Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
62001	Find the Average Value of the Function	f(x)=x(x-1) ; [2,5]	$f (x) = x (x - 1)$ ; $[2, 5]$
62002	Find the Antiderivative	f(x)=1/2x	$f (x) = \frac{1}{2} x$
62003	Find the Antiderivative	f(x)=1/( square root of 1-x^2)	$f (x) = \frac{1}{\sqrt{1 - x^{2}}}$
62004	Find the Domain	f(x,y)=e^(-xy)	$f (x, y) = e^{- x y}$
62005	Find Where the Mean Value Theorem is Satisfied	f(x)=x^3 , [0,3]	$f (x) = x^{3}$ , $[0, 3]$
62006	Find Where the Mean Value Theorem is Satisfied	f(x)=x^3+5x^2 , [0,3]	$f (x) = x^{3} + 5 x^{2}$ , $[0, 3]$
62007	Find Where the Mean Value Theorem is Satisfied	f(x)=8x-16 ; [1,5]	$f (x) = 8 x - 16$ ; $[1, 5]$
62008	Find Where the Mean Value Theorem is Satisfied	f(x)=x^2 , [0,2]	$f (x) = x^{2}$ , $[0, 2]$
62009	Find the Antiderivative	f(x)=5/( square root of x)	$f (x) = \frac{5}{\sqrt{x}}$
62010	Find the Antiderivative	f(x)=(3x^4-x^3+6x^2)/(x^4)	$f (x) = \frac{3 x^{4} - x^{3} + 6 x^{2}}{x^{4}}$
62011	Find the Antiderivative	f(x)=10/( square root of 1-x^2)	$f (x) = \frac{10}{\sqrt{1 - x^{2}}}$
62012	Find the Antiderivative	f(x)=1/5-8/x	$f (x) = \frac{1}{5} - \frac{8}{x}$
62013	Find the Antiderivative	f(x)=1/5x	$f (x) = \frac{1}{5} x$
62014	Find the Antiderivative	f(x)=(2x^3-3x^2+1)/(x^2)	$f (x) = \frac{2 x^{3} - 3 x^{2} + 1}{x^{2}}$
62015	Find the Antiderivative	f(x)=5 square root of x	$f (x) = 5 \sqrt{x}$
62016	Find the Antiderivative	f(x)=4-2x	$f (x) = 4 - 2 x$
62017	Find the Antiderivative	f(x)=3x^6-2x^4+14x^2	$f (x) = 3 x^{6} - 2 x^{4} + 14 x^{2}$
62018	Find the Antiderivative	f(x)=3x^(4/3)+4x^(5/4)	$f (x) = 3 x^{\frac{4}{3}} + 4 x^{\frac{5}{4}}$
62019	Find the Antiderivative	f(x)=2 square root of x	$f (x) = 2 \sqrt{x}$
62020	Find the Antiderivative	f(x)=-2+24x-12x^2	$f (x) = - 2 + 24 x - 12 x^{2}$
62021	Find the Antiderivative	f(x)=2x-4	$f (x) = 2 x - 4$
62022	Find the Antiderivative	f(x)=-2xe^(-x^2+1)	$f (x) = - 2 x e^{- x^{2} + 1}$
62023	Find the Antiderivative	f(x)=2x^4-3x^3+5	$f (x) = 2 x^{4} - 3 x^{3} + 5$
62024	Find the Antiderivative	f(x)=11x- square root of x	$f (x) = 11 x - \sqrt{x}$
62025	Find the Antiderivative	f(x)=11x^(4/7)+4x^(-6/7)	$f (x) = 11 x^{\frac{4}{7}} + 4 x^{- \frac{6}{7}}$
62026	Find the Antiderivative	f(x)=\|x\|	$f (x) = \| x \|$
62027	Find the Antiderivative	f(x)=10	$f (x) = 10$
62028	Find the Antiderivative	f(x)=10e^x	$f (x) = 10 e^{x}$
62029	Find the Antiderivative	f(x)=12x^11	$f (x) = 12 x^{11}$
62030	Find the Antiderivative	f(x)=15e^x	$f (x) = 15 e^{x}$
62031	Find the Antiderivative	f(x)=-13x	$f (x) = - 13 x$
62032	Find the Antiderivative	f(x)=17x^16	$f (x) = 17 x^{16}$
62033	Find the Antiderivative	f(x) = fourth root of x	$f (x) = \sqrt[4]{x}$
62034	Find the Antiderivative	f(x) = fifth root of 39x^7	$f (x) = \sqrt[5]{39 x^{7}}$
