Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
83501	Evaluate the Limit	limit as x approaches 0 of (3x+4x^2-x^3)^4	$lim_{x \to 0} {(3 x + 4 x^{2} - x^{3})}^{4}$
83502	Evaluate the Integral	integral from -5 to 5 of square root of 5^2-x^2 with respect to x	$\int_{- 5}^{5} \sqrt{5^{2} - x^{2}} d x$
83503	Evaluate the Limit	limit as x approaches 1 of (xe^x-e)/(x^2-1)	$lim_{x \to 1} \frac{x e^{x} - e}{x^{2} - 1}$
83504	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of cos(x)^(1/x)	$lim_{x \to 0^{+}} {\cos (x)}^{\frac{1}{x}}$
83505	Evaluate the Integral	integral of x*e^(-x^2) with respect to x	$\int x \cdot e^{- x^{2}} d x$
83506	Find the Antiderivative	1+e^x	$1 + e^{x}$
83507	Find dy/dx	2x^3+y=-y^2	$2 x^{3} + y = - y^{2}$
83508	Find the Derivative - d/dx	-1/(2 square root of x^3)	$- \frac{1}{2 \sqrt{x^{3}}}$
83509	Find the Derivative - d/dx	If square root of x+ square root of y=3 ; then (dy)/(dx) is	If $\sqrt{x} + \sqrt{y} = 3$ ; then $\frac{d y}{d x}$ is
83510	Integrate Using u-Substitution	integral of xe^(-x) with respect to x	$\int x e^{- x} d x$
83511	Find the Center and Radius	9y^2-16x^2=144	$9 y^{2} - 16 x^{2} = 144$
83512	Find the Antiderivative	f(x)=x^2+3/( square root of x)	$f (x) = x^{2} + \frac{3}{\sqrt{x}}$
83513	Find the Center and Radius	x^2+y^2=3^2	$x^{2} + y^{2} = 3^{2}$
83514	Evaluate the Summation	sum from k=1 to 3 of (k^2)/(k+1)	$\sum_{k = 1}^{3} \frac{k^{2}}{k + 1}$
83515	Evaluate the Summation	2 sum from p=0 to 5 of 9-p	$2 \sum_{p = 0}^{5} 9 - p$
83516	Evaluate the Integral	integral from 2 to 4 of x/( square root of x^2-4) with respect to x	$\int_{2}^{4} \frac{x}{\sqrt{x^{2} - 4}} d x$
83517	Find the Derivative - d/dx	e^(5x)=sin(x+3y)	$e^{5 x} = \sin (x + 3 y)$
83518	Find the Domain and Range	f(x)=2x,x<1; 5,x=1; x^2,x>1	$f (x) = {\begin{cases} 2 x, x < 1 \\ 5, x = 1 \\ x^{2}, x > 1 \end{cases}$
83519	Find dy/dx	-1=5x^2+xy	$- 1 = 5 x^{2} + x y$
83520	Find the Derivative of the Integral	integral from 1 to 3x+2 of t/(1+t^3) with respect to t	$\int_{1}^{3 x + 2} \frac{t}{1 + t^{3}} d t$
83521	Find the Derivative - d/dx	sinh(7 natural log of x)	$\sinh (7 \ln (x))$
83522	Find the Second Derivative	y=-4x^2-2/5x^-4+2/3x^4	$y = - 4 x^{2} - \frac{2}{5} x^{- 4} + \frac{2}{3} x^{4}$
83523	Evaluate the Integral	2 integral of sec(x)tan(x) with respect to x	$2 \int \sec (x) \tan (x) d x$
83524	Evaluate the Limit	limit as x approaches -1 of 4/(x^2-1)+2/(x+1)	$lim_{x \to - 1} \frac{4}{x^{2} - 1} + \frac{2}{x + 1}$
83525	Integrate Using u-Substitution	integral from 0 to 2 of x^2 square root of 1+x^3 with respect to x	$\int_{0}^{2} x^{2} \sqrt{1 + x^{3}} d x$
