(x^2)-5/(sin(x)^2)	$f (x) = \frac{3}{x} + \frac{4}{x^{2}} - \frac{5}{\sin^{2} (x)}$
84012	Evaluate the Integral	integral of (2x^5+x-6x^3) with respect to x	$\int (2 x^{5} + x - 6 x^{3}) d x$
84013	Find the Antiderivative	square root of x* natural log of x	$\sqrt{x} \cdot \ln (x)$
84014	Evaluate the Limit	limit as x approaches -2 of (2/(x-8)+x/(3x-4))/(x/(2x-16)+1/(3x-4))	$lim_{x \to - 2} \frac{\frac{2}{x - 8} + \frac{x}{3 x - 4}}{\frac{x}{2 x - 16} + \frac{1}{3 x - 4}}$
84015	Evaluate the Integral	integral from 0 to 1 of (2x+1)e^(x^2+x) with respect to x	$\int_{0}^{1} (2 x + 1) e^{x^{2} + x} d x$
84016	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x-x)^(1/(tan(x)))	$lim_{x \to 0} {(e^{x} - x)}^{\frac{1}{\tan (x)}}$
84017	Find the Derivative - d/dx	1/3pix^2y	$\frac{1}{3} π x^{2} y$
84018	Find the Derivative - d/dx	natural log of x^2+y^2+1	$\ln (x^{2} + y^{2} + 1)$
84019	Find the Antiderivative	f(x)=5 fourth root of x-3/x	$f (x) = 5 \sqrt[4]{x} - \frac{3}{x}$
84020	Find the Second Derivative	( square root of x)/(1+ square root of x)	$\frac{\sqrt{x}}{1 + \sqrt{x}}$
84021	Evaluate the Integral	integral of (4(x^3+3))/((x^4+12x)^3) with respect to x	$\int \frac{4 (x^{3} + 3)}{{(x^{4} + 12 x)}^{3}} d x$
84022	Find the Third Derivative	y=-2/3x^3+3x^2+3/10x^5-3	$y = - \frac{2}{3} x^{3} + 3 x^{2} + \frac{3}{10} x^{5} - 3$
84023	Evaluate the Limit	limit as x approaches infinity of (8-4x^2)/(9x^2+5x)	$lim_{x \to \infty} \frac{8 - 4 x^{2}}{9 x^{2} + 5 x}$
84024	Evaluate the Limit	limit as v approaches -3 of ( square root of 4-v- square root of 7)/(v+3)	$lim_{v \to - 3} \frac{\sqrt{4 - v} - \sqrt{7}}{v + 3}$
84025	Find Where Increasing/Decreasing	f(x)=-\|x\|+7	$f (x) = - \| x \| + 7$
84026	Evaluate the Integral	integral of (5x^-3+6x) with respect to x	$\int (5 x^{- 3} + 6 x) d x$
84027	Evaluate the Limit	limit as theta approaches 0 of (1-cos(theta))/(sin(2theta))	$lim_{θ \to 0} \frac{1 - \cos (θ)}{\sin (2 θ)}$
84028	Find dy/dx	y=sec(3x)	$y = \sec (3 x)$
84029	Find the Derivative - d/dx	-5/(2x^(3/2))	$- \frac{5}{2 x^{\frac{3}{2}}}$
84030	Evaluate the Limit	limit as x approaches 0 of \|x\|=0	$lim_{x \to 0} \| x \| = 0$
84031	Find the Antiderivative	f(x)=xe^(2x)	$f (x) = x e^{2 x}$
84032	Find the Derivative - d/dx	1/(x(x+1))	$\frac{1}{x (x + 1)}$
84033	Evaluate the Integral	integral of (-3x^5+1+3x^3) with respect to x	$\int (- 3 x^{5} + 1 + 3 x^{3}) d x$
84034	Find the Integral	e^(2x+1)	$e^{2 x + 1}$
84035	Determine if Continuous	f(x)=x+1/x	$f (x) = x + \frac{1}{x}$
84036	Evaluate the Integral	integral from 0 to pi of (2+cos(x)) with respect to x	$\int_{0}^{π} (2 + \cos (x)) d x$
84037	Find dy/dx	4+xy-4x=5y	$4 + x y - 4 x = 5 y$
84038	Determine if Continuous	f(x)=(x^2-1)/(x+1) if x!=-1; 1 if x=-1	$f (x) = {\begin{cases} \frac{x^{2} - 1}{x + 1} & x \neq - 1 \\ 1 & x = - 1 \end{cases}$
84039	Find the Derivative - d/dx	(2x(x^2-3))/((x^2+1)^3)	$\frac{2 x (x^{2} - 3)}{{(x^{2} + 1)}^{3}}$
84040	Evaluate Using Summation Formulas	sum from i=1 to 14 of 5i^2+13	$\sum_{i = 1}^{14} 5 i^{2} + 13$
