Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
69801	Evaluate the Limit	limit as x approaches negative infinity of (2x^3)/(x^2+4)	$lim_{x \to - \infty} \frac{2 x^{3}}{x^{2} + 4}$
69802	Evaluate the Limit	limit as x approaches 2pi from the left of xcsc(x)	$lim_{x \to {(2 π)}^{-}} x \csc (x)$
69803	Evaluate the Integral	integral of (e^(3x)-2)^2 with respect to x	$\int {(e^{3 x} - 2)}^{2} d x$
69804	Find the Derivative - d/dx	1/(1+ square root of x)	$\frac{1}{1 + \sqrt{x}}$
69805	Find the Derivative - d/dx	25(x^2-y^2)	$25 (x^{2} - y^{2})$
69806	Find Where Increasing/Decreasing	f(x)=-(x^4)/4+x^3-x^2	$f (x) = - \frac{x^{4}}{4} + x^{3} - x^{2}$
69807	Evaluate the Integral	integral of ( square root of x+ cube root of x)/x with respect to x	$\int \frac{\sqrt{x} + \sqrt[3]{x}}{x} d x$
69808	Find the Derivative - d/dx	square root of 1+sin(x)^2	$\sqrt{1 + \sin^{2} (x)}$
69809	Evaluate the Limit	limit as h approaches infinity of (5h^4-2h^2+3)/(3h^3+2h^2+h)	$lim_{h \to \infty} \frac{5 h^{4} - 2 h^{2} + 3}{3 h^{3} + 2 h^{2} + h}$
69810	Find the Derivative - d/dx	y=(csc(x))/(1+csc(x))	$y = \frac{\csc (x)}{1 + \csc (x)}$
69811	Evaluate the Integral	integral of (e^x-e^(-x))^2 with respect to x	$\int {(e^{x} - e^{- x})}^{2} d x$
69812	Find the Derivative - d/dθ	4sec(theta)	$4 \sec (θ)$
69813	Find the Derivative - d/dx	x square root of 1+x^2	$x \sqrt{1 + x^{2}}$
69814	Find the Derivative - d/dx	x1/2	$x \frac{1}{2}$
69815	Find the Center and Radius	y^2+2x+x^2=24y-120	$y^{2} + 2 x + x^{2} = 24 y - 120$
69816	Find the Integral	-2/x	$- \frac{2}{x}$
69817	Find dy/dx	y=e^x square root of x^2+1	$y = e^{x} \sqrt{x^{2} + 1}$
69818	Use Logarithmic Differentiation to Find the Derivative	y=cos(2x)^x	$y = {\cos (2 x)}^{x}$
69819	Find dx/dy	(x^2)/(x+y)=y^2+1	$\frac{x^{2}}{x + y} = y^{2} + 1$
69820	Find the Derivative - d/dx	2 square root of x-1/( square root of x)	$2 \sqrt{x} - \frac{1}{\sqrt{x}}$
69821	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (1-1/(5x))^(6x)	$lim_{x \to \infty} {(1 - \frac{1}{5 x})}^{6 x}$
69822	Find the Antiderivative	(e^x)/x	$\frac{e^{x}}{x}$
69823	Find dr/dθ	r=cos(theta)cot(theta)	$r = \cos (θ) \cot (θ)$
69824	Find the Second Derivative	x/(e^x)	$\frac{x}{e^{x}}$
69825	Evaluate the Limit	limit as x approaches 0 of (ax^2+bx^3)/(cx^2+dx^3)	$lim_{x \to 0} \frac{a x^{2} + b x^{3}}{c x^{2} + d x^{3}}$
69826	Evaluate the Limit	limit as x approaches -2 of (3-x)^2	$lim_{x \to - 2} {(3 - x)}^{2}$
69827	Find the Derivative of the Integral	h(x) = integral from 1 to e^x of 2 natural log of t with respect to t	$h (x) = \int_{1}^{e^{x}} 2 \ln (t) d t$
69828	Find the Derivative - d/dx	y=(e^x+e^(-x))/2	$y = \frac{e^{x} + e^{- x}}{2}$
69829	Evaluate the Integral	integral from -3 to -1 of (1/(x^2)-1/(x^3)) with respect to x	$\int_{- 3}^{- 1} (\frac{1}{x^{2}} - \frac{1}{x^{3}}) d x$
69830	Find dy/dx	xy-3x+4x^2=7	$x y - 3 x + 4 x^{2} = 7$
69831	Find the Derivative - d/dx	sin(xy^2)	$\sin (x y^{2})$
69832	Evaluate the Integral	integral of tan(x)(6cos(x)-6sec(x)) with respect to x	$\int \tan (x) (6 \cos (x) - 6 \sec (x)) d x$
