Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
84701	Find the Maximum/Minimum Value	y=x^4	$y = x^{4}$
84702	Integrate Using u-Substitution	integral of (e^x+e^(-x))/(e^x-e^(-x)) with respect to x	$\int \frac{e^{x} + e^{- x}}{e^{x} - e^{- x}} d x$
84703	Evaluate the Limit	limit as x approaches 0 of (2e^(2x)-2)/(x^2+x)	$lim_{x \to 0} \frac{2 e^{2 x} - 2}{x^{2} + x}$
84704	Evaluate the Limit	limit as x approaches 2 from the right of 1/(x-2)-4/( natural log of 2x-3)	$lim_{x \to 2^{+}} \frac{1}{x - 2} - \frac{4}{\ln (2 x - 3)}$
84705	Find the Derivative - d/dx	x^3+x^2+3	$x^{3} + x^{2} + 3$
84706	Evaluate the Summation	sum from i=1 to 14 of -28+3n	$\sum_{i = 1}^{14} - 28 + 3 n$
84707	Evaluate the Integral	integral of (sec(x)^2-1) with respect to x	$\int (\sec^{2} (x) - 1) d x$
84708	Find dy/dx	y=x^(sin(2x+1))	$y = x^{\sin (2 x + 1)}$
84709	Find the Inflection Points	( cube root of x)/(e^x)+1	$\frac{\sqrt[3]{x}}{e^{x}} + 1$
84710	Evaluate the Summation	3 sum from t=2 to 5 of 2t^2-8t	$3 \sum_{t = 2}^{5} 2 t^{2} - 8 t$
84711	Find dx/dy	f(x)=e^(xy)	$f (x) = e^{x y}$
84712	Evaluate the Limit	limit as x approaches infinity of x/(x^2)	$lim_{x \to \infty} \frac{x}{x^{2}}$
84713	Find the Derivative - d/dx	2^x+x^2	$2^{x} + x^{2}$
84714	Evaluate the Limit	limit as x approaches -3 of (4x+36)/(3-x)	$lim_{x \to - 3} \frac{4 x + 36}{3 - x}$
84715	Find the Derivative - d/dx	1/(x^2+x)	$\frac{1}{x^{2} + x}$
84716	Find the Antiderivative	-13sin(x)+5/(cos(x)^2)	$- 13 \sin (x) + \frac{5}{\cos^{2} (x)}$
84717	Find the Derivative - d/dx	y=7x^3-arcsec(x)	$y = 7 x^{3} - arcsec (x)$
84718	Find the Derivative - d/dx	-(x^2)/2+x-1/2	$- \frac{x^{2}}{2} + x - \frac{1}{2}$
84719	Find the Antiderivative	square root of 4+x^2	$\sqrt{4 + x^{2}}$
84720	Find the Derivative - d/dt	y = natural log of t*5^t	$y = \ln (t \cdot 5^{t})$
84721	Find the Second Derivative	f(x)=1/4x^4+1/4+1/3x^3	$f (x) = \frac{1}{4} x^{4} + \frac{1}{4} + \frac{1}{3} x^{3}$
84722	Evaluate the Limit	limit as x approaches -3 of (9-x^2)/(x^3+3x^2)	$lim_{x \to - 3} \frac{9 - x^{2}}{x^{3} + 3 x^{2}}$
84723	Find dy/dx	cos(xy)=x^2	$\cos (x y) = x^{2}$
84724	Find the Derivative - d/dx	e^(2x)-3e^(-x)	$e^{2 x} - 3 e^{- x}$
84725	Find the Derivative - d/dx	y=(x^2+x+1)(x-1)	$y = (x^{2} + x + 1) (x - 1)$
84726	Find the Domain and Range	f(x)=3-2x,x<-1; x^2,x>=-1	$f (x) = {\begin{cases} 3 - 2 x, x < - 1 \\ x^{2}, x \geq - 1 \end{cases}$
84727	Find the Derivative - d/dx	(2x^2)/(2-x^2)	$\frac{2 x^{2}}{2 - x^{2}}$
