Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
84801	Evaluate the Limit	limit as x approaches 4 of ( natural log of x- natural log of 4)/(x-4)	$lim_{x \to 4} \frac{\ln (x) - \ln (4)}{x - 4}$
84802	Evaluate the Integral	integral from 0 to 1 of (x+ square root of x) with respect to x	$\int_{0}^{1} (x + \sqrt{x}) d x$
84803	Find the Maximum/Minimum Value	f(x)=(x^2-x-2)/(x^2-6x+9)	$f (x) = \frac{x^{2} - x - 2}{x^{2} - 6 x + 9}$
84804	Evaluate the Summation	sum from k=0 to 6 of (3/2)*k^2	$\sum_{k = 0}^{6} (\frac{3}{2}) \cdot k^{2}$
84805	Evaluate the Integral	integral of (15x fourth root of 3x^2+4)/4 with respect to x	$\int \frac{15 x \sqrt[4]{3 x^{2} + 4}}{4} d x$
84806	Evaluate the Limit	limit as x approaches 0 of (e^(-x)-e^x)/(e^(-x)+1)	$lim_{x \to 0} \frac{e^{- x} - e^{x}}{e^{- x} + 1}$
84807	Find the Derivative - d/dx	(1- square root of x)*(1- cube root of x)	$(1 - \sqrt{x}) \cdot (1 - \sqrt[3]{x})$
84808	Find the Antiderivative	4sec(3x)tan(3x)	$4 \sec (3 x) \tan (3 x)$
84809	Evaluate the Limit	limit as x approaches 0 from the right of 9x-8 square root of x	$lim_{x \to 0^{+}} 9 x - 8 \sqrt{x}$
84810	Evaluate the Limit	limit as x approaches infinity of (-2x^4)/(3x^2-1)	$lim_{x \to \infty} \frac{- 2 x^{4}}{3 x^{2} - 1}$
84811	Evaluate the Integral	integral from 0 to 3 of (3/4y-1/4y^2) with respect to y	$\int_{0}^{3} (\frac{3}{4} y - \frac{1}{4} y^{2}) d y$
84812	Evaluate the Integral	integral from -2 to 6 of [4y-(y^2-12)] with respect to y	$\int_{- 2}^{6} [4 y - (y^{2} - 12)] d y$
84813	Find dy/dx	y=(1+3x)/(2-x^2)	$y = \frac{1 + 3 x}{2 - x^{2}}$
84814	Find the Antiderivative	x^2+1/(x^2)	$x^{2} + \frac{1}{x^{2}}$
84815	Find the Antiderivative	y=x^2-3x+1/x	$y = x^{2} - 3 x + \frac{1}{x}$
84816	Evaluate the Integral	integral of 4tan(x)^2 with respect to x	$\int 4 \tan^{2} (x) d x$
84817	Evaluate the Integral	integral of 5/(2 square root of x^3) with respect to x	$\int \frac{5}{2 \sqrt{x^{3}}} d x$
84818	Integrate Using u-Substitution	integral from 0 to 4 of x/( square root of 1+2x) with respect to x	$\int_{0}^{4} \frac{x}{\sqrt{1 + 2 x}} d x$
84819	Evaluate the Summation	4 sum from i=1 to 5 of i^2-4	$4 \sum_{i = 1}^{5} i^{2} - 4$
84820	Find the Derivative - d/dx	cos(x)^4-sin(x)^4	$\cos^{4} (x) - \sin^{4} (x)$
84821	Evaluate the Integral	integral of (4x-1)(3x+1) with respect to x	$\int (4 x - 1) (3 x + 1) d x$
84822	Evaluate the Integral	integral of 1/(x(1+( natural log of x)^2)) with respect to x	$\int \frac{1}{x (1 + \ln^{2} (x))} d x$
84823	Evaluate the Integral	integral of (x-1)/x with respect to x	$\int \frac{x - 1}{x} d x$