69833	Find the Maximum/Minimum Value	f(x)=\|x-2\|	$f (x) = \| x - 2 \|$
69834	Find the Derivative - d/dx	y=k square root of x+x square root of k	$y = k \sqrt{x} + x \sqrt{k}$
69835	Integrate Using Trig Substitution	integral of x/( square root of x^2-25) with respect to x	$\int \frac{x}{\sqrt{x^{2} - 25}} d x$
69836	Find du/dv	square root of u+ square root of v=5	$\sqrt{u} + \sqrt{v} = 5$
69837	Find dx/dy	cos(xy)=1+sin(y)	$\cos (x y) = 1 + \sin (y)$
69838	Evaluate the Integral	integral of cube root of t(5t^2-3t+2) with respect to t	$\int \sqrt[3]{t} (5 t^{2} - 3 t + 2) d t$
69839	Find Where Increasing/Decreasing	f''''(x)=(e^(-x)-e^5)(e^x+e^-3)	$f'' (x) = (e^{- x} - e^{5}) (e^{x} + e^{- 3})$
69840	Find the Derivative - d/dx	limit as x approaches 2 of (x^2-4)/(x-2)	$lim_{x \to 2} \frac{x^{2} - 4}{x - 2}$
69841	Find dy/dx	y^3=(x-y)/(x+y)	$y^{3} = \frac{x - y}{x + y}$
69842	Find the Derivative - d/dx	natural log of x^2e^(2x)	$\ln (x^{2} e^{2 x})$
69843	Evaluate the Integral	integral of (5e^x-6^x) with respect to x	$\int (5 e^{x} - 6^{x}) d x$
69844	Find Where Increasing/Decreasing	f(x)=(x^2-4)^2	$f (x) = {(x^{2} - 4)}^{2}$
69845	Find the Second Derivative	f(x)=5x^2(x+47)	$f (x) = 5 x^{2} (x + 47)$
69846	Evaluate the Integral	integral of 1/( square root of a-by) with respect to y	$\int \frac{1}{\sqrt{a - b y}} d y$
69847	Find the Derivative - d/dx	2 natural log of x+1	$2 \ln (x + 1)$
69848	Find the Derivative - d/dx	d/(dx)f(g(x))	$\frac{d}{d x} f (g (x))$
69849	Find the Concavity	f(x)=(x^3)/3-5x^2+21x+1	$f (x) = \frac{x^{3}}{3} - 5 x^{2} + 21 x + 1$
69850	Find dy/dx	x^2+xy+y^2=9	$x^{2} + x y + y^{2} = 9$
69851	Evaluate the Limit	limit as x approaches infinity of (3x^5+21x^3)/(7x^5-18x+4)	$lim_{x \to \infty} \frac{3 x^{5} + 21 x^{3}}{7 x^{5} - 18 x + 4}$
69852	Evaluate the Integral	integral of fifth root of x^10 with respect to x	$\int \sqrt[5]{x^{10}} d x$
69853	Find the Derivative - d/dT	cos(T^2)	$\cos (T^{2})$
69854	Evaluate the Integral	integral of 2xsec(x^2)tan(x^2) with respect to x	$\int 2 x \sec (x^{2}) \tan (x^{2}) d x$
69855	Find Where Increasing/Decreasing	f(x)=(x^4)/4-x^3+x^2	$f (x) = \frac{x^{4}}{4} - x^{3} + x^{2}$
69856	Evaluate the Limit	limit as x approaches 5 of square root of (x^2-7x+10)/(x-5)	$lim_{x \to 5} \sqrt{\frac{x^{2} - 7 x + 10}{x - 5}}$
69857	Find dy/dx	y=cos(sin(x))	$y = \cos (\sin (x))$
69858	Find the Second Derivative	f(x)	$f (x)$
69859	Evaluate the Integral	integral of cube root of 1-3x with respect to x	$\int \sqrt[3]{1 - 3 x} d x$
69860	Find the Derivative - d/dx	3/( square root of 2x+1)	$\frac{3}{\sqrt{2 x + 1}}$
69861	Evaluate the Integral	integral from -3 to 2 of (x^2+x-6) with respect to x	$\int_{- 3}^{2} (x^{2} + x - 6) d x$
69862	Evaluate the Integral	integral of (1-tan(x)^2)/(sec(x)^2) with respect to x	$\int \frac{1 - \tan^{2} (x)}{\sec^{2} (x)} d x$
69863	Find the Second Derivative	y=e^(2sin(x))	$y = e^{2 \sin (x)}$
69864	Find the Derivative - d/dx	(2x)^3	${(2 x)}^{3}$
69865	Find the Derivative - d/dx	(2x+2)(x-5)^8	$(2 x + 2) {(x - 5)}^{8}$
