Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
83701	Evaluate the Limit	limit as x approaches infinity of 4-3/(x^2)	$lim_{x \to \infty} 4 - \frac{3}{x^{2}}$
83702	Find dy/dx	2x^3+2y^2+5y=0	$2 x^{3} + 2 y^{2} + 5 y = 0$
83703	Find the Derivative - d/dx	- natural log of cos(x)	$- \ln (\cos (x))$
83704	Integrate Using u-Substitution	integral of square root of x with respect to x	$\int \sqrt{x} d x$
83705	Find the Derivative - d/dx	2x^2-x^2sin(x)	$2 x^{2} - x^{2} \sin (x)$
83706	Find the Derivative - d/dx	square root of 4-x^2-y^2	$\sqrt{4 - x^{2} - y^{2}}$
83707	Find Where Increasing/Decreasing	y=(2/3)^x	$y = {(\frac{2}{3})}^{x}$
83708	Find the Derivative - d/dp	pp	$p \cdot p$
83709	Integrate Using u-Substitution	integral from 0 to 1/6 of 1/( square root of 1-9x^2) with respect to x	$\int_{0}^{\frac{1}{6}} \frac{1}{\sqrt{1 - 9 x^{2}}} d x$
83710	Find the Derivative - d/dx	e^(-3x)-4x+50	$e^{- 3 x} - 4 x + 50$
83711	Evaluate the Integral	integral from -2 to 2 of (\|x-1\|+2) with respect to x	$\int_{- 2}^{2} (\| x - 1 \| + 2) d x$
83712	Find the Derivative - d/dx	y=2e^x-x+5sin(x)-12	$y = 2 e^{x} - x + 5 \sin (x) - 12$
83713	Evaluate the Limit	limit as x approaches 2 of ( square root of 2x-2)/( square root of 14x-3-5)	$lim_{x \to 2} \frac{\sqrt{2 x} - 2}{\sqrt{14 x - 3} - 5}$
83714	Find the Derivative - d/dx	Find the derivative of cube root of 6x+2	Find the derivative of $\sqrt[3]{6 x + 2}$
83715	Evaluate the Integral	integral from -2 to 1 of (4x^3+5x^2-x+1) with respect to x	$\int_{- 2}^{1} (4 x^{3} + 5 x^{2} - x + 1) d x$
83716	Find the Derivative - d/dx	(3x^3)/(2x^3-1)	$\frac{3 x^{3}}{2 x^{3} - 1}$
83717	Find the Second Derivative	5x^(-1/2)	$5 x^{- \frac{1}{2}}$
83718	Find the Center and Radius	x^2+y^2+z^2-6x+4y-2z=11	$x^{2} + y^{2} + z^{2} - 6 x + 4 y - 2 z = 11$
83719	Find dy/dx	y^3-3y^2-9y+2x^2+20x=-27	$y^{3} - 3 y^{2} - 9 y + 2 x^{2} + 20 x = - 27$
83720	Find the Derivative - d/dx	Find the derivative of sin(x+5)^2	Find the derivative of $\sin^{2} (x + 5)$
83721	Find the Derivative - d/dx	1+ square root of 2x	$1 + \sqrt{2 x}$
83722	Find dy/dx	y=x(2x+1)^4	$y = x {(2 x + 1)}^{4}$
83723	Find the Maximum/Minimum Value	x(x-3)^2(x+1)	$x {(x - 3)}^{2} (x + 1)$
83724	Find the Third Derivative	f(x)=-3x-5/8x^-2+1/2x^3-1/10x^5	$f (x) = - 3 x - \frac{5}{8} x^{- 2} + \frac{1}{2} x^{3} - \frac{1}{10} x^{5}$
83725	Evaluate the Integral	integral from 0 to 5 of x/(x+10) with respect to x	$\int_{0}^{5} \frac{x}{x + 10} d x$
83726	Find the Derivative - d/dt	5sin(3t+2)	$5 \sin (3 t + 2)$
83727	Find the Derivative - d/dy	cos(y^2)	$\cos (y^{2})$
83728	Evaluate the Limit	limit as x approaches 0 of sec(e^x-1)^2	$lim_{x \to 0} \sec^{2} (e^{x} - 1)$
83729	Find dy/dx	sin(x^2y^2)=3y	$\sin (x^{2} y^{2}) = 3 y$
83730	Find the Derivative - d/dy	-y/(x+2y)	$- \frac{y}{x + 2 y}$
83731	Find the Derivative - d/dx	square root of 1+cos(x)	$\sqrt{1 + \cos (x)}$
83732	Find dx/dy	e^y-xy=e	$e^{y} - x y = e$
83733	Find the Maximum/Minimum Value	f(x)=-x^3+3x^2-3x	$f (x) = - x^{3} + 3 x^{2} - 3 x$
83734	Find the Antiderivative	f(x)=(e^x)/x	$f (x) = \frac{e^{x}}{x}$
83735	Evaluate the Integral	pi integral from 0 to 1 of [(x^4)^2-(x^7)^2] with respect to x	$π \int_{0}^{1} [{(x^{4})}^{2} - {(x^{7})}^{2}] d x$
83736	Find the Second Derivative	-1/10x^5-2x^4-12x^3	$- \frac{1}{10} x^{5} - 2 x^{4} - 12 x^{3}$
83737	Find the Derivative - d/dx	y=xe^(x^3)	$y = x e^{x^{3}}$
83738	Find the Antiderivative	f(x)=1/(cos(x)^2)-1/(sin(x)^2)	$f (x) = \frac{1}{\cos^{2} (x)} - \frac{1}{\sin^{2} (x)}$
83739	Evaluate the Integral	integral of 3sec(2x) with respect to x	$\int 3 \sec (2 x) d x$
83740	Find the Antiderivative	f(x)=x square root of x+1	$f (x) = x \sqrt{x + 1}$
83741	Evaluate the Limit	limit as z approaches 1 of (z-1)/( square root of 2-z-1)	$lim_{z \to 1} \frac{z - 1}{\sqrt{2 - z} - 1}$
83742	Evaluate the Integral	integral of (5sec(x)tan(x)-3/2csc(x)^2+9) with respect to x	$\int (5 \sec (x) \tan (x) - \frac{3}{2} \csc^{2} (x) + 9) d x$
83743	Evaluate the Integral	integral from 7 to e^3 of 1/x with respect to x	$\int_{7}^{e^{3}} \frac{1}{x} d x$
83744	Evaluate the Integral	integral of (20x)/( cube root of 7-3x^2) with respect to x	$\int \frac{20 x}{\sqrt[3]{7 - 3 x^{2}}} d x$
83745	Evaluate the Limit	limit as n approaches -5 of (2/(n+3)-3/(n+2))/(n+5)	$lim_{n \to - 5} \frac{\frac{2}{n + 3} - \frac{3}{n + 2}}{n + 5}$
83746	Find Where Increasing/Decreasing	y=2*(1/3)^x	$y = 2 \cdot {(\frac{1}{3})}^{x}$
83747	Find the Maximum/Minimum Value	y=1-3cos(3(x-pi/3))	$y = 1 - 3 \cos (3 (x - \frac{π}{3}))$
83748	Find dy/dx	y=e^(x^2-1)	$y = e^{x^{2} - 1}$
83749	Find dy/dx	y=x^(2^x)	$y = x^{2^{x}}$
83750	Find the Derivative - d/dx	d/(dx)tan(x)^2	$\frac{d}{d x} \tan^{2} (x)$
83751	Find the Antiderivative	f(x)=(sin(x))/(12+cos(x))	$f (x) = \frac{\sin (x)}{12 + \cos (x)}$
83752	Evaluate the Integral	integral of ((x+1)(x-2))/( square root of x) with respect to x	$\int \frac{(x + 1) (x - 2)}{\sqrt{x}} d x$
83753	Find the Maximum/Minimum Value	y=1+3sin(2(x+pi/2))	$y = 1 + 3 \sin (2 (x + \frac{π}{2}))$
83754	Find the Derivative - d/dx	xx	$x \cdot x$
83755	Find the Second Derivative	arcsin(x)	$\arcsin (x)$
83756	Evaluate Using Summation Formulas	sum from k=1 to n of 12k+8	$\sum_{k = 1}^{n} 12 k + 8$
83757	Find the Antiderivative	((x-1)^3)/(x^3)	$\frac{{(x - 1)}^{3}}{x^{3}}$
83758	Find the Derivative - d/dw	S=( square root of hw)/60	$S = \frac{\sqrt{h w}}{60}$
83759	Evaluate the Integral	integral of x^2 natural log of \|x\| with respect to x	$\int x^{2} \ln (\| x \|) d x$
83760	Find the Local Maxima and Minima	f(x)=3/4x^4+15x^3+75x^2-23	$f (x) = \frac{3}{4} x^{4} + 15 x^{3} + 75 x^{2} - 23$
83761	Evaluate from the Right	limit as x approaches 2 of 2x+1	$lim_{x \to 2} 2 x + 1$
83762	Integrate Using u-Substitution	integral of (x^3)/(x+3) with respect to x	$\int \frac{x^{3}}{x + 3} d x$
83763	Find the Derivative - d/dx	e^x- square root of e	$e^{x} - \sqrt{e}$
83764	Find the Derivative - d/dx	-sin(x)+cos(x)	$- \sin (x) + \cos (x)$
83765	Find the Maximum/Minimum Value	f(x) = square root of x+4-1	$f (x) = \sqrt{x + 4} - 1$
83766	Find the Maximum/Minimum Value	5x-3(x-1)^2	$5 x - 3 {(x - 1)}^{2}$
83767	Find the Derivative - d/dt	-3/t	$- \frac{3}{t}$
83768	Evaluate the Integral	integral from 0 to pi/2 of 3cos(x)sin(sin(x)) with respect to x	$\int_{0}^{\frac{π}{2}} 3 \cos (x) \sin (\sin (x)) d x$
83769	Find the Derivative - d/dx	y=-1/2x^2	$y = - \frac{1}{2} x^{2}$
83770	Find the Antiderivative	(x+1)*e^x	$(x + 1) \cdot e^{x}$
83771	Find the Derivative - d/dx	e^(xy)=y-x	$e^{x y} = y - x$
83772	Find the Antiderivative	(3x-1)/((x-1)^2)	$\frac{3 x - 1}{{(x - 1)}^{2}}$
83773	Find the Second Derivative	2x-5x^6	$2 x - 5 x^{6}$
83774	Evaluate the Summation	sum from i=1 to 10 of 3/8n+3/8	$\sum_{i = 1}^{10} \frac{3}{8} n + \frac{3}{8}$
83775	Integrate Using u-Substitution	integral of (x+ square root of x) with respect to x	$\int (x + \sqrt{x}) d x$
83776	Find dy/dx	cos(xy)=2x	$\cos (x y) = 2 x$
83777	Find dx/dy	y=sin(4x)-8x^2+9x+pi	$y = \sin (4 x) - 8 x^{2} + 9 x + π$
83778	Evaluate the Limit	limit as x approaches -2 of (x^2+4x+4)/(x^3+x^2-8x-12)	$lim_{x \to - 2} \frac{x^{2} + 4 x + 4}{x^{3} + x^{2} - 8 x - 12}$
83779	Evaluate the Limit	limit as x approaches infinity of 5+x-x^2	$lim_{x \to \infty} 5 + x - x^{2}$
83780	Find the Antiderivative	(2x+1)/((x+2)^2)	$\frac{2 x + 1}{{(x + 2)}^{2}}$
83781	Evaluate the Integral	integral of (5e^x-2/x) with respect to x	$\int (5 e^{x} - \frac{2}{x}) d x$
83782	Evaluate the Integral	integral of 1/( square root of x)- square root of x with respect to x	$\int \frac{1}{\sqrt{x}} - \sqrt{x} d x$
83783	Find the Antiderivative	e^(2x)+1/(x+1)	$e^{2 x} + \frac{1}{x + 1}$
83784	Find the Antiderivative	cos(3x+pi/6)	$\cos (3 x + \frac{π}{6})$
83785	Find the Derivative - d/dx	1/( square root of x)dx	$\frac{1}{\sqrt{x}} d x$
83786	Evaluate the Summation	sum from k=1 to 20 of 100(k^2-5k+1)	$\sum_{k = 1}^{20} 100 (k^{2} - 5 k + 1)$
83787	Evaluate the Limit	limit as x approaches negative infinity of (x^2-9)/(x(x-3))	$lim_{x \to - \infty} \frac{x^{2} - 9}{x (x - 3)}$
83788	Evaluate the Summation	4 sum from d=0 to 4 of 1-4d	$4 \sum_{d = 0}^{4} 1 - 4 d$
83789	Find the Area Between the Curves	y=x^2-5 and y=4	$y = x^{2} - 5$ and $y = 4$
83790	Find the Third Derivative	f(x)=5/24x^-2+1/8x^2-3/10x^5	$f (x) = \frac{5}{24} x^{- 2} + \frac{1}{8} x^{2} - \frac{3}{10} x^{5}$
83791	Evaluate the Integral	integral from 4 to 6 of square root of x^3+1 with respect to x	$\int_{4}^{6} \sqrt{x^{3} + 1} d x$
83792	Evaluate the Integral	integral from 0 to pi of (sin(x))/(1+cos(x)) with respect to x	$\int_{0}^{π} \frac{\sin (x)}{1 + \cos (x)} d x$
83793	Find the Antiderivative	f(x)=3x^2sin(x^3+2003)	$f (x) = 3 x^{2} \sin (x^{3} + 2003)$
83794	Evaluate the Integral	integral of (x-5)/(-2x+2) with respect to x	$\int \frac{x - 5}{- 2 x + 2} d x$
83795	Evaluate the Integral	integral of (8x^4-21x^3+10x^2)/x with respect to x	$\int \frac{8 x^{4} - 21 x^{3} + 10 x^{2}}{x} d x$
83796	Evaluate the Limit	limit as x approaches 3 from the left of (\|x-3\|)/(3-x)	$lim_{x \to 3^{-}} \frac{\| x - 3 \|}{3 - x}$
83797	Find the Antiderivative	x^3*e^(x^2)	$x^{3} \cdot e^{x^{2}}$
83798	Find the Derivative - d/dx	square root of 1/x	$\sqrt{\frac{1}{x}}$
83799	Integrate Using u-Substitution	integral of x^3e^(x^2) with respect to x	$\int x^{3} e^{x^{2}} d x$
83800	Find the Upper and Lower Bounds	f(x)=x^3+4x^2+8x+5	$f (x) = x^{3} + 4 x^{2} + 8 x + 5$