84728	Find the Antiderivative	1/(x(x^2+1))	$\frac{1}{x (x^{2} + 1)}$
84729	Find the Maximum/Minimum Value	y=10+12x-3x^2-2x^3	$y = 10 + 12 x - 3 x^{2} - 2 x^{3}$
84730	Find the Derivative - d/dx	(e^( square root of x))/( square root of x)	$\frac{e^{\sqrt{x}}}{\sqrt{x}}$
84731	Evaluate the Integral	integral from -4 to -1 of x^2(3-4x) with respect to x	$\int_{- 4}^{- 1} x^{2} (3 - 4 x) d x$
84732	Evaluate the Limit	limit as z approaches 3 of (z-3)/( square root of 4-z-1)	$lim_{z \to 3} \frac{z - 3}{\sqrt{4 - z} - 1}$
84733	Evaluate the Integral	integral from 0 to 4 of (x-3)^2+3 with respect to x	$\int_{0}^{4} {(x - 3)}^{2} + 3 d x$
84734	Evaluate the Limit	limit as x approaches infinity of x^-5	$lim_{x \to \infty} x^{- 5}$
84735	Find the Second Derivative	y=-2/5x^5-1/2x^2-1/2x^-2	$y = - \frac{2}{5} x^{5} - \frac{1}{2} x^{2} - \frac{1}{2} x^{- 2}$
84736	Evaluate the Limit	limit as x approaches infinity of (x^2)/(x^3)	$lim_{x \to \infty} \frac{x^{2}}{x^{3}}$
84737	Find the Second Derivative	y=cos(2x-6)	$y = \cos (2 x - 6)$
84738	Find the Antiderivative	xtan(x)^2	$x \tan^{2} (x)$
84739	Find the Derivative - d/dx	xcos(x)^3	$x \cos^{3} (x)$
84740	Find the Derivative - d/dx	natural log of 3+x-x^3	$\ln (3 + x - x^{3})$
84741	Find the Derivative - d/dx	y = square root of cos(2x)-sin(x)	$y = \sqrt{\cos (2 x) - \sin (x)}$
84742	Find the Critical Points	(x^2+2)/(2x-1)	$\frac{x^{2} + 2}{2 x - 1}$
84743	Find dy/dx	y=1/( fourth root of 9x^2-5)	$y = \frac{1}{\sqrt[4]{9 x^{2} - 5}}$
84744	Find dy/dx	square root of x^3+y^3=2y	$\sqrt{x^{3} + y^{3}} = 2 y$
84745	Evaluate the Integral	integral of (2^t+e^pi) with respect to t	$\int (2^{t} + e^{π}) d t$
84746	Find Where Increasing/Decreasing	f(x)=- square root of x	$f (x) = - \sqrt{x}$
84747	Find the Area Between the Curves	x=2y^2 , x=0 ; and y=3	$x = 2 y^{2}$ , $x = 0$ ; and $y = 3$
84748	Find the Antiderivative	x cube root of x^2+1	$x \sqrt[3]{x^{2} + 1}$
84749	Find the Derivative - d/dx	d/(dx)((1+x^2)/((1-x^2)^(3/2)))	$\frac{d}{d x} (\frac{1 + x^{2}}{{(1 - x^{2})}^{\frac{3}{2}}})$
84750	Find the Antiderivative	f(x)=1/(2 cube root of x)-1/(x^2)	$f (x) = \frac{1}{2 \sqrt[3]{x}} - \frac{1}{x^{2}}$
84751	Find the Derivative - d/dx	6 square root of 1/x+8x^4	$6 \sqrt{\frac{1}{x} + 8 x^{4}}$
84752	Find dy/dx	y = natural log of sec(x)	$y = \ln (\sec (x))$
84753	Find the Derivative - d/dx	11x^5-3x^2+9x-pi	$11 x^{5} - 3 x^{2} + 9 x - π$
84754	Integrate Using u-Substitution	integral of cos(x)^5 with respect to x	$\int \cos^{5} (x) d x$