69866	Evaluate the Integral	integral from 2 to infinity of 1/(v^2+2v-3) with respect to v	$\int_{2}^{\infty} \frac{1}{v^{2} + 2 v - 3} d v$
69867	Evaluate the Integral	integral of (1/x+2/(x^2)+3/(x^3)) with respect to x	$\int (\frac{1}{x} + \frac{2}{x^{2}} + \frac{3}{x^{3}}) d x$
69868	Evaluate the Limit	limit as x approaches 0 of 3^x+cos(x)	$lim_{x \to 0} 3^{x} + \cos (x)$
69869	Find the Normal Line at (0,9)	y=x^4+9e^x , (0,9)	$y = x^{4} + 9 e^{x}$ , $(0, 9)$
69870	Find the Derivative - d/dx	x^2cot(x)	$x^{2} \cot (x)$
69871	Find the Slope of the Tangent Line at (-1,8)	f(x)=3-5x , (-1,8)	$f (x) = 3 - 5 x$ , $(- 1, 8)$
69872	Evaluate the Integral	integral of (x^2+1+1/(x^2+1)) with respect to x	$\int (x^{2} + 1 + \frac{1}{x^{2} + 1}) d x$
69873	Find dy/dx	5y^2=(3x-4)/(3x+4)	$5 y^{2} = \frac{3 x - 4}{3 x + 4}$
69874	Find dx/dy	y=sin(x)cos(x)	$y = \sin (x) \cos (x)$
69875	Find the Tangent Line at (5,4)	f(x)=((x+3)/(x-1))^2 , (5,4)	$f (x) = {(\frac{x + 3}{x - 1})}^{2}$ , $(5, 4)$
69876	Find the Derivative - d/dx	2x-tan(x)	$2 x - \tan (x)$
69877	Find Where Increasing/Decreasing	f(x)=(x^2-3)/(x-2)	$f (x) = \frac{x^{2} - 3}{x - 2}$
69878	Find dy/dx	3xe^(x^2y^2)=x^2	$3 x e^{x^{2} y^{2}} = x^{2}$
69879	Find the Maximum/Minimum Value	x+32/(x^2)	$x + \frac{32}{x^{2}}$
69880	Verify the Differential Equation Solution	y''''=(3y)/x , y=x^3	$y'' = \frac{3 y}{x}$ , $y = x^{3}$
69881	Evaluate the Integral	integral of cube root of at with respect to t	$\int \sqrt[3]{a t} d t$
69882	Find dy/dx	y=x^6	$y = x^{6}$
69883	Solve the Differential Equation	2y''''+y=0	$2 y'' + y = 0$
69884	Find the Derivative - d/dx	y=2/3 square root of 2x^2+6x	$y = \frac{2}{3} \sqrt{2 x^{2} + 6 x}$
69885	Integrate Using Trig Substitution	integral of 1/( square root of 4+x^2) with respect to x	$\int \frac{1}{\sqrt{4 + x^{2}}} d x$
69886	Find dy/dx	sin(xy)=x^2-y	$\sin (x y) = x^{2} - y$
69887	Evaluate the Limit	limit as x approaches -2 from the left of (x+3)(\|x+2\|)/(x+2)	$lim_{x \to {(- 2)}^{-}} (x + 3) \frac{\| x + 2 \|}{x + 2}$
69888	Integrate Using u-Substitution	integral of (5x+4)^5 with respect to x	$\int {(5 x + 4)}^{5} d x$
69889	Find dt/dy	y=tan( square root of 3t)	$y = \tan (\sqrt{3 t})$
69890	Find dy/dx	y=x^2+3	$y = x^{2} + 3$
69891	Integrate Using Trig Substitution	integral of square root of 9-x^2 with respect to x	$\int \sqrt{9 - x^{2}} d x$
69892	Evaluate the Limit	limit as x approaches infinity of xe^x	$lim_{x \to \infty} x e^{x}$
69893	Evaluate the Integral	integral of (8t^3-6t^-2) with respect to t	$\int (8 t^{3} - 6 t^{- 2}) d t$
69894	Find dx/dy	square root of x+ square root of y=4	$\sqrt{x} + \sqrt{y} = 4$
69895	Find the Tangent Line at (1,4)	y=5x^2-x^3 , (1,4)	$y = 5 x^{2} - x^{3}$ , $(1, 4)$
69896	Find dy/dx	y^2-3xy+x^2=7	$y^{2} - 3 x y + x^{2} = 7$
69897	Find the Second Derivative	(5x^2+3)(2x-1)	$(5 x^{2} + 3) (2 x - 1)$
69898	Integrate By Parts	integral of xarctan(x) with respect to x	$\int x \arctan (x) d x$
69899	Find the Derivative - d/dx	e^(-1/2x)	$e^{- \frac{1}{2} x}$
69900	Find the Derivative - d/dx	d/(dx)((f(x))/(g(x)))	$\frac{d}{d x} (\frac{f (x)}{g (x)})$