Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
82101	Find the Derivative - d/dx	y=1/27(9x^2+6)^(3/2)	$y = \frac{1}{27} {(9 x^{2} + 6)}^{\frac{3}{2}}$
82102	Evaluate the Integral	integral of [3sec(t)^2+1/( square root of t)] with respect to t	$\int [3 \sec^{2} (t) + \frac{1}{\sqrt{t}}] d t$
82103	Evaluate the Limit	limit as x approaches 3 of (3-x)/(x+4)	$lim_{x \to 3} \frac{3 - x}{x + 4}$
82104	Find dV/dr	V=1/3pir^2h	$V = \frac{1}{3} π r^{2} h$
82105	Evaluate the Limit	limit as x approaches 1 of (f(x)-8)/(x-1)=10	$lim_{x \to 1} \frac{f (x) - 8}{x - 1} = 10$
82106	Evaluate the Integral	integral from -1 to 6 of [5y-(y^2-6)] with respect to y	$\int_{- 1}^{6} [5 y - (y^{2} - 6)] d y$
82107	Find Where Increasing/Decreasing	f(x)=2(1/3)^x-1	$f (x) = 2 {(\frac{1}{3})}^{x} - 1$
82108	Evaluate the Limit	limit as x approaches -2 of 2/(x+2)-(x-6)/(x^2-4)	$lim_{x \to - 2} \frac{2}{x + 2} - \frac{x - 6}{x^{2} - 4}$
82109	Find the Maximum/Minimum Value	f(x)=ax^2+7x-3	$f (x) = a x^{2} + 7 x - 3$
82110	Evaluate the Integral	integral of -2(5x+1)e^(25x^2+10x+25) with respect to x	$\int - 2 (5 x + 1) e^{25 x^{2} + 10 x + 25} d x$
82111	Find the Derivative - d/dx	2cos(x^2+2)^2	$2 \cos^{2} (x^{2} + 2)$
82112	Find dy/dx	-x^3y+x^2=4y^2	$- x^{3} y + x^{2} = 4 y^{2}$
82113	Evaluate the Integral	integral from 0 to infinity of e^(-x^3) with respect to x	$\int_{0}^{\infty} e^{- x^{3}} d x$
82114	Find dy/dx	square root of 2x+y=2x	$\sqrt{2 x + y} = 2 x$
82115	Find the Turning Points	y=3x^3-x-3	$y = 3 x^{3} - x - 3$
82116	Integrate Using u-Substitution	integral of x/(1+x^2) with respect to x	$\int \frac{x}{1 + x^{2}} d x$
82117	Evaluate the Integral	integral of (2-3e^x) with respect to x	$\int (2 - 3 e^{x}) d x$
82118	Evaluate the Integral	integral from 1 to e of (( natural log of x)^2)/x with respect to x	$\int_{1}^{e} \frac{\ln^{2} (x)}{x} d x$
82119	Find the Maximum/Minimum Value	y=2sin(x-pi/2)	$y = 2 \sin (x - \frac{π}{2})$
82120	Evaluate the Limit	limit as x approaches 3 of f(x)-2g(x)	$lim_{x \to 3} f (x) - 2 g (x)$
82121	Find the Derivative - d/dx	square root of cos(2x)	$\sqrt{\cos (2 x)}$
82122	Find Where Increasing/Decreasing	g(x)=(x^3)/(3x^2+1)	$g (x) = \frac{x^{3}}{3 x^{2} + 1}$
82123	Evaluate the Integral	integral of x3/5 with respect to x	$\int x \frac{3}{5} d x$
82124	Find the Antiderivative	6/(x^3)-4e^(2x)+7	$\frac{6}{x^{3}} - 4 e^{2 x} + 7$
82125	Evaluate the Limit	limit as x approaches 0 of (-2x)/(4-(2+x)^2)	$lim_{x \to 0} \frac{- 2 x}{4 - {(2 + x)}^{2}}$
