Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
80701	Find the Maximum/Minimum Value	-(x+1)(x-1)^2	$- (x + 1) {(x - 1)}^{2}$
80702	Find the Derivative - d/dx	natural log of x^3 fifth root of x^2+1	$\ln (x^{3} \sqrt[5]{x^{2} + 1})$
80703	Evaluate the Limit	limit as x approaches c of (64)^(2/3)	$lim_{x \to c} {(64)}^{\frac{2}{3}}$
80704	Find the Derivative - d/dx	1/( cube root of x-1)	$\frac{1}{\sqrt[3]{x - 1}}$
80705	Find the Antiderivative	f(x)=2/( square root of 4x+3)-4/(x^5)	$f (x) = \frac{2}{\sqrt{4 x + 3}} - \frac{4}{x^{5}}$
80706	Evaluate the Integral	integral from 0 to 3 of (2sin(x)-e^x) with respect to x	$\int_{0}^{3} (2 \sin (x) - e^{x}) d x$
80707	Find the Derivative - d/dx	y=(x-1) square root of 2x-x^2+arcsin(x-1)	$y = (x - 1) \sqrt{2 x - x^{2}} + \arcsin (x - 1)$
80708	Evaluate the Limit	limit as x approaches infinity of ( square root of 49x^2-4+3)/(x+3)	$lim_{x \to \infty} \frac{\sqrt{49 x^{2} - 4} + 3}{x + 3}$
80709	Find the Derivative - d/dx	d/(dx)(4^(x^2))	$\frac{d}{d x} (4^{x^{2}})$
80710	Evaluate the Integral	integral from pi/6 to pi/2 of x+cos(x) with respect to x	$\int_{\frac{π}{6}}^{\frac{π}{2}} x + \cos (x) d x$
80711	Find the Antiderivative	1/( square root of 1-x* square root of 1+x)	$\frac{1}{\sqrt{1 - x} \cdot \sqrt{1 + x}}$
80712	Evaluate the Limit	limit as x approaches 2 of (x-2)/(3x-6)	$lim_{x \to 2} \frac{x - 2}{3 x - 6}$
80713	Find the Derivative - d/dx	-3x^(2/3)	$- 3 x^{\frac{2}{3}}$
80714	Evaluate the Integral	integral from -3 to 5 of [2y-(y^2-15)] with respect to y	$\int_{- 3}^{5} [2 y - (y^{2} - 15)] d y$
80715	Find the Center and Radius	x^2+y^2+8x=6y	$x^{2} + y^{2} + 8 x = 6 y$
80716	Evaluate the Integral	integral from 0 to 4 of 1/( square root of x(1+ square root of x)) with respect to x	$\int_{0}^{4} \frac{1}{\sqrt{x} (1 + \sqrt{x})} d x$
80717	Find the Antiderivative	f(x)=1/(x square root of x)	$f (x) = \frac{1}{x \sqrt{x}}$
80718	Evaluate the Integral	integral of (12x^2)/(2x+1) with respect to x	$\int \frac{12 x^{2}}{2 x + 1} d x$
80719	Evaluate the Limit	limit as x approaches infinity of (x^2-3)/(2x^2+x+4)	$lim_{x \to \infty} \frac{x^{2} - 3}{2 x^{2} + x + 4}$
80720	Find dy/dx	x^2y=4	$x^{2} y = 4$
80721	Find Where Increasing/Decreasing	f(x)=3/4x^4-x^3-84x^2-2	$f (x) = \frac{3}{4} x^{4} - x^{3} - 84 x^{2} - 2$
80722	Find the Antiderivative	(x+1)e^x	$(x + 1) e^{x}$
80723	Find the Maximum/Minimum Value	g(x)=x^4-x^5	$g (x) = x^{4} - x^{5}$
80724	Evaluate the Integral	integral of -csc(x)^2cot(x)^3 with respect to x	$\int - \csc^{2} (x) \cot^{3} (x) d x$