83526	Evaluate the Integral	integral from pi/2 to pi of 5cos(x) with respect to x	$\int_{\frac{π}{2}}^{π} 5 \cos (x) d x$
83527	Find the Antiderivative	f(x)=-sin(2x)	$f (x) = - \sin (2 x)$
83528	Integrate Using u-Substitution	integral of (x^3)/(1+x^8) with respect to x	$\int \frac{x^{3}}{1 + x^{8}} d x$
83529	Evaluate the Limit	limit as x approaches 3 of (sin(x-3)+14x+4)/( square root of x^2-5)	$lim_{x \to 3} \frac{\sin (x - 3) + 14 x + 4}{\sqrt{x^{2} - 5}}$
83530	Evaluate the Integral	integral of 5x(x-4)(3x+5) with respect to x	$\int 5 x (x - 4) (3 x + 5) d x$
83531	Find the Derivative - d/dx	x(e^x-1)	$x (e^{x} - 1)$
83532	Find the Derivative - d/dx	y=1/(arccot(x))	$y = \frac{1}{arccot (x)}$
83533	Integrate By Parts	integral of (e^x)/x with respect to x	$\int \frac{e^{x}}{x} d x$
83534	Determine if Continuous	f(x)=7-x^2,x<=c; x,x>c	$f (x) = {\begin{cases} 7 - x^{2}, x \leq c \\ x, x > c \end{cases}$
83535	Evaluate the Summation	2 sum from p=1 to 4 of -p^2+3	$2 \sum_{p = 1}^{4} - p^{2} + 3$
83536	Evaluate Using L'Hospital's Rule	limit as x approaches negative infinity of (x^2)/(e^(1-x))	$lim_{x \to - \infty} \frac{x^{2}}{e^{1 - x}}$
83537	Evaluate the Integral	integral from -1 to 1 of (3x^2+2x+1)/(x+2) with respect to x	$\int_{- 1}^{1} \frac{3 x^{2} + 2 x + 1}{x + 2} d x$
83538	Evaluate the Integral	integral of (tan( natural log of x))/x with respect to x	$\int \frac{\tan (\ln (x))}{x} d x$
83539	Evaluate the Limit	limit as x approaches 3 from the left of (x^2\|x-3\|)/(x-3)	$lim_{x \to 3^{-}} \frac{x^{2} \| x - 3 \|}{x - 3}$
83540	Find dy/dx	-xy+1+x^2=-2y	$- x y + 1 + x^{2} = - 2 y$
83541	Evaluate the Limit	limit as x approaches 0 of (a^x-1)/x	$lim_{x \to 0} \frac{a^{x} - 1}{x}$
83542	Find dy/dx	-2y^2-2+x^2=0	$- 2 y^{2} - 2 + x^{2} = 0$
83543	Evaluate the Integral	integral from 100 to infinity of x/( square root of 1+x^2) with respect to x	$\int_{100}^{\infty} \frac{x}{\sqrt{1 + x^{2}}} d x$
83544	Find the Center and Radius	(x-4)^2+(y)=16	${(x - 4)}^{2} + (y) = 16$
83545	Find the Antiderivative	(x^2+1)^3	${(x^{2} + 1)}^{3}$
83546	Evaluate the Integral	integral of 2x^3sin(3x^4) with respect to x	$\int 2 x^{3} \sin (3 x^{4}) d x$
83547	Find the Antiderivative	f(x)=(1-3x)^2	$f (x) = {(1 - 3 x)}^{2}$
83548	Evaluate the Limit	limit as x approaches negative infinity of (x^3-1)/(x^3+3)	$lim_{x \to - \infty} \frac{x^{3} - 1}{x^{3} + 3}$
83549	Find dy/dx	y = cube root of -4x+5	$y = \sqrt[3]{- 4 x + 5}$