82126	Find dy/dx	5x^3+2y^3-y^2+3=-5x^2	$5 x^{3} + 2 y^{3} - y^{2} + 3 = - 5 x^{2}$
82127	Evaluate the Integral	integral of e^( natural log of x) with respect to x	$\int e^{\ln (x)} d x$
82128	Evaluate the Limit	limit as x approaches 0 of 1/x-1/(sin(x))	$lim_{x \to 0} \frac{1}{x} - \frac{1}{\sin (x)}$
82129	Evaluate the Integral	integral from 1 to 3 of ((1+ natural log of x)^3)/x with respect to x	$\int_{1}^{3} \frac{{(1 + \ln (x))}^{3}}{x} d x$
82130	Integrate Using Trig Substitution	integral from 0 to 1 of (x^2)/( square root of 4-x^2) with respect to x	$\int_{0}^{1} \frac{x^{2}}{\sqrt{4 - x^{2}}} d x$
82131	Find the Second Derivative	f(x) = square root of 8x	$f (x) = \sqrt{8 x}$
82132	Find the Antiderivative	e^x*x	$e^{x} \cdot x$
82133	Find the Derivative of the Integral	A(x) = integral from 1 to x of sin(e^t) with respect to t	$A (x) = \int_{1}^{x} \sin (e^{t}) d t$
82134	Evaluate Using L'Hospital's Rule	limit as x approaches negative infinity of x/(2x-3)	$lim_{x \to - \infty} \frac{x}{2 x - 3}$
82135	Find the Second Derivative	x^(4/3)+4x^(1/3)	$x^{\frac{4}{3}} + 4 x^{\frac{1}{3}}$
82136	Evaluate the Integral	integral from -3 to 2 of (1/2x^2+x+6) with respect to x	$\int_{- 3}^{2} (\frac{1}{2} x^{2} + x + 6) d x$
82137	Find the Maximum/Minimum Value	x^2e^(-x^2)	$x^{2} e^{- x^{2}}$
82138	Find dx/dy	xy+y^2=2	$x y + y^{2} = 2$
82139	Evaluate the Limit	limit as x approaches infinity of (3x^3+2x-1)/(2x^4-3x^3-2)	$lim_{x \to \infty} \frac{3 x^{3} + 2 x - 1}{2 x^{4} - 3 x^{3} - 2}$
82140	Find the Derivative - d/dx	y=8e^(tan(x^2))	$y = 8 e^{\tan (x^{2})}$
82141	Find dy/dx	-xy+y^2-4x^2=0	$- x y + y^{2} - 4 x^{2} = 0$
82142	Find the Derivative - d/dx	x^2+1/x+xy+1/y+y^2	$x^{2} + \frac{1}{x} + x y + \frac{1}{y} + y^{2}$
82143	Evaluate the Limit	limit as x approaches 8 of (-5x+9) square root of 68-x^2	$lim_{x \to 8} (- 5 x + 9) \sqrt{68 - x^{2}}$
82144	Find the Antiderivative	2/( square root of 2x-1)	$\frac{2}{\sqrt{2 x - 1}}$
82145	Find the Antiderivative	2sin(x)^2+1	$2 \sin^{2} (x) + 1$
82146	Evaluate the Integral	integral of 1/2sin(2x) with respect to x	$\int \frac{1}{2} \sin (2 x) d x$
82147	Evaluate the Limit	limit as x approaches infinity of (3x^3+2x^2+8)/(4x^3+6x^2)	$lim_{x \to \infty} \frac{3 x^{3} + 2 x^{2} + 8}{4 x^{3} + 6 x^{2}}$
82148	Integrate Using u-Substitution	integral of sin(x)^3 with respect to x	$\int \sin^{3} (x) d x$
82149	Find the Derivative - d/dx	(3+x)/(2-5x^2)	$\frac{3 + x}{2 - 5 x^{2}}$
82150	Evaluate the Integral	integral of 4x^2(4x-5)^2 with respect to x	$\int 4 x^{2} {(4 x - 5)}^{2} d x$