80725	Find the Maximum/Minimum Value	f(x)=-3x^4-8x^3-6x^2+1	$f (x) = - 3 x^{4} - 8 x^{3} - 6 x^{2} + 1$
80726	Find the Derivative Using Quotient Rule - d/dx	integral of (sec(x)+csc(x)+cot(x))/(tan(x)^2+sin(x)^2+cos(x)^2) with respect to x	$\int \frac{\sec (x) + \csc (x) + \cot (x)}{\tan^{2} (x) + \sin^{2} (x) + \cos^{2} (x)} d x$
80727	Find Where Increasing/Decreasing	f(x)=1/2x^4-2x^3-54x^2+15	$f (x) = \frac{1}{2} x^{4} - 2 x^{3} - 54 x^{2} + 15$
80728	Find the Upper and Lower Bounds	f(x)=x^4-4x^3-9x^2+x-16	$f (x) = x^{4} - 4 x^{3} - 9 x^{2} + x - 16$
80729	Find the Antiderivative	(x^3)/( square root of 1-x^2)	$\frac{x^{3}}{\sqrt{1 - x^{2}}}$
80730	Find the Concavity	f(x)=-1/5x^6+5x^4	$f (x) = - \frac{1}{5} x^{6} + 5 x^{4}$
80731	Find dZ/dX	Z=(XY)/(X+Y)	$Z = \frac{X Y}{X + Y}$
80732	Find the Maximum/Minimum Value	f(x)=( natural log of x)/(x^2)	$f (x) = \frac{\ln (x)}{x^{2}}$
80733	Determine if Continuous	h(x)=-x^2+k^2,0<=x<=1; (4x+4)/(2-x),x>1	$h (x) = {\begin{cases} - x^{2} + k^{2}, 0 \leq x \leq 1 \\ \frac{4 x + 4}{2 - x}, x > 1 \end{cases}$
80734	Evaluate the Integral	integral of (10^(20t)-e^(20t)) with respect to t	$\int (10^{20 t} - e^{20 t}) d t$
80735	Evaluate the Integral	integral of ( square root of x^5)/6 with respect to x	$\int \frac{\sqrt{x^{5}}}{6} d x$
80736	Evaluate the Integral	integral of (x+2)/( square root of x^2+4x) with respect to x	$\int \frac{x + 2}{\sqrt{x^{2} + 4 x}} d x$
80737	Evaluate the Integral	integral of ((x^3+ square root of x)/(x^5)) with respect to x	$\int (\frac{x^{3} + \sqrt{x}}{x^{5}}) d x$
80738	Evaluate the Integral	integral from 0 to 2 of (x+1)/( square root of x^2+2x+1) with respect to x	$\int_{0}^{2} \frac{x + 1}{\sqrt{x^{2} + 2 x + 1}} d x$
80739	Find Where Increasing/Decreasing	f(x)=-3/5x^5-6x^4-15x^3+50	$f (x) = - \frac{3}{5} x^{5} - 6 x^{4} - 15 x^{3} + 50$
80740	Find the Concavity	f(x)=-1/6x^4+19x^2	$f (x) = - \frac{1}{6} x^{4} + 19 x^{2}$
80741	Find dy/dx	y=tan(2x)	$y = \tan (2 x)$
80742	Find the Maximum/Minimum Value	x^5+x^4	$x^{5} + x^{4}$
80743	Find the Derivative - d/dx	y=1/(3x^5-2x)	$y = \frac{1}{3 x^{5} - 2 x}$
80744	Evaluate the Integral	integral of x( square root of x+2/(x^3)) with respect to x	$\int x (\sqrt{x} + \frac{2}{x^{3}}) d x$
80745	Evaluate the Integral	integral of 3/( square root of x^5) with respect to x	$\int \frac{3}{\sqrt{x^{5}}} d x$
80746	Find the Derivative - d/dx	y=e^(x-e)+ natural log of x-x/e	$y = e^{x - e} + \ln (x) - \frac{x}{e}$
80747	Find the Derivative of the Integral	h(x) = integral from 0 to e^x of natural log of t with respect to t	$h (x) = \int_{0}^{e^{x}} \ln (t) d t$