84824	Find the Antiderivative	1/(4 fourth root of x^3)	$\frac{1}{4 \sqrt[4]{x^{3}}}$
84825	Evaluate the Integral	integral of (3x^3+5x^-2+6x^2) with respect to x	$\int (3 x^{3} + 5 x^{- 2} + 6 x^{2}) d x$
84826	Evaluate the Integral	integral of ( fourth root of x^3)/4 with respect to x	$\int \frac{\sqrt[4]{x^{3}}}{4} d x$
84827	Evaluate the Limit	limit as x approaches -3 of (-4\|x+3\|)/(-3(x+3))	$lim_{x \to - 3} \frac{- 4 \| x + 3 \|}{- 3 (x + 3)}$
84828	Find the Antiderivative	2x^2-1/(x^2)	$2 x^{2} - \frac{1}{x^{2}}$
84829	Find the Integral	1/(x square root of x)dx	$\frac{1}{x \sqrt{x}} d x$
84830	Evaluate the Limit	limit as x approaches 2 from the right of (x-2)/(\|x-2\|)	$lim_{x \to 2^{+}} \frac{x - 2}{\| x - 2 \|}$
84831	Find the Derivative - d/dx	e^2x	$e^{2} x$
84832	Evaluate the Integral	integral of (4t)/(t-t^2) with respect to t	$\int \frac{4 t}{t - t^{2}} d t$
84833	Find the Derivative - d/dx	2* square root of x	$2 \cdot \sqrt{x}$
84834	Evaluate the Limit	limit as h approaches 0 of ((-3+h)^-1+3^-1)/h	$lim_{h \to 0} \frac{{(- 3 + h)}^{- 1} + 3^{- 1}}{h}$
84835	Find the Antiderivative	(2x)/((x+1)^2)	$\frac{2 x}{{(x + 1)}^{2}}$
84836	Find the Derivative - d/dx	tan(xdx)	$\tan (x d x)$
84837	Find the Tangent Line at x=-1	f(x)=-x^3-5x^2+2 at x=-1	$f (x) = - x^{3} - 5 x^{2} + 2$ at $x = - 1$
84838	Evaluate the Limit	limit as x approaches infinity of (2x+3)/(x^2+1)	$lim_{x \to \infty} \frac{2 x + 3}{x^{2} + 1}$
84839	Evaluate the Limit	limit as x approaches 2 of (x/2)^(1/(x-2))	$lim_{x \to 2} {(\frac{x}{2})}^{\frac{1}{x - 2}}$
84840	Evaluate the Integral	integral of (2+e^x)^-6e^x with respect to x	$\int {(2 + e^{x})}^{- 6} e^{x} d x$
84841	Find the Antiderivative	f(x)=-9e^(-9x)+(-7x+5x^5)/(x^2)	$f (x) = - 9 e^{- 9 x} + \frac{- 7 x + 5 x^{5}}{x^{2}}$
84842	Find the Derivative - d/dx	x-1/(x^2)	$x - \frac{1}{x^{2}}$
84843	Evaluate the Integral	integral of (2x+1)(x-6)^2 with respect to x	$\int (2 x + 1) {(x - 6)}^{2} d x$
84844	Evaluate the Limit	limit as x approaches 5 of ( square root of x+11)/( square root of x-1)	$lim_{x \to 5} \frac{\sqrt{x + 11}}{\sqrt{x - 1}}$
84845	Find Where Increasing/Decreasing	f(x)=4/(x^2-2x-3)	$f (x) = \frac{4}{x^{2} - 2 x - 3}$
84846	Evaluate the Integral	integral from 0 to 2 of pi(2x)^2 with respect to x	$\int_{0}^{2} π {(2 x)}^{2} d x$
84847	Find the Derivative - d/dx	1+ log of x	$1 + \log (x)$
84848	Solve the Differential Equation	y''+3y'+2y=6	$y'' + 3 y' + 2 y = 6$
84849	Evaluate the Integral	integral of 4/( cube root of 2x+1) with respect to x	$\int \frac{4}{\sqrt[3]{2 x + 1}} d x$
84850	Find the Derivative - d/dx	d/(dx)( integral from 0 to x^2 of sin(t^3) with respect to t)	$\frac{d}{d x} (\int_{0}^{x^{2}} \sin (t^{3}) d t)$
