Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
68701	Find Where Increasing/Decreasing	f(x)=(x^2)/(x^2+1)	$f (x) = \frac{x^{2}}{x^{2} + 1}$
68702	Find dx/dy	y=x^4	$y = x^{4}$
68703	Find the Linearization at a=4	f(x) = square root of x , a=4	$f (x) = \sqrt{x}$ , $a = 4$
68704	Evaluate the Integral	integral of (x^2-9x+3) with respect to x	$\int (x^{2} - 9 x + 3) d x$
68705	Find the Derivative - d/dx	e^(x^2-y^2)	$e^{x^{2} - y^{2}}$
68706	Find dy/dx	y^4-2x=5	$y^{4} - 2 x = 5$
68707	Evaluate the Integral	integral of square root of 3x^2 with respect to x	$\int \sqrt{3} x^{2} d x$
68708	Evaluate the Limit	limit as x approaches a of 1/infinity	$lim_{x \to a} \frac{1}{\infty}$
68709	Find the Derivative - d/dx	y = square root of x+8 cube root of x-2 fourth root of x	$y = \sqrt{x} + 8 \sqrt[3]{x} - 2 \sqrt[4]{x}$
68710	Find the Slope	-3/5	$- \frac{3}{5}$
68711	Evaluate the Limit	limit as x approaches infinity of 2/( square root of 5x)	$lim_{x \to \infty} \frac{2}{\sqrt{5 x}}$
68712	Find the Center and Radius	y^2-2x^2-4x-4y=0	$y^{2} - 2 x^{2} - 4 x - 4 y = 0$
68713	Evaluate the Limit	limit as x approaches 3 from the right of ( square root of x^2-9)/(x-3)	$lim_{x \to 3^{+}} \frac{\sqrt{x^{2} - 9}}{x - 3}$
68714	Find the Center and Radius	(x^2)/4-(y^2)/25=1	$\frac{x^{2}}{4} - \frac{y^{2}}{25} = 1$
68715	Evaluate the Limit	limit as x approaches 1 of (x-1)/( square root of x^2+3-2)	$lim_{x \to 1} \frac{x - 1}{\sqrt{x^{2} + 3 - 2}}$
68716	Find the Slope of the Tangent Line at (4,36)	y=x^2+5x , (4,36)	$y = x^{2} + 5 x$ , $(4, 36)$
68717	Find the Derivative - d/dθ	2tan(theta)	$2 \tan (θ)$
68718	Evaluate the Limit	limit as t approaches 0 of ( square root of t^2+2^2-2)/(t^2)	$lim_{t \to 0} \frac{\sqrt{t^{2} + 2^{2}} - 2}{t^{2}}$
68719	Find the Derivative - d/dx	y=x^2(x^3-1)	$y = x^{2} (x^{3} - 1)$
68720	Evaluate the Limit	limit as x approaches 1 of ( cube root of x^2-2 cube root of x+1)/((x-1)^2)	$lim_{x \to 1} \frac{\sqrt[3]{x^{2}} - 2 \sqrt[3]{x} + 1}{{(x - 1)}^{2}}$
68721	Find dy/dx	x^3+y^3=12xy	$x^{3} + y^{3} = 12 x y$
68722	Find the Linearization at a=0	f(x) = square root of 1-x , a=0	$f (x) = \sqrt{1 - x}$ , $a = 0$
68723	Evaluate the Integral	integral of (x^2-9x+4) with respect to x	$\int (x^{2} - 9 x + 4) d x$
68724	Find the Derivative - d/dx	2x^2-1/(x^2)+1/(x^3)	$2 x^{2} - \frac{1}{x^{2}} + \frac{1}{x^{3}}$
68725	Find dy/dx	y=x^2sin(x)+2xcos(x)-2sin(x)	$y = x^{2} \sin (x) + 2 x \cos (x) - 2 \sin (x)$
68726	Find the Derivative - d/dx	x-2/x	$x - \frac{2}{x}$
