Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
82401	Evaluate the Limit	limit as x approaches infinity of -arctan(x)	$lim_{x \to \infty} - \arctan (x)$
82402	Evaluate the Summation	sum from i=1 to 3 of 1/(x_i^2)	$\sum_{i = 1}^{3} \frac{1}{{x_{i}}^{2}}$
82403	Find dy/dx	y^3+y-2y^2+5x^2=0	$y^{3} + y - 2 y^{2} + 5 x^{2} = 0$
82404	Evaluate the Summation	6 sum from m=0 to 5 of 8-m^2	$6 \sum_{m = 0}^{5} 8 - m^{2}$
82405	Evaluate the Limit	limit as x approaches 2 of - square root of 2x+1	$lim_{x \to 2} - \sqrt{2 x + 1}$
82406	Find Where Increasing/Decreasing	f(x)=1/2x^(3/2)	$f (x) = \frac{1}{2} x^{\frac{3}{2}}$
82407	Evaluate the Integral	integral of (2sin( square root of x)^3)/( square root of x) with respect to x	$\int \frac{2 \sin^{3} (\sqrt{x})}{\sqrt{x}} d x$
82408	Find Where Increasing/Decreasing	f(x)=5* log of -x	$f (x) = 5 \cdot \log (- x)$
82409	Find Where Increasing/Decreasing	f(x)=(4x)/(x-1)	$f (x) = \frac{4 x}{x - 1}$
82410	Find the Third Derivative	f(x)=3/4x^-2+1/2x^4-x^3	$f (x) = \frac{3}{4} x^{- 2} + \frac{1}{2} x^{4} - x^{3}$
82411	Find the Integral	e^(-x/2)	$e^{- \frac{x}{2}}$
82412	Find the Derivative - d/dh	h=40t-4.9t^2	$h = 40 t - 4.9 t^{2}$
82413	Integrate Using u-Substitution	integral of 1/( square root of 1-x^2) with respect to x	$\int \frac{1}{\sqrt{1 - x^{2}}} d x$
82414	Find the Second Derivative	x/( natural log of x)	$\frac{x}{\ln (x)}$
82415	Evaluate the Integral	integral from 1 to 3 of (y^3-2y^2-y)/(y^2) with respect to y	$\int_{1}^{3} \frac{y^{3} - 2 y^{2} - y}{y^{2}} d y$
82416	Find the Antiderivative	1/(2 square root of x)-1/(x^2)	$\frac{1}{2 \sqrt{x}} - \frac{1}{x^{2}}$
82417	Find the Integral	1/(1+2x)	$\frac{1}{1 + 2 x}$
82418	Find the Derivative of the Integral	g(x) = integral from -19 to x^2 of (t-169)^92(5t-245)^37 with respect to t	$g (x) = \int_{- 19}^{x^{2}} {(t - 169)}^{92} {(5 t - 245)}^{37} d t$
82419	Find dy/dx	5y^3-x^3=x^2y	$5 y^{3} - x^{3} = x^{2} y$
82420	Find the Antiderivative	(x+2)/x	$\frac{x + 2}{x}$
82421	Find dy/dx	-x-4x^2=y^2	$- x - 4 x^{2} = y^{2}$
82422	Evaluate Using L'Hospital's Rule	limit as x approaches -3 of (3sin(2x+6))/(3+x)	$lim_{x \to - 3} \frac{3 \sin (2 x + 6)}{3 + x}$
82423	Find the Linearization at θ=0	f(theta)=sin(theta+pi/3) , theta=0	$f (θ) = \sin (θ + \frac{π}{3})$ , $θ = 0$
82424	Integrate Using u-Substitution	integral of (2x^3+2x)u(x) with respect to x=x^6+2x^4+x^2+C	$\int (2 x^{3} + 2 x) u (x) d x = x^{6} + 2 x^{4} + x^{2} + C$