84851	Find dy/dx	y=(4x^3+8)(2x^7-3)	$y = (4 x^{3} + 8) (2 x^{7} - 3)$
84852	Find the Concavity	f(x)=-0.5*x^4+3x^2	$f (x) = - 0.5 \cdot x^{4} + 3 x^{2}$
84853	Evaluate the Limit	limit as x approaches 2 of 3f(x)^2+g(x)	$lim_{x \to 2} 3 f {(x)}^{2} + g (x)$
84854	Find the Antiderivative	(x^3)/(x+2)	$\frac{x^{3}}{x + 2}$
84855	Evaluate Using Summation Formulas	limit as n approaches infinity of sum from j=1 to n of (9j)/(n^2)	$lim_{n \to \infty} \sum_{j = 1}^{n} \frac{9 j}{n^{2}}$
84856	Find the Concavity	-1/6x^4+19x^2	$- \frac{1}{6} x^{4} + 19 x^{2}$
84857	Find the Antiderivative	f(x)=3^x natural log of 3	$f (x) = 3^{x} \ln (3)$
84858	Find the Second Derivative	f(x)=cos(2x)-sin(2x)	$f (x) = \cos (2 x) - \sin (2 x)$
84859	Evaluate the Integral	integral from 1 to e of 1/(y(1+ natural log of y)) with respect to y	$\int_{1}^{e} \frac{1}{y (1 + \ln (y))} d y$
84860	Find the Derivative - d/dx	(2x)/(1+x^4)	$\frac{2 x}{1 + x^{4}}$
84861	Evaluate the Integral	integral of (2x^2+3/x+5/(x^7)-4sin(x)+2e^x) with respect to x	$\int (2 x^{2} + \frac{3}{x} + \frac{5}{x^{7}} - 4 \sin (x) + 2 e^{x}) d x$
84862	Evaluate the Integral	integral of (x^(3/2)+8)^5 square root of x with respect to x	$\int {(x^{\frac{3}{2}} + 8)}^{5} \sqrt{x} d x$
84863	Find the Derivative - d/dx	y=x^2-x^5	$y = x^{2} - x^{5}$
84864	Find the Derivative - d/dz	y=e^(cot(3z))	$y = e^{\cot (3 z)}$
84865	Evaluate the Limit	limit as x approaches 1 of (1/( square root of x)-1)/(x-1)	$lim_{x \to 1} \frac{\frac{1}{\sqrt{x}} - 1}{x - 1}$
84866	Find the Maximum/Minimum Value	f(x) = natural log of x^2+1	$f (x) = \ln (x^{2} + 1)$
84867	Find Where Increasing/Decreasing	y=x^3-6x^2+9x	$y = x^{3} - 6 x^{2} + 9 x$
84868	Find the Antiderivative	(sin(x)-cos(x))^2	${(\sin (x) - \cos (x))}^{2}$
84869	Find the Integral	2cos(2x)	$2 \cos (2 x)$
84870	Find the Maximum/Minimum Value	f(x)=1/2(x-2)^3-4	$f (x) = \frac{1}{2} {(x - 2)}^{3} - 4$
84871	Evaluate the Integral	integral of (-4cos(x))/(1-cos(x)^2) with respect to x	$\int \frac{- 4 \cos (x)}{1 - \cos^{2} (x)} d x$
84872	Find dy/dx	y=((4x^2)/(6-2x^2))^5	$y = {(\frac{4 x^{2}}{6 - 2 x^{2}})}^{5}$
84873	Find the Second Derivative	xy	$x y$
84874	Evaluate the Limit	limit as x approaches infinity of (2x^5+3x^4-31x)/(8x^4-31x^2+12)	$lim_{x \to \infty} \frac{2 x^{5} + 3 x^{4} - 31 x}{8 x^{4} - 31 x^{2} + 12}$
84875	Find the Maximum/Minimum Value	f(x)=7x^2+x	$f (x) = 7 x^{2} + x$
84876	Integrate Using u-Substitution	integral of x with respect to x	$\int x d x$
84877	Evaluate the Integral	integral of (x^2+2+4x^4) with respect to x	$\int (x^{2} + 2 + 4 x^{4}) d x$