62035	Find the Antiderivative	f(x)=9x^(2/7)+2x^(-6/7)	$f (x) = 9 x^{\frac{2}{7}} + 2 x^{- \frac{6}{7}}$
62036	Find the Antiderivative	f(x)=8x^3	$f (x) = 8 x^{3}$
62037	Find the Antiderivative	f(x)=8x^-4	$f (x) = 8 x^{- 4}$
62038	Find the Antiderivative	f(x)=8x+5	$f (x) = 8 x + 5$
62039	Find the Antiderivative	f(x)=8sec(x)(sec(x)-4tan(x))	$f (x) = 8 \sec (x (\sec (x) - 4 \tan (x)))$
62040	Find the Antiderivative	f(x)=7x^6	$f (x) = 7 x^{6}$
62041	Find the Antiderivative	f(x)=800-x/3	$f (x) = 800 - \frac{x}{3}$
62042	Find the Antiderivative	f(x)=6x^2-8x+3	$f (x) = 6 x^{2} - 8 x + 3$
62043	Find the Antiderivative	f(x)=6x+7	$f (x) = 6 x + 7$
62044	Find the Antiderivative	f(x)=6x-7	$f (x) = 6 x - 7$
62045	Find the Antiderivative	f(x)=6-3x	$f (x) = 6 - 3 x$
62046	Find the Antiderivative	f(x)=x^7-3x^-4-5	$f (x) = x^{7} - 3 x^{- 4} - 5$
62047	Find the Antiderivative	f(x)=e^(7x)	$f (x) = e^{7 x}$
62048	Find the Antiderivative	f(x)=e^(-7x)	$f (x) = e^{- 7 x}$
62049	Find the Antiderivative	f(x)=e^(-8x)	$f (x) = e^{- 8 x}$
62050	Find the Antiderivative	r(theta)=sec(theta)tan(theta)-6e^theta	$r (θ) = \sec (θ) \tan (θ) - 6 e^{θ}$
62051	Find the Antiderivative	q(y)=y^3+1/y	$q (y) = y^{3} + \frac{1}{y}$
62052	Find the Antiderivative	h(z)=6/z	$h (z) = \frac{6}{z}$
62053	Find the Antiderivative	p(z)=( square root of z)^3	$p (z) = {(\sqrt{z})}^{3}$
62054	Find the Antiderivative	h(x)=8/9x^(-1/9)	$h (x) = \frac{8}{9} x^{- \frac{1}{9}}$
62055	Find the Antiderivative	f(y)=-25/(y^26)	$f (y) = \frac{- 25}{y^{26}}$
62056	Find the Antiderivative	f(x)=x-4	$f (x) = x - 4$
62057	Find the Antiderivative	f(x)=x-5	$f (x) = x - 5$
62058	Find the Antiderivative	g(t)=t^2+t	$g (t) = t^{2} + t$
62059	Find the Fourth Derivative	f(x)=7x^3-8x^4	$f (x) = 7 x^{3} - 8 x^{4}$
62060	Find the Second Derivative	f(x)=(x^3)/3-3x^2-27x	$f (x) = \frac{x^{3}}{3} - 3 x^{2} - 27 x$
62061	Find the Second Derivative	f(x)=3e^x	$f (x) = 3 e^{x}$
62062	Find the Second Derivative	f(x)=(2x+4)^4	$f (x) = {(2 x + 4)}^{4}$
62063	Find the Second Derivative	g(t)=t^2(3t+9)^4	$g (t) = t^{2} {(3 t + 9)}^{4}$
62064	Find the Second Derivative	G(r) = square root of r+ sixth root of r	$G (r) = \sqrt{r} + \sqrt[6]{r}$
62065	Find the Second Derivative	f(x)=-x^6	$f (x) = - x^{6}$
62066	Evaluate from the Left	limit as x approaches 5 of f(x)	$lim_{x \to 5} f (x)$
62067	Identify the Conic	2x^2+2y^2-16x-20y-8=0	$2 x^{2} + 2 y^{2} - 16 x - 20 y - 8 = 0$
62068	Find Where Increasing/Decreasing Using Derivatives	f(t)=t+cos(t)	$f (t) = t + \cos (t)$
62069	Find Where Increasing/Decreasing Using Derivatives	f(x)=5/(x-7)	$f (x) = \frac{5}{x - 7}$
62070	Find the Vertex	x^2-10x+21	$x^{2} - 10 x + 21$
62071	Find Where Increasing/Decreasing Using Derivatives	f(x)=3sin(x)+3cos(x)	$f (x) = 3 \sin (x) + 3 \cos (x)$