84041	Evaluate the Limit	limit as x approaches negative infinity of ( square root of x^2+3)/(2x-8)	$lim_{x \to - \infty} \frac{\sqrt{x^{2} + 3}}{2 x - 8}$
84042	Find the Derivative - d/dy	1/(2y^2)+(y^4)/16	$\frac{1}{2 y^{2}} + \frac{y^{4}}{16}$
84043	Find the Maximum/Minimum Value	y=x^3-2x+4	$y = x^{3} - 2 x + 4$
84044	Evaluate the Integral	integral from theta_1 to theta_2 of 1/(theta_2-theta_1)x with respect to x	$\int_{θ_{1}}^{θ_{2}} \frac{1}{θ_{2} - θ_{1}} x d x$
84045	Find the Integral	1+x	$1 + x$
84046	Evaluate the Integral	integral of (-3/x+3e^x) with respect to x	$\int (- \frac{3}{x} + 3 e^{x}) d x$
84047	Evaluate the Limit	limit as x approaches 4 from the right of x^3-cx	$lim_{x \to 4^{+}} x^{3} - c x$
84048	Evaluate the Limit	limit as x approaches negative infinity of ((x+2)(x+5)(x-5))/(13(x+3)(x+5))	$lim_{x \to - \infty} \frac{(x + 2) (x + 5) (x - 5)}{13 (x + 3) (x + 5)}$
84049	Find the Antiderivative	f(x)=( square root of 2x)/x+3/(x^5)	$f (x) = \frac{\sqrt{2 x}}{x} + \frac{3}{x^{5}}$
84050	Find the Derivative - d/dx	6 natural log of x-2^x	$6 \ln (x) - 2^{x}$
84051	Find the Derivative - d/dx	3(4)^x+5e^x	$3 {(4)}^{x} + 5 e^{x}$
84052	Find the Derivative - d/dx	-27/( cube root of x-6)	$- \frac{27}{\sqrt[3]{x - 6}}$
84053	Evaluate the Integral	integral from 3 to 5 of (2x^2+x+4)/(x-1) with respect to x	$\int_{3}^{5} \frac{2 x^{2} + x + 4}{x - 1} d x$
84054	Find the Derivative - d/dt	y=e^t(cos(2t)+2sin(2t))	$y = e^{t} (\cos (2 t) + 2 \sin (2 t))$
84055	Find Where Increasing/Decreasing	y=5/2x^4	$y = \frac{5}{2} x^{4}$
84056	Find the Antiderivative	2^(3-x/2)	$2^{3 - \frac{x}{2}}$
84057	Evaluate the Integral	integral of 6 square root of 4x-5 with respect to x	$\int 6 \sqrt{4 x - 5} d x$
84058	Integrate Using u-Substitution	integral of x/( square root of x-2) with respect to x	$\int \frac{x}{\sqrt{x - 2}} d x$
84059	Find the Derivative - d/dx	arcsin((x^2)/(x^2-1))	$\arcsin (\frac{x^{2}}{x^{2} - 1})$
84060	Find Where Increasing/Decreasing	f(x) = log base 2 of x-4	$f (x) = \log_{2} (x) - 4$
84061	Find the Derivative - d/dx	3/4x^(4/3)-3/8x^(2/3)+9	$\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{8} x^{\frac{2}{3}} + 9$
84062	Find the Derivative - d/dx	square root of 2+2x(x^2+1)^3	$\sqrt{2 + 2 x} {(x^{2} + 1)}^{3}$
84063	Evaluate Using L'Hospital's Rule	limit as x approaches 2 of (4 natural log of 2x-3)/(2e^(2x-4)-2)	$lim_{x \to 2} \frac{4 \ln (2 x - 3)}{2 e^{2 x - 4} - 2}$
84064	Find the Derivative - d/dx	y=30x^(-2/4)+3x	$y = 30 x^{- \frac{2}{4}} + 3 x$
84065	Find dy/dx	y=xe^(-x^2)	$y = x e^{- x^{2}}$
84066	Find the Antiderivative	sin(x)^2-cos(x)^2	$\sin^{2} (x) - \cos^{2} (x)$
84067	Evaluate the Limit	limit as x approaches infinity of (4(4-x)(x-5))/(13(x-1)(x+8))	$lim_{x \to \infty} \frac{4 (4 - x) (x - 5)}{13 (x - 1) (x + 8)}$
84068	Find the Maximum/Minimum Value	y=2-(sin(5x))/3	$y = 2 - \frac{\sin (5 x)}{3}$
84069	Find the Fourth Derivative	4 fifth root of x^3-1/(8x^2)- square root of x	$4 \sqrt[5]{x^{3}} - \frac{1}{8 x^{2}} - \sqrt{x}$