84878	Evaluate the Limit	limit as x approaches 0 of (2+x)^(1/x)	$lim_{x \to 0} {(2 + x)}^{\frac{1}{x}}$
84879	Evaluate the Integral	integral of (18tan(x)^2sec(x)^2)/((2+tan(x)^3)^2) with respect to x	$\int \frac{18 \tan^{2} (x) \sec^{2} (x)}{{(2 + \tan^{3} (x))}^{2}} d x$
84880	Integrate Using u-Substitution	integral of (e^x-e^(-x))/(e^x+e^(-x)) with respect to x	$\int \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}} d x$
84881	Evaluate the Limit	limit as x approaches 5 of (2x^2-50)/(3x-15)	$lim_{x \to 5} \frac{2 x^{2} - 50}{3 x - 15}$
84882	Evaluate the Integral	integral of (9x)/( square root of 3x^2+8) with respect to x	$\int \frac{9 x}{\sqrt{3 x^{2} + 8}} d x$
84883	Find the Concavity	-1/3x^3-x^2	$- \frac{1}{3} x^{3} - x^{2}$
84884	Find the Antiderivative	e^x*e^(x+1)	$e^{x} \cdot e^{x + 1}$
84885	Determine if Continuous	f(x)=x^2+3 if x<-2; 5 if x=-2; -3x+1 if x>-2	$f (x) = {\begin{cases} x^{2} + 3 & x < - 2 \\ 5 & x = - 2 \\ - 3 x + 1 & x > - 2 \end{cases}$
84886	Evaluate the Limit	limit as x approaches negative infinity of (x^2-4)/(x^2+4x+3)	$lim_{x \to - \infty} \frac{x^{2} - 4}{x^{2} + 4 x + 3}$
84887	Find the Antiderivative	x*sin(2x)	$x \cdot \sin (2 x)$
84888	Find dy/dx	y=1/( cube root of x^2-6x)	$y = \frac{1}{\sqrt[3]{x^{2} - 6 x}}$
84889	Find the Antiderivative	x^2y	$x^{2} y$
84890	Evaluate the Limit	limit as x approaches 3 of (x^2-9)(x-3)/(\|x-3\|)	$lim_{x \to 3} (x^{2} - 9) \frac{x - 3}{\| x - 3 \|}$
84891	Evaluate the Limit	limit as x approaches ( square root of 3)/2 of (arcsin(x)-arcsin(( square root of 3)/2))/(x-( square root of 3)/2)	$lim_{x \to \frac{\sqrt{3}}{2}} \frac{\arcsin (x) - \arcsin (\frac{\sqrt{3}}{2})}{x - \frac{\sqrt{3}}{2}}$
84892	Evaluate the Limit	limit as x approaches 2 of ( natural log of x+3- natural log of 5)/(x-2)	$lim_{x \to 2} \frac{\ln (x + 3) - \ln (5)}{x - 2}$
84893	Evaluate the Integral	integral from pi/4 to pi/2 of -3cot(x)csc(x)^2 with respect to x	$\int_{\frac{π}{4}}^{\frac{π}{2}} - 3 \cot (x) \csc^{2} (x) d x$
84894	Find the Derivative - d/dt	arctan(pi/2-t/10)	$\arctan (\frac{π}{2} - \frac{t}{10})$
84895	Find Where Increasing/Decreasing	y=-2^(x+2)+1	$y = - 2^{x + 2} + 1$
84896	Evaluate the Integral	integral of (sec(x)^2)/(tan(x)^2) with respect to x	$\int \frac{\sec^{2} (x)}{\tan^{2} (x)} d x$
84897	Evaluate the Limit	limit as x approaches infinity of (x-1)/(x^2+x+1)	$lim_{x \to \infty} \frac{x - 1}{x^{2} + x + 1}$
84898	Find Where Increasing/Decreasing	y=2x-3	$y = 2 x - 3$
84899	Find the Derivative - d/dx	y=2x^(1/2)	$y = 2 x^{\frac{1}{2}}$
84900	Find dy/dx	3y^3+xy-6x+3=0	$3 y^{3} + x y - 6 x + 3 = 0$