82425	Find the Antiderivative	f(x)=5sin(x/5)+cos(2x)	$f (x) = 5 \sin (\frac{x}{5}) + \cos (2 x)$
82426	Evaluate the Integral	integral of (-5x^3+6x^4+5x^-3) with respect to x	$\int (- 5 x^{3} + 6 x^{4} + 5 x^{- 3}) d x$
82427	Find the Derivative - d/dx	1/2sin(x)^2	$\frac{1}{2} \sin^{2} (x)$
82428	Find the Antiderivative	2/(x^3)+cos(x)	$\frac{2}{x^{3}} + \cos (x)$
82429	Find the Derivative - d/dy	x^(2y)	$x^{2 y}$
82430	Find the Derivative of the Integral	integral from 9 to square root of x of t with respect to t	$\int_{9}^{\sqrt{x}} t d t$
82431	Find the Derivative - d/dx	y=x^2e^(-x^2)	$y = x^{2} e^{- x^{2}}$
82432	Find dy/dx	y=cos(5x^2-x)	$y = \cos (5 x^{2} - x)$
82433	Find the Derivative - d/dx	90+4/(x+1)	$90 + \frac{4}{x + 1}$
82434	Find the Area Between the Curves	y=x^2-1 , y=3/(x^2+1)	$y = x^{2} - 1$ , $y = \frac{3}{x^{2} + 1}$
82435	Evaluate the Integral	integral from -1 to 1 of [(2-x^2)-(x^2)] with respect to x	$\int_{- 1}^{1} [(2 - x^{2}) - (x^{2})] d x$
82436	Find the Derivative - d/dx	d/(dx)(arctan( square root of x))	$\frac{d}{d x} (\arctan (\sqrt{x}))$
82437	Find the Derivative - d/dx	natural log of x-2x^2	$\ln (x) - 2 x^{2}$
82438	Integrate Using u-Substitution	integral of (x+1) square root of 2-x with respect to x	$\int (x + 1) \sqrt{2 - x} d x$
82439	Find dy/dx	xy^2+x=3y	$x y^{2} + x = 3 y$
82440	Find dy/dx	-xy^3-5x^2=2y^3+2	$- x y^{3} - 5 x^{2} = 2 y^{3} + 2$
82441	Find dy/dx	-x^2+xy=2	$- x^{2} + x y = 2$
82442	Find dy/dx	0=-2y^2+x^2+x	$0 = - 2 y^{2} + x^{2} + x$
82443	Find dy/dx	0=xy+y^3-5-x^2	$0 = x y + y^{3} - 5 - x^{2}$
82444	Find Where Increasing/Decreasing	y=350(1+0.75)^t	$y = 350 {(1 + 0.75)}^{t}$
82445	Evaluate the Limit	limit as x approaches 0 of \|sin(x)\|cos(1/x)	$lim_{x \to 0} \| \sin (x) \| \cos (\frac{1}{x})$
82446	Find the Antiderivative	1/(cos(3x)^2)	$\frac{1}{\cos^{2} (3 x)}$
82447	Evaluate the Integral	integral from 0 to infinity of 5/((x+4)^4) with respect to x	$\int_{0}^{\infty} \frac{5}{{(x + 4)}^{4}} d x$
82448	Find the Derivative - d/dx	tan(x)+7x^2-pix+2	$\tan (x) + 7 x^{2} - π x + 2$
82449	Find the Derivative - d/dx	1/2(e^x-e^(-x))	$\frac{1}{2} (e^{x} - e^{- x})$
82450	Evaluate the Integral	integral from 1 to 3 of 1/((x-1)^(4/3)) with respect to x	$\int_{1}^{3} \frac{1}{{(x - 1)}^{\frac{4}{3}}} d x$
82451	Find the Antiderivative	1/(x^2+2x)	$\frac{1}{x^{2} + 2 x}$
82452	Find dy/dx	y=(3x^3)/(2x^3-1)	$y = \frac{3 x^{3}}{2 x^{3} - 1}$