84070	Evaluate the Integral	integral from 1 to 6 of 9/(4 fourth root of 3x-2) with respect to x	$\int_{1}^{6} \frac{9}{4 \sqrt[4]{3 x - 2}} d x$
84071	Evaluate the Limit	limit as r approaches -3/2 of ( square root of 31-12r^2)/(16r^3+10)	$lim_{r \to - \frac{3}{2}} \frac{\sqrt{31 - 12 r^{2}}}{16 r^{3} + 10}$
84072	Find the Derivative - d/dg	gg	$g \cdot g$
84073	Find the Derivative - d/dx	1.8sin(pi/12x-pi/2)^3+98.6	$1.8 \sin^{3} (\frac{π}{12} x - \frac{π}{2}) + 98.6$
84074	Find dy/dx	y = square root of x(3x-1)	$y = \sqrt{x} (3 x - 1)$
84075	Find Where Increasing/Decreasing	f(x)=-2x^4-2/3x^3+1/2x^2+1	$f (x) = - 2 x^{4} - \frac{2}{3} x^{3} + \frac{1}{2} x^{2} + 1$
84076	Integrate Using u-Substitution	integral from 1 to 2 of 2x^2 square root of x^3+1 with respect to x	$\int_{1}^{2} 2 x^{2} \sqrt{x^{3} + 1} d x$
84077	Find the Antiderivative	e^(2x-1)y^-2	$e^{2 x - 1} y^{- 2}$
84078	Find the Antiderivative	(x+2)/(x+1)	$\frac{x + 2}{x + 1}$
84079	Find the Derivative - d/dx	2xe^x+x^2e^x	$2 x e^{x} + x^{2} e^{x}$
84080	Integrate By Parts	integral of 2x^2 natural log of x with respect to x	$\int 2 x^{2} \ln (x) d x$
84081	Find the Derivative - d/dx	y=4arcsin(x/2)	$y = 4 \arcsin (\frac{x}{2})$
84082	Evaluate the Integral	integral of (x^4-1)/(x-1) with respect to x	$\int \frac{x^{4} - 1}{x - 1} d x$
84083	Find the Antiderivative	1/3x^3-5x	$\frac{1}{3} x^{3} - 5 x$
84084	Find Where Increasing/Decreasing	f(x) = log base 1/3 of x+1-2	$f (x) = \log_{\frac{1}{3}} (x + 1) - 2$
84085	Evaluate the Integral	integral from 2 to 3 of (4/(x^2)+1) with respect to x	$\int_{2}^{3} (\frac{4}{x^{2}} + 1) d x$
84086	Find Where Increasing/Decreasing	f(x)=(sin(x))e^(-x)	$f (x) = (\sin (x)) e^{- x}$
84087	Find the Derivative - d/dx	(1-cos(x))/(1+cos(x))	$\frac{1 - \cos (x)}{1 + \cos (x)}$
84088	Evaluate the Integral	integral of (2x^2+2+5x^3) with respect to x	$\int (2 x^{2} + 2 + 5 x^{3}) d x$
84089	Find the Maximum/Minimum Value	f(t)=-0.3t^3+80t+425	$f (t) = - 0.3 t^{3} + 80 t + 425$
84090	Find the Antiderivative	1÷(x^2)	$1 \div x^{2}$
84091	Find the Maximum/Minimum Value	f(x)=8cos(x)+2	$f (x) = 8 \cos (x) + 2$
84092	Integrate Using u-Substitution	integral of 15x^4(3x^5-9)^2 with respect to x	$\int 15 x^{4} {(3 x^{5} - 9)}^{2} d x$
84093	Find the Tangent Line at (1,2)	f(x)=2x^3 at (1,2)	$f (x) = 2 x^{3}$ at $(1, 2)$
84094	Integrate Using u-Substitution	integral from e to e^4 of 1/(x square root of natural log of x) with respect to x	$\int_{e}^{e^{4}} \frac{1}{x \sqrt{\ln (x)}} d x$
84095	Evaluate the Limit	limit as x approaches infinity of (x+6)/(4x-1)	$lim_{x \to \infty} \frac{x + 6}{4 x - 1}$
84096	Evaluate the Limit	limit as x approaches 2 of (x^3-8)/(2x-4)	$lim_{x \to 2} \frac{x^{3} - 8}{2 x - 4}$
84097	Find the Derivative - d/dy	yx^(y-1)	$y x^{y - 1}$
84098	Evaluate the Integral	integral of ( natural log of x) with respect to x	$\int (\ln (x)) d x$
84099	Evaluate the Integral	integral from 0 to 1 of e^(1-2x) with respect to x	$\int_{0}^{1} e^{1 - 2 x} d x$
84100	Find the Derivative - d/dx	D_x(3^(3x^2))	$D_{x} (3^{3 x^{2}})$