62072	Find Where Increasing/Decreasing Using Derivatives	f(x)=7sin(x)+7cos(x)	$f (x) = 7 \sin (x) + 7 \cos (x)$
62073	Find Where Increasing/Decreasing Using Derivatives	f(x)=5+3x-x^3	$f (x) = 5 + 3 x - x^{3}$
62074	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3+3x^2-24x+8	$f (x) = x^{3} + 3 x^{2} - 24 x + 8$
62075	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3+3x^2-45x+4	$f (x) = x^{3} + 3 x^{2} - 45 x + 4$
62076	Find Where Increasing/Decreasing Using Derivatives	f(x)=-x^3+12x^2-45x	$f (x) = - x^{3} + 12 x^{2} - 45 x$
62077	Find Where Increasing/Decreasing Using Derivatives	f(x)=9tan(x)	$f (x) = 9 \tan (x)$
62078	Find Where Increasing/Decreasing Using Derivatives	f(x)=190+8x^3+x^4	$f (x) = 190 + 8 x^{3} + x^{4}$
62079	Find Where Increasing/Decreasing Using Derivatives	f(x)=10x^4-60x^2	$f (x) = 10 x^{4} - 60 x^{2}$
62080	Find Where Increasing/Decreasing Using Derivatives	f(x)=-12x^5+90x^4-100x^3	$f (x) = - 12 x^{5} + 90 x^{4} - 100 x^{3}$
62081	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x(x-3)^3	$f (x) = 2 x {(x - 3)}^{3}$
62082	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x^3-12x^2+18x	$f (x) = 2 x^{3} - 12 x^{2} + 18 x$
62083	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x^3-9x^2+12x-3	$f (x) = 2 x^{3} - 9 x^{2} + 12 x - 3$
62084	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x^3-6x^2-48x	$f (x) = 2 x^{3} - 6 x^{2} - 48 x$
62085	Find Where Increasing/Decreasing Using Derivatives	f(x)=(x^2-24)/(x-5)	$f (x) = \frac{x^{2} - 24}{x - 5}$
62086	Find the Inverse	f(x)=12x-10	$f (x) = 12 x - 10$
62087	Find the Inverse	f(x)=9/16x-13	$f (x) = \frac{9}{16} x - 13$
62088	Find Where Increasing/Decreasing Using Derivatives	f(x)=x-15x^(1/3)	$f (x) = x - 15 x^{\frac{1}{3}}$
62089	Find Where Increasing/Decreasing Using Derivatives	f(x)=x-x^-1	$f (x) = x - x^{- 1}$
62090	Find Where Increasing/Decreasing Using Derivatives	g(t)=-2t^2-3t+5	$g (t) = - 2 t^{2} - 3 t + 5$
62091	Find Where Increasing/Decreasing Using Derivatives	f(x)=xe^(-3x)	$f (x) = x e^{- 3 x}$
62092	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^5-5x^4	$f (x) = x^{5} - 5 x^{4}$
62093	Find Where Increasing/Decreasing Using Derivatives	H(t)=t^8-4/5t^10	$H (t) = t^{8} - \frac{4}{5} t^{10}$
62094	Find Where Increasing/Decreasing Using Derivatives	g(x)=150+8x^3+x^4	$g (x) = 150 + 8 x^{3} + x^{4}$
62095	Find Where Increasing/Decreasing Using Derivatives	h(x)=6x^5-15x^4+10x^3	$h (x) = 6 x^{5} - 15 x^{4} + 10 x^{3}$
62096	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3-6x^2-135x	$f (x) = x^{3} - 6 x^{2} - 135 x$
62097	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3-6x	$f (x) = x^{3} - 6 x$
62098	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3-48x	$f (x) = x^{3} - 48 x$
62099	Find the Inverse	f(x)=x^7-5	$f (x) = x^{7} - 5$
62100	Find the Inverse	f(x)=x^3+4x-1	$f (x) = x^{3} + 4 x - 1$