82453	Integrate Using u-Substitution	integral of x/( square root of x^2+1) with respect to x	$\int \frac{x}{\sqrt{x^{2} + 1}} d x$
82454	Evaluate the Limit	limit as x approaches -2 of (x+3)(2-x)	$lim_{x \to - 2} (x + 3) (2 - x)$
82455	Evaluate the Integral	integral of sin(2x)^3cos(2x)^2 with respect to x	$\int \sin^{3} (2 x) \cos^{2} (2 x) d x$
82456	Evaluate the Integral	integral from 0 to pi/4 of (1-sin(theta)^2)/(cos(theta)^2) with respect to theta	$\int_{0}^{\frac{π}{4}} \frac{1 - \sin^{2} (θ)}{\cos^{2} (θ)} d θ$
82457	Evaluate the Limit	limit as x approaches pi/(()/())*2 of 9sin(x)	$lim_{x \to \frac{π}{\frac{}{}} \cdot 2} 9 \sin (x)$
82458	Find the Fourth Derivative	f(x)=sin(ax)	$f (x) = \sin (a x)$
82459	Evaluate the Integral	integral of (10x^3+ square root of x) with respect to x	$\int (10 x^{3} + \sqrt{x}) d x$
82460	Evaluate the Integral	Evaluate integral of 4x^-5 with respect to x	Evaluate $\int 4 x^{- 5} d x$
82461	Find dy/dx	y^3=x^3+1	$y^{3} = x^{3} + 1$
82462	Find the Derivative - d/dx	3csc(2x)	$3 \csc (2 x)$
82463	Find the Center and Radius	9x^2-4y^2-90x-32y=-305	$9 x^{2} - 4 y^{2} - 90 x - 32 y = - 305$
82464	Integrate Using u-Substitution	integral of 1/(x^2+1) with respect to x	$\int \frac{1}{x^{2} + 1} d x$
82465	Find the Antiderivative	x*cos(x)	$x \cdot \cos (x)$
82466	Evaluate the Limit	limit as x approaches 2 of (x^2+3x-10)/( square root of 4x-4-x)	$lim_{x \to 2} \frac{x^{2} + 3 x - 10}{\sqrt{4 x - 4} - x}$
82467	Evaluate the Integral	integral of (1-csc(x)cot(x)) with respect to x	$\int (1 - \csc (x) \cot (x)) d x$
82468	Evaluate the Integral	integral from 0 to 4 of \| square root of x+2-x\| with respect to x	$\int_{0}^{4} \| \sqrt{x + 2} - x \| d x$
82469	Evaluate the Limit	limit as x approaches 0 of (x+cos(5x)-1)/(-3x)	$lim_{x \to 0} \frac{x + \cos (5 x) - 1}{- 3 x}$
82470	Find the Derivative - d/dx	y=(tan(2x))/(1-cot(2x))	$y = \frac{\tan (2 x)}{1 - \cot (2 x)}$
82471	Find the Derivative - d/dx	y=(sin(x^3+7)^5)^9	$y = {(\sin^{5} (x^{3} + 7))}^{9}$
82472	Evaluate the Limit	limit as x approaches square root of 3 of (x^2)/( square root of 12-x^2)	$lim_{x \to \sqrt{3}} \frac{x^{2}}{\sqrt{12 - x^{2}}}$
82473	Evaluate the Integral	integral of 4(tan(x)^2+tan(x)^4) with respect to x	$\int 4 (\tan^{2} (x) + \tan^{4} (x)) d x$
82474	Evaluate the Integral	integral from 0 to 12 of square root of 36-(x-6)^2 with respect to x	$\int_{0}^{12} \sqrt{36 - {(x - 6)}^{2}} d x$