83550	Evaluate the Limit	limit as x approaches 2 of natural log of x-1	$lim_{x \to 2} \ln (x - 1)$
83551	Find the Third Derivative	f(x)=1/24x^6+1/15x^-4-1/5x^5+2x^-1	$f (x) = \frac{1}{24} x^{6} + \frac{1}{15} x^{- 4} - \frac{1}{5} x^{5} + 2 x^{- 1}$
83552	Evaluate the Limit	limit as h approaches 0 of (\|x+h\|-\|x\|)/h	$lim_{h \to 0} \frac{\| x + h \| - \| x \|}{h}$
83553	Find the Derivative - d/dx	1/(1-sin(x))	$\frac{1}{1 - \sin (x)}$
83554	Evaluate the Integral	integral of (12x^(3/4)-9x^(5/3)) with respect to x	$\int (12 x^{\frac{3}{4}} - 9 x^{\frac{5}{3}}) d x$
83555	Evaluate the Integral	integral of (3sin(2x))/(4sin(x)^2-4) with respect to x	$\int \frac{3 \sin (2 x)}{4 \sin^{2} (x) - 4} d x$
83556	Evaluate the Integral	integral from 0 to 4 of (2 square root of y-y) with respect to y	$\int_{0}^{4} (2 \sqrt{y} - y) d y$
83557	Evaluate the Limit	limit as x approaches infinity of 5+3x^2+x	$lim_{x \to \infty} 5 + 3 x^{2} + x$
83558	Find the Area Under the Curve	f(x)=2x+3 , [2,8] , n=3	$f (x) = 2 x + 3$ , $[2, 8]$ , $n = 3$
83559	Evaluate the Integral	integral of 7x3/4 with respect to x	$\int 7 x \frac{3}{4} d x$
83560	Find the Derivative - d/dx	1+sin(2x)	$1 + \sin (2 x)$
83561	Evaluate the Limit	limit as x approaches 0 of (4-3cos(x))^(1/(x^2))	$lim_{x \to 0} {(4 - 3 \cos (x))}^{\frac{1}{x^{2}}}$
83562	Find the Second Derivative	f(x)=3x^2+2/3x^-3+2/3x^3-x^-1	$f (x) = 3 x^{2} + \frac{2}{3} x^{- 3} + \frac{2}{3} x^{3} - x^{- 1}$
83563	Find the Derivative - d/dx	(e^(3x)+sin(2x))^4	${(e^{3 x} + \sin (2 x))}^{4}$
83564	Find the Volume	xy=8 , x=1 and x=5	$x y = 8$ , $x = 1$ and $x = 5$
83565	Find the Antiderivative	f(x)=1/( square root of 2x-1)	$f (x) = \frac{1}{\sqrt{2 x - 1}}$
83566	Find the Derivative - d/dx	4/(3 fifth root of x^3)	$\frac{4}{3 \sqrt[5]{x^{3}}}$
83567	Find the Derivative - d/dy	x^2+1/x+xy+1/y+y^2	$x^{2} + \frac{1}{x} + x y + \frac{1}{y} + y^{2}$
83568	Find the Third Derivative	y=cos(2x-6)	$y = \cos (2 x - 6)$
83569	Find the Area Between the Curves	y=tan(7x) , y=2sin(7x) , -pi/21<=x<=pi/21	$y = \tan (7 x)$ , $y = 2 \sin (7 x)$ , $- \frac{π}{21} \leq x \leq \frac{π}{21}$
83570	Evaluate the Limit	limit as theta approaches -1 of (theta+1)/(-2theta^2-6theta-4)	$lim_{θ \to - 1} \frac{θ + 1}{- 2 θ^{2} - 6 θ - 4}$
83571	Evaluate the Integral	integral of f(x)g(x) with respect to x	$\int f (x) g (x) d x$
83572	Find Where Increasing/Decreasing	-8/3x^3+19x^2-42x+28	$- \frac{8}{3} x^{3} + 19 x^{2} - 42 x + 28$
83573	Evaluate the Integral	integral from 0 to 1 of pi(1-x^2)^2 with respect to x	$\int_{0}^{1} π {(1 - x^{2})}^{2} d x$