68727	Find the Antiderivative	f(x)=x^2+pi	$f (x) = x^{2} + π$
68728	Find dx/dy	y=tan(x)	$y = \tan (x)$
68729	Evaluate the Integral	integral of (ax)/(x^2-bx) with respect to x	$\int \frac{a x}{x^{2} - b x} d x$
68730	Find the Turning Points	f(x)=x^3+3x^2-5x-6	$f (x) = x^{3} + 3 x^{2} - 5 x - 6$
68731	Find dy/dx	xy=2	$x y = 2$
68732	Find dy/dx	x^4+y^2=17	$x^{4} + y^{2} = 17$
68733	Evaluate the Integral	integral from 0 to 5 of 6 square root of x+4 with respect to x	$\int_{0}^{5} 6 \sqrt{x + 4} d x$
68734	Find dy/dx	square root of x+ square root of y=5	$\sqrt{x} + \sqrt{y} = 5$
68735	Evaluate the Integral	integral of (x^(4/3)-3x^(5/2)) with respect to x	$\int (x^{\frac{4}{3}} - 3 x^{\frac{5}{2}}) d x$
68736	Find the Derivative - d/dx	ysin(x)	$y \sin (x)$
68737	Find the Second Derivative	f(x) = cube root of x	$f (x) = \sqrt[3]{x}$
68738	Find the Center and Radius	(x^2)/81+((y+7)^2)/9=1	$\frac{x^{2}}{81} + \frac{{(y + 7)}^{2}}{9} = 1$
68739	Find the Derivative - d/dx	(x+1)^x	${(x + 1)}^{x}$
68740	Evaluate Using Summation Formulas	sum from i=1 to n of (4i+7)/(n^2)	$\sum_{i = 1}^{n} \frac{4 i + 7}{n^{2}}$
68741	Find the Derivative - d/dx	x^(1/3)(x+3)^(2/3)	$x^{\frac{1}{3}} {(x + 3)}^{\frac{2}{3}}$
68742	Evaluate the Limit	limit as x approaches 1/4 of 4x(x-1/3)	$lim_{x \to \frac{1}{4}} 4 x (x - \frac{1}{3})$
68743	Find the Derivative - d/dt	y=arcsin(arccos(t))	$y = \arcsin (\arccos (t))$
68744	Find the Derivative - d/dx	y=1/( cube root of (8-x^3)^8)	$y = \frac{1}{\sqrt[3]{{(8 - x^{3})}^{8}}}$
68745	Find dy/dx	3y^2-2x^2=6-2xy	$3 y^{2} - 2 x^{2} = 6 - 2 x y$
68746	Find the Domain and Range	f(x)=x+3 if -2<=x<1; 9 if x=1; -x+2 if x>1	$f (x) = {\begin{cases} x + 3 & - 2 \leq x < 1 \\ 9 & x = 1 \\ - x + 2 & x > 1 \end{cases}$
68747	Find the Derivative - d/dx	x^2sec(x)	$x^{2} \sec (x)$
68748	Find dx/dy	f(x,y) = square root of x^2+y^2	$f (x, y) = \sqrt{x^{2} + y^{2}}$
68749	Evaluate the Integral	integral of (9-x) with respect to x	$\int (9 - x) d x$
68750	Evaluate the Integral	integral from 0 to infinity of 1/( sixth root of 1+x) with respect to x	$\int_{0}^{\infty} \frac{1}{\sqrt[6]{1 + x}} d x$
68751	Find dy/dx	y=4x^2	$y = 4 x^{2}$
68752	Evaluate the Integral	integral of 64x^3(4x^2-1)^3 with respect to x	$\int 64 x^{3} {(4 x^{2} - 1)}^{3} d x$
68753	Find dy/dx	y=csc(x)	$y = \csc (x)$
68754	Find the Derivative - d/dx	2xdx	$2 x d x$
68755	Evaluate the Limit	limit as x approaches 8 from the right of 1/(x+8)	$lim_{x \to 8^{+}} \frac{1}{x + 8}$