82475	Evaluate the Limit	limit as x approaches 1 of (2x+y)/(x+1)=5	$lim_{x \to 1} \frac{2 x + y}{x + 1} = 5$
82476	Find the Concavity	1/4x^4+4x^3+24x^2	$\frac{1}{4} x^{4} + 4 x^{3} + 24 x^{2}$
82477	Find the Derivative - d/dx	xy^2-5y+6	$x y^{2} - 5 y + 6$
82478	Find dy/dx	1+3y^3=x^2	$1 + 3 y^{3} = x^{2}$
82479	Integrate By Parts	integral from negative infinity to 0 of (xe^x)/((x+1)^2) with respect to x	$\int_{- \infty}^{0} \frac{x e^{x}}{{(x + 1)}^{2}} d x$
82480	Evaluate the Integral	integral of (4+2x^2+6x) with respect to x	$\int (4 + 2 x^{2} + 6 x) d x$
82481	Find the Antiderivative	f(x)=4/(x^5)-3	$f (x) = \frac{4}{x^{5}} - 3$
82482	Find the Antiderivative	y=e^x	$y = e^{x}$
82483	Find the Antiderivative	(1+sin(x))^2	${(1 + \sin (x))}^{2}$
82484	Evaluate the Integral	pi integral from 0 to 2 of (4-x^2)^2 with respect to x	$π \int_{0}^{2} {(4 - x^{2})}^{2} d x$
82485	Find dy/dx	(x^2+y^2)^4=3y^3	${(x^{2} + y^{2})}^{4} = 3 y^{3}$
82486	Find the Antiderivative	x/(2x-1)	$\frac{x}{2 x - 1}$
82487	Evaluate the Integral	integral of ( cube root of x^4)/3 with respect to x	$\int \frac{\sqrt[3]{x^{4}}}{3} d x$
82488	Find the Derivative - d/dx	cos(x^2+x)	$\cos (x^{2} + x)$
82489	Find the Derivative - d/dx	x+ square root of 1+x^2	$x + \sqrt{1 + x^{2}}$
82490	Evaluate the Integral	integral from -3 to 3 of [(18-x^2)-(x^2)] with respect to x	$\int_{- 3}^{3} [(18 - x^{2}) - (x^{2})] d x$
82491	Find Where Increasing/Decreasing	f(x)=-3/4 cube root of x+1	$f (x) = - \frac{3}{4} \sqrt[3]{x + 1}$
82492	Integrate By Parts	integral of 1 with respect to x	$\int d x$
82493	Find the Concavity	f(x)=1/12x^4-1/2x^3+x^2+2x-1	$f (x) = \frac{1}{12} x^{4} - \frac{1}{2} x^{3} + x^{2} + 2 x - 1$
82494	Find the Derivative - d/dx	cube root of x+ square root of x^5	$\sqrt[3]{x + \sqrt{x^{5}}}$
82495	Evaluate the Limit	limit as x approaches infinity of (5x^3-6x^2-9x-10)/(4x^4-3x^2+4x+7)	$lim_{x \to \infty} \frac{5 x^{3} - 6 x^{2} - 9 x - 10}{4 x^{4} - 3 x^{2} + 4 x + 7}$
82496	Evaluate the Limit	limit as x approaches infinity of (3x^7-4x^2+1)/(5-10x^2)	$lim_{x \to \infty} \frac{3 x^{7} - 4 x^{2} + 1}{5 - 10 x^{2}}$
82497	Find dx/dy	y=x^3-2x^2-6x+pi	$y = x^{3} - 2 x^{2} - 6 x + π$
82498	Find dy/dx	x^2-2y^3+4y=2	$x^{2} - 2 y^{3} + 4 y = 2$
82499	Find the Inflection Points	-1/15x^6+x^5-4x^4	$- \frac{1}{15} x^{6} + x^{5} - 4 x^{4}$
82500	Evaluate the Limit	limit as x approaches 1 of 2^((x-7)/3)	$lim_{x \to 1} 2^{\frac{x - 7}{3}}$