82151	Find the Derivative - d/dx	e^(sin(x))cos(x)	$e^{\sin (x)} \cos (x)$
82152	Solve the Differential Equation	y'-y=0	$y' - y = 0$
82153	Find the Derivative of the Integral	integral from square root of x to pi/6 of thetatan(theta) with respect to theta	$\int_{\sqrt{x}}^{\frac{π}{6}} θ \tan (θ) d θ$
82154	Evaluate the Limit	limit as x approaches 0 of (cos(x))/(x+8)	$lim_{x \to 0} \frac{\cos (x)}{x + 8}$
82155	Evaluate the Integral	integral from pi/6 to pi/2 of (cos(x))/(3+sin(x)) with respect to x	$\int_{\frac{π}{6}}^{\frac{π}{2}} \frac{\cos (x)}{3 + \sin (x)} d x$
82156	Find the Derivative - d/dx	4- square root of x+2	$4 - \sqrt{x + 2}$
82157	Evaluate the Integral	integral from -10 to -2 of (1/x) with respect to x	$\int_{- 10}^{- 2} (\frac{1}{x}) d x$
82158	Find dy/dx	5y-4y^3+4x^3=-1	$5 y - 4 y^{3} + 4 x^{3} = - 1$
82159	Evaluate the Limit	limit as x approaches infinity of 1/2x-4/(x^2)	$lim_{x \to \infty} \frac{1}{2} x - \frac{4}{x^{2}}$
82160	Evaluate the Integral	integral from 0 to 1 of x^2* square root of x^3+2 with respect to x	$\int_{0}^{1} x^{2} \cdot \sqrt{x^{3} + 2} d x$
82161	Find dy/dx	2x+5-y=xy	$2 x + 5 - y = x y$
82162	Find the Derivative - d/dx	2/3xy^2+2x-1/3xy^2+2/3x^2y-5x	$\frac{2}{3} x y^{2} + 2 x - \frac{1}{3} x y^{2} + \frac{2}{3} x^{2} y - 5 x$
82163	Evaluate the Limit	limit as x approaches 3 of (x^n-3)/(x^m-3)	$lim_{x \to 3} \frac{x^{n} - 3}{x^{m} - 3}$
82164	Find the Center and Radius	y^2+x^2-20x+14y-32=0	$y^{2} + x^{2} - 20 x + 14 y - 32 = 0$
82165	Find the Slope	f(x)=x-2	$f (x) = x - 2$
82166	Find Where Increasing/Decreasing	f(x)=sin(x)^2	$f (x) = \sin^{2} (x)$
82167	Evaluate the Limit	limit as x approaches -2 of (3x^4+7x^3+x^2-6x-10)^8	$lim_{x \to - 2} {(3 x^{4} + 7 x^{3} + x^{2} - 6 x - 10)}^{8}$
82168	Evaluate the Limit	limit as x approaches 0 of ((1-4x)^2-1)/(-10x)	$lim_{x \to 0} \frac{{(1 - 4 x)}^{2} - 1}{- 10 x}$
82169	Find the Integral	sec(x)^2tan(x)^2	$\sec^{2} (x) \tan^{2} (x)$
82170	Evaluate the Integral	integral of 7(sin(2x))/(sin(x)) with respect to x	$\int 7 \frac{\sin (2 x)}{\sin (x)} d x$
82171	Evaluate the Integral	integral from 0 to pi/6 of (sin(2x))/(cos(2x)^2) with respect to x	$\int_{0}^{\frac{π}{6}} \frac{(\sin (2 x))}{\cos^{2} (2 x)} d x$
82172	Find the Derivative - d/dx	square root of (x+2)^2	$\sqrt{{(x + 2)}^{2}}$
82173	Find dy/dx	x^2y-3x=y^3-3	$x^{2} y - 3 x = y^{3} - 3$
82174	Evaluate the Limit	limit as x approaches infinity of (5x^2+2)/(4x^2+7)	$lim_{x \to \infty} \frac{5 x^{2} + 2}{4 x^{2} + 7}$