84755	Find the Antiderivative	e^x+x^2	$e^{x} + x^{2}$
84756	Find the Derivative of the Integral	integral from pi/6 to pi/3 of sec(x)tg(x) square root of sec(x)+1 with respect to x	$\int_{\frac{π}{6}}^{\frac{π}{3}} \sec (x) t g (x) \sqrt{\sec (x) + 1} d x$
84757	Find the Antiderivative	e^(3x)dx	$e^{3 x} d x$
84758	Find dy/dx	y=3/(4x^2)	$y = \frac{3}{4 x^{2}}$
84759	Find dy/dx	y=(5+3x^3)/(1+2x^3)	$y = \frac{5 + 3 x^{3}}{1 + 2 x^{3}}$
84760	Evaluate the Limit	limit as x approaches 0 of (x^2)/(1- square root of 1+x^2)	$lim_{x \to 0} \frac{x^{2}}{1 - \sqrt{1 + x^{2}}}$
84761	Evaluate the Integral	integral from 0 to pi/2 of 3sin(x)^2cos(x) with respect to x	$\int_{0}^{\frac{π}{2}} 3 \sin^{2} (x) \cos (x) d x$
84762	Evaluate the Integral	integral from 0 to 2 of square root of 2x+1 with respect to x	$\int_{0}^{2} \sqrt{2 x + 1} d x$
84763	Find dy/dx	y=arctan( square root of x-6)	$y = \arctan (\sqrt{x - 6})$
84764	Evaluate the Limit	limit as h approaches 0 of (e^(2+h)-e^2)/h	$lim_{h \to 0} \frac{e^{2 + h} - e^{2}}{h}$
84765	Find the Second Derivative	x^4+2x^2y^2=8	$x^{4} + 2 x^{2} y^{2} = 8$
84766	Find the Derivative - d/dx	y=sin(x)cos(x)^2	$y = \sin (x) \cos^{2} (x)$
84767	Evaluate the Integral	integral of (x-3)^2+3 with respect to x	$\int {(x - 3)}^{2} + 3 d x$
84768	Find the Turning Points	f(x) = cube root of x-1	$f (x) = \sqrt[3]{x - 1}$
84769	Find the Domain and Range	f(x) = square root of 64-x^2,0<=x<8; 8,8<=x<16; 16,x=16	$f (x) = {\begin{cases} \sqrt{64 - x^{2}}, 0 \leq x < 8 \\ 8, 8 \leq x < 16 \\ 16, x = 16 \end{cases}$
84770	Evaluate the Integral	integral of (1/(x^(3/2))-x^(4/5)) with respect to x	$\int (\frac{1}{x^{\frac{3}{2}}} - x^{\frac{4}{5}}) d x$
84771	Evaluate the Limit	limit as x approaches 1 from the right of (x-2)^2	$lim_{x \to 1^{+}} {(x - 2)}^{2}$
84772	Solve the Differential Equation	(dy)/(dx)=(-2x)/(3y^2) , y(2)=1	$\frac{d y}{d x} = \frac{- 2 x}{3 y^{2}}$ , $y (2) = 1$
84773	Find the Maximum/Minimum Value	y=4x^4+2x^3-x^2+10	$y = 4 x^{4} + 2 x^{3} - x^{2} + 10$
84774	Find the Derivative - d/dx	square root of e^(2x)	$\sqrt{e^{2 x}}$
84775	Evaluate the Integral	integral of (-4x)/((1-2x^2)^2) with respect to x	$\int \frac{- 4 x}{{(1 - 2 x^{2})}^{2}} d x$
84776	Find Where Increasing/Decreasing	y=1/2*4^x	$y = \frac{1}{2} \cdot 4^{x}$
84777	Evaluate the Integral	The definite integral integral from 0 to 1 of (e^(-x)+e^x)/(e^x) with respect to x is equal to:	The definite integral $\int_{0}^{1} \frac{e^{- x} + e^{x}}{e^{x}} d x$ is equal to:
84778	Evaluate the Integral	integral of cube root of 1+7x with respect to x	$\int \sqrt[3]{1 + 7 x} d x$
84779	Find the Derivative - d/dx	(5 fourth root of x^5)/2	$\frac{5 \sqrt[4]{x^{5}}}{2}$
84780	Evaluate the Limit	limit as x approaches pi/6 of tan(-2x)-sin(2x)	$lim_{x \to \frac{π}{6}} \tan (- 2 x) - \sin (2 x)$
84781	Find the Derivative - d/dx	y=e^(-2x^6-2x^5)	$y = e^{- 2 x^{6} - 2 x^{5}}$
84782	Evaluate the Integral	integral of (t^3+5t^2+7t+1)/(t^2+3t) with respect to t	$\int \frac{t^{3} + 5 t^{2} + 7 t + 1}{t^{2} + 3 t} d t$
84783	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of sin(x)^(tan(x))	$lim_{x \to 0^{+}} {\sin (x)}^{\tan (x)}$
84784	Find the Domain and Range	f(x)=x^2+1 , -2<x<3	$f (x) = x^{2} + 1$ , $- 2 < x < 3$
84785	Evaluate the Limit	limit as x approaches infinity of ((2x^3-4)^2(3x+7)^3)/((3x^2-2)^4(4x+13))	$lim_{x \to \infty} \frac{{(2 x^{3} - 4)}^{2} {(3 x + 7)}^{3}}{{(3 x^{2} - 2)}^{4} (4 x + 13)}$
84786	Evaluate the Limit	limit as x approaches infinity of (4x^4-49)/((x^2+49)(4x^2-49))	$lim_{x \to \infty} \frac{4 x^{4} - 49}{(x^{2} + 49) (4 x^{2} - 49)}$
84787	Evaluate the Integral	integral of 14/( cube root of 3x+1) with respect to x	$\int \frac{14}{\sqrt[3]{3 x + 1}} d x$
84788	Find the Derivative - d/dx	y=(4x^5+x^2+4)/(5x^2-2)	$y = \frac{4 x^{5} + x^{2} + 4}{5 x^{2} - 2}$
84789	Find the Antiderivative	(6x^3-3x+2)/5	$\frac{6 x^{3} - 3 x + 2}{5}$
84790	Integrate By Parts	integral of xe^(-x^2) with respect to x	$\int x e^{- x^{2}} d x$
84791	Find the Derivative - d/dx	9/( cube root of x+1)	$\frac{9}{\sqrt[3]{x + 1}}$
84792	Integrate By Parts	integral of e^(-theta)cos(2theta) with respect to theta	$\int e^{- θ} \cos (2 θ) d θ$
84793	Find the Derivative - d/dx	d/(dx)(-4x^-2-5x^(-5/2))	$\frac{d}{d x} (- 4 x^{- 2} - 5 x^{- \frac{5}{2}})$
84794	Evaluate the Integral	integral of x^2+y^2 with respect to x	$\int x^{2} + y^{2} d x$
84795	Find the Antiderivative	sin(x)*e^x	$\sin (x) \cdot e^{x}$
84796	Integrate Using u-Substitution	integral from 0 to 2 of 1/(4+x^2) with respect to x	$\int_{0}^{2} \frac{1}{4 + x^{2}} d x$
84797	Find the Antiderivative	4/(x^2-4)	$\frac{4}{x^{2} - 4}$
84798	Find Where Increasing/Decreasing	f(x) = square root of x-7+2	$f (x) = \sqrt{x - 7} + 2$
84799	Find dy/dx	y=4/( cube root of -2x-4)	$y = \frac{4}{\sqrt[3]{- 2 x - 4}}$
84800	Evaluate Using L'Hospital's Rule	limit as x approaches 2 from the right of 8/(x^2-4)-x/(x-2)	$lim_{x \to 2^{+}} \frac{8}{x^{2} - 4} - \frac{x}{x - 2}$