68756	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of x^(2x)	$lim_{x \to 0^{+}} x^{2 x}$
68757	Find the Derivative - d/dx	y=(-7x^-3)/3	$y = \frac{- 7 x^{- 3}}{3}$
68758	Find the Derivative - d/dt	thx	$t h x$
68759	Find the Derivative - d/dx	(3x^2-x-2)/(3x^2)	$\frac{3 x^{2} - x - 2}{3 x^{2}}$
68760	Evaluate the Integral	integral from -1 to 2 of (x+1)/( square root of x^2+2x+4) with respect to x	$\int_{- 1}^{2} \frac{x + 1}{\sqrt{x^{2} + 2 x + 4}} d x$
68761	Find the Derivative - d/dx	d/(dx)(x^3-cos(x))	$\frac{d}{d x} (x^{3} - \cos (x))$
68762	Find the Derivative - d/dx	1/(x^2)+1/x	$\frac{1}{x^{2}} + \frac{1}{x}$
68763	Find the Normal Line at (0,2)	y=x^4+2e^x , (0,2)	$y = x^{4} + 2 e^{x}$ , $(0, 2)$
68764	Evaluate the Integral	integral of 9x square root of 1-x^4 with respect to x	$\int 9 x \sqrt{1 - x^{4}} d x$
68765	Find the Derivative - d/dx	x square root of 3	$x \sqrt{3}$
68766	Find dy/dx	y=3 square root of x	$y = 3 \sqrt{x}$
68767	Find dy/dx	x^3+y^3-3xy=0	$x^{3} + y^{3} - 3 x y = 0$
68768	Find dy/dx	y^2+2y=2x+1	$y^{2} + 2 y = 2 x + 1$
68769	Find the Derivative - d/ds	y=(s- square root of s)/(s^2)	$y = \frac{s - \sqrt{s}}{s^{2}}$
68770	Integrate Using u-Substitution	integral of (5x^2+1)^2(10x) with respect to x	$\int {(5 x^{2} + 1)}^{2} (10 x) d x$
68771	Find dy/dx	x^3+y^3=24xy	$x^{3} + y^{3} = 24 x y$
68772	Evaluate the Limit	limit as h approaches -4 of (h^2-4^2)/(2h^2+9h+4)	$lim_{h \to - 4} \frac{h^{2} - 4^{2}}{2 h^{2} + 9 h + 4}$
68773	Evaluate the Integral	integral from 0 to 1 of (x^2-2x+3) with respect to x	$\int_{0}^{1} (x^{2} - 2 x + 3) d x$
68774	Evaluate the Limit	limit as x approaches infinity of ( square root of 5x+4- square root of 3x+9)/(4x)	$lim_{x \to \infty} \frac{\sqrt{5 x + 4} - \sqrt{3 x + 9}}{4 x}$
68775	Evaluate the Integral	integral from -1 to 0 of (2x-1) with respect to x	$\int_{- 1}^{0} (2 x - 1) d x$
68776	Find dy/dx	x^2y=y-7	$x^{2} y = y - 7$
68777	Find the Second Derivative	sin(x)cos(x)	$\sin (x) \cos (x)$
68778	Find dy/dx	y=(4x^2-13)^-14	$y = {(4 x^{2} - 13)}^{- 14}$
68779	Find the Derivative - d/dx	y = natural log of x^2+y^2	$y = \ln (x^{2} + y^{2})$
68780	Find the Derivative - d/dx	d/(dx)(5x^4-2x^3-x^2)	$\frac{d}{d x} (5 x^{4} - 2 x^{3} - x^{2})$
68781	Integrate By Parts	integral of e^(x^2) with respect to x	$\int e^{x^{2}} d x$
68782	Evaluate the Integral	integral from -1 to 5 of (1+3x) with respect to x	$\int_{- 1}^{5} (1 + 3 x) d x$
68783	Find the Center and Radius	36