82175	Evaluate the Integral	integral of x(x^3+1) with respect to x	$\int x (x^{3} + 1) d x$
82176	Evaluate the Integral	integral of (t^2-pi square root of t+ square root of tcsc(t))/( square root of t) with respect to t	$\int \frac{t^{2} - π \sqrt{t} + \sqrt{t} \csc (t)}{\sqrt{t}} d t$
82177	Evaluate the Summation	sum from k=0 to 5 of 2k+2k^2	$\sum_{k = 0}^{5} 2 k + 2 k^{2}$
82178	Find the Second Derivative	-xy+x=-4	$- x y + x = - 4$
82179	Find the Derivative - d/dx	(x^2+1)^(2^x)	${(x^{2} + 1)}^{2^{x}}$
82180	Find dy/dx	e^(x/y)=x	$e^{\frac{x}{y}} = x$
82181	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (4 natural log of 2x+1+x^3)/(5x^2+3x)	$lim_{x \to 0} \frac{4 \ln (2 x + 1) + x^{3}}{5 x^{2} + 3 x}$
82182	Find the Concavity	f(x)=-1/10x^5+2x^4-12x^3	$f (x) = - \frac{1}{10} x^{5} + 2 x^{4} - 12 x^{3}$
82183	Find the Derivative - d/dx	cube root of x-3x^3	$\sqrt[3]{x} - 3 x^{3}$
82184	Evaluate the Limit	limit as x approaches infinity of square root of x^2+7x+1-x	$lim_{x \to \infty} \sqrt{x^{2} + 7 x + 1} - x$
82185	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (arcsin(x)-x)/(arctan(x)-x)	$lim_{x \to 0} \frac{\arcsin (x) - x}{\arctan (x) - x}$
82186	Evaluate the Limit	limit as x approaches 0 from the right of \|x\|	$lim_{x \to 0^{+}} \| x \|$
82187	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (x+2x^2)/(3 natural log of x+1-3x)	$lim_{x \to 0} \frac{x + 2 x^{2}}{3 \ln (x + 1) - 3 x}$
82188	Find dy/dx	y=3^( natural log of x)	$y = 3^{\ln (x)}$
82189	Find the Derivative - d/dx	1/3x^3-x	$\frac{1}{3} x^{3} - x$
82190	Evaluate the Integral	integral from 0 to 2 of y^2 square root of 1+y^3 with respect to y	$\int_{0}^{2} y^{2} \sqrt{1 + y^{3}} d y$
82191	Find the Antiderivative	(x-1)/(x+1)	$\frac{x - 1}{x + 1}$
82192	Evaluate the Limit	limit as x approaches infinity of 3/(x^2)-2	$lim_{x \to \infty} \frac{3}{x^{2}} - 2$
82193	Evaluate the Integral	integral of 4x(2x-1)(4x+1) with respect to x	$\int 4 x (2 x - 1) (4 x + 1) d x$
82194	Find dy/dx	-y-2x^3=y^2	$- y - 2 x^{3} = y^{2}$
82195	Find the Local Maxima and Minima	f(x)=1/2x^4-4x^3+8x^2+46	$f (x) = \frac{1}{2} x^{4} - 4 x^{3} + 8 x^{2} + 46$
82196	Find the Derivative - d/dx	y=sin(pi-x)^2	$y = \sin^{2} (π - x)$
82197	Find the Derivative - d/dx	3x+2e^(-3x)	$3 x + 2 e^{- 3 x}$
82198	Find the Antiderivative	f(x)=e^x-e^(-x)	$f (x) = e^{x} - e^{- x}$
82199	Find the Second Derivative	1/2x^4+2x^3	$\frac{1}{2} x^{4} + 2 x^{3}$
82200	Evaluate the Limit	limit as x approaches negative infinity of (5x+5)/(7x^2+1)	$lim_{x \to - \infty} \frac{5 x + 5}{7 x^{2} + 1}$