80748	Find the Maximum/Minimum Value	2cos(x-2pi)	$2 \cos (x - 2 π)$
80749	Evaluate the Limit	limit as x approaches 0 of (3^(2x)-1)/(3^(x+2)-9)	$lim_{x \to 0} \frac{3^{2 x} - 1}{3^{x + 2} - 9}$
80750	Find the Second Derivative	S(t)=2t^(3/2)-9t+6	$S (t) = 2 t^{\frac{3}{2}} - 9 t + 6$
80751	Find Where Increasing/Decreasing	f(x)=(3/4)^(2(x+1))-5	$f (x) = {(\frac{3}{4})}^{2 (x + 1)} - 5$
80752	Find the Antiderivative	x/(x-1)	$\frac{x}{x - 1}$
80753	Evaluate the Limit	limit as x approaches negative infinity of (2x^3+3x+2)/(5x^2+x)	$lim_{x \to - \infty} \frac{2 x^{3} + 3 x + 2}{5 x^{2} + x}$
80754	Find the Inflection Points	f(x)=3/10x^5+5x^4	$f (x) = \frac{3}{10} x^{5} + 5 x^{4}$
80755	Find the Derivative - d/dx	y = natural log of 4x^2+b	$y = \ln (4 x^{2} + b)$
80756	Find the Antiderivative	x^2*e^(x^3+1)	$x^{2} \cdot e^{x^{3} + 1}$
80757	Find the Antiderivative	(3x-1)/(x+2)	$\frac{3 x - 1}{x + 2}$
80758	Evaluate the Limit	limit as x approaches 0 of ((x+2)^2-4)/(x^2+x)	$lim_{x \to 0} \frac{{(x + 2)}^{2} - 4}{x^{2} + x}$
80759	Find the Derivative - d/dx	-1/(3x^3)	$\frac{- 1}{3 x^{3}}$
80760	Find dy/dx	-2x^3y+2x=3-3y^2	$- 2 x^{3} y + 2 x = 3 - 3 y^{2}$
80761	Find the Antiderivative	f(x)=31/(sin(x)^2)	$f (x) = \frac{31}{\sin^{2} (x)}$
80762	Find the Integral	(8(4^x))dx	$(8 (4^{x})) d x$
80763	Find the Derivative - d/dt	y=4 log base 3 of t	$y = 4 \log_{3} (t)$
80764	Evaluate the Integral	integral of ((x^2+1)/( square root of x)) with respect to x	$\int (\frac{x^{2} + 1}{\sqrt{x}}) d x$
80765	Evaluate the Limit	limit as x approaches infinity of (2-15e^(-5x))/(1/x+4cos(5/x))	$lim_{x \to \infty} \frac{2 - 15 e^{- 5 x}}{\frac{1}{x} + 4 \cos (\frac{5}{x})}$
80766	Find dy/dx	x^3-2x^2=4-y^2	$x^{3} - 2 x^{2} = 4 - y^{2}$
80767	Find the Inflection Points	y=e^(-x)+2xe^(-x)+x^2e^(-x)	$y = e^{- x} + 2 x e^{- x} + x^{2} e^{- x}$
80768	Integrate Using u-Substitution	integral of x^2 square root of 3x+2 with respect to x	$\int x^{2} \sqrt{3 x + 2} d x$
80769	Find the Inflection Points	2/15x^6-3x^4	$\frac{2}{15} x^{6} - 3 x^{4}$
80770	Find the Absolute Max and Min over the Interval	f(x)=2/(x^4-16) on interval (-2,2)	$f (x) = \frac{2}{x^{4} - 16}$ on interval $(- 2, 2)$
80771	Find the Antiderivative	y=(3x^3-7x^2+4)/(x^2)	$y = \frac{3 x^{3} - 7 x^{2} + 4}{x^{2}}$
80772	Evaluate the Integral	integral of (csc(x)cot(x)+3) with respect to x	$\int (\csc (x) \cot (x) + 3) d x$
80773	Integrate Using u-Substitution	integral of cot(x) with respect to x	$\int \cot (x) d x$