83574	Find the Area Between the Curves	y=sec(x)^2 , y=8cos(x) , -pi/3<=x<=pi/3	$y = \sec^{2} (x)$ , $y = 8 \cos (x)$ , $- \frac{π}{3} \leq x \leq \frac{π}{3}$
83575	Find dy/dx	5x+y-x^2=y^2	$5 x + y - x^{2} = y^{2}$
83576	Find Where Increasing/Decreasing	f(x)=3 square root of x+1	$f (x) = 3 \sqrt{x + 1}$
83577	Find dy/dx	y = square root of square root of 3x+8	$y = \sqrt{\sqrt{3 x} + 8}$
83578	Find the Integral	cos(ecx)	$\cos (e c x)$
83579	Find the Antiderivative	x square root of 1-x	$x \sqrt{1 - x}$
83580	Find dy/dx	0=-2y^2+x^3-5y^3	$0 = - 2 y^{2} + x^{3} - 5 y^{3}$
83581	Find the Maximum/Minimum Value	2sin(x-2pi)	$2 \sin (x - 2 π)$
83582	Find dx/dy	y=x^3+3x^2+1	$y = x^{3} + 3 x^{2} + 1$
83583	Find the Derivative - d/dx	( natural log of 3x)/x	$\frac{\ln (3 x)}{x}$
83584	Evaluate the Integral	integral of (x-1)/(2x+4) with respect to x	$\int \frac{x - 1}{2 x + 4} d x$
83585	Evaluate the Integral	integral from 0 to a of (x^3)/( square root of a^4+x^4) with respect to x	$\int_{0}^{a} \frac{x^{3}}{\sqrt{a^{4} + x^{4}}} d x$
83586	Evaluate the Limit	limit as x approaches 5 of (-5(x-5))/(3\|x-5\|)	$lim_{x \to 5} \frac{- 5 (x - 5)}{3 \| x - 5 \|}$
83587	Find the Derivative - d/dx	natural log of x^2+1	$\ln (x^{2}) + 1$
83588	Evaluate the Integral	integral of 3xcos(x^2) with respect to x	$\int 3 x \cos (x^{2}) d x$
83589	Evaluate the Limit	limit as x approaches -2 of x^3+x^2-x	$lim_{x \to - 2} x^{3} + x^{2} - x$
83590	Find the Antiderivative	2x+4x^3+ square root of x^3+8	$2 x + 4 x^{3} + \sqrt{x^{3}} + 8$
83591	Evaluate the Limit	limit as x approaches negative infinity of (4x)/(x^2-8x+3)	$lim_{x \to - \infty} \frac{4 x}{x^{2} - 8 x + 3}$
83592	Find the Antiderivative	f(x)=(2x^2)/1	$f (x) = \frac{2 x^{2}}{1}$
83593	Find the Maximum/Minimum Value	f(x)=-1/2x^4+4x^3-5x^2-1	$f (x) = - \frac{1}{2} x^{4} + 4 x^{3} - 5 x^{2} - 1$
83594	Find the Derivative - d/dx	y=(x^3-2) square root of x^2+1	$y = (x^{3} - 2) \sqrt{x^{2} + 1}$
83595	Find the Derivative of the Integral	integral from 4 to x^2 of square root of t with respect to t	$\int_{4}^{x^{2}} \sqrt{t} d t$
83596	Evaluate the Integral	integral of (4x^3-8x^2+1)/(x^2) with respect to x	$\int \frac{4 x^{3} - 8 x^{2} + 1}{x^{2}} d x$
83597	Evaluate the Integral	integral from 0 to infinity of x/((1+x^2)^2) with respect to x	$\int_{0}^{\infty} \frac{x}{{(1 + x^{2})}^{2}} d x$
83598	Find the Derivative - d/dx	x/4arcsin(x)	$\frac{x}{4} \arcsin (x)$
83599	Find the Derivative - d/dx	natural log of 2+sin(x)	$\ln (2 + \sin (x))$
83600	Find the Antiderivative	2x*e^x	$2 x \cdot e^{x}$