80774	Evaluate the Limit	limit as x approaches infinity of 6/(3+e^(-2x))	$lim_{x \to \infty} \frac{6}{3 + e^{- 2 x}}$
80775	Evaluate the Integral	integral of (2-1/(x^5)+7/(x^3)) with respect to x	$\int (2 - \frac{1}{x^{5}} + \frac{7}{x^{3}}) d x$
80776	Find the Derivative - d/dx	2x+3e^(-5x)	$2 x + 3 e^{- 5 x}$
80777	Evaluate the Integral	integral from 0 to 1 of x^2 square root of 3x^3+6 with respect to x	$\int_{0}^{1} x^{2} \sqrt{3 x^{3} + 6} d x$
80778	Find the Antiderivative	f(x)=sin(pi/2-6x)	$f (x) = \sin (\frac{π}{2} - 6 x)$
80779	Find the Second Derivative	y=(4x^2-16)/(x-2)	$y = \frac{4 x^{2} - 16}{x - 2}$
80780	Find the Derivative - d/dx	( square root of x)/(1+ square root of x)	$\frac{\sqrt{x}}{1 + \sqrt{x}}$
80781	Find dy/dx	y=1/( cube root of x-1)	$y = \frac{1}{\sqrt[3]{x - 1}}$
80782	Find Where Increasing/Decreasing	6x^5-15x^4+10x^3	$6 x^{5} - 15 x^{4} + 10 x^{3}$
80783	Find the Antiderivative	f(x)=e^(x^2)	$f (x) = e^{x^{2}}$
80784	Find the Derivative - d/dx	y=ce^(2x)	$y = c e^{2 x}$
80785	Find the Antiderivative	sin(x)^2*cos(x)	$\sin^{2} (x) \cdot \cos (x)$
80786	Find the Derivative - d/dx	y=(10x^7)^9	$y = {(10 x^{7})}^{9}$
80787	Evaluate the Integral	integral of (5+x)^-5 with respect to x	$\int {(5 + x)}^{- 5} d x$
80788	Find the Antiderivative	f(x)=2-x^4+3x^7	$f (x) = 2 - x^{4} + 3 x^{7}$
80789	Find the Inflection Points	f(x)=1/5x^5-x^4-12x^3	$f (x) = \frac{1}{5} x^{5} - x^{4} - 12 x^{3}$
80790	Find the Slope at (1/2,16) Using Implicit Differentiation	f(t)=t^-4 ;, (1/2,16)	$f (t) = t^{- 4}$ ;, $(\frac{1}{2}, 16)$
80791	Evaluate the Limit	limit as y approaches -1 of (1/(4+3y)+1/y)/(y+1)	$lim_{y \to - 1} \frac{\frac{1}{4 + 3 y} + \frac{1}{y}}{y + 1}$
80792	Find the Antiderivative	(5/8x^4-3x^2+2x^-1)dx	$(\frac{5}{8} x^{4} - 3 x^{2} + 2 x^{- 1}) d x$
80793	Find the Antiderivative	9x^(4/5)+x-2/(x^3)- square root of x	$9 x^{\frac{4}{5}} + x - \frac{2}{x^{3}} - \sqrt{x}$
80794	Find the Maximum/Minimum Value	P(t)=-0.3t^3+80t+800	$P (t) = - 0.3 t^{3} + 80 t + 800$
80795	Evaluate the Integral	integral of (2 cube root of x^5)/3 with respect to x	$\int \frac{2 \sqrt[3]{x^{5}}}{3} d x$
80796	Find Where Increasing/Decreasing	x^5-10x^4+25x^3	$x^{5} - 10 x^{4} + 25 x^{3}$
80797	Evaluate the Integral	integral of x^2(3x+2)(4x-5) with respect to x	$\int x^{2} (3 x + 2) (4 x - 5) d x$
80798	Find the Fourth Derivative	y=sin(4x-7)	$y = \sin (4 x - 7)$
80799	Find the Antiderivative	(x^2)/(x^2+1)	$\frac{x^{2}}{x^{2} + 1}$
80800	Evaluate the Limit	limit as x approaches 1 of e^(-9x^5-4x^4-3x^2)	$lim_{x \to 1} e^{- 9 x^{5} - 4 x^{4} - 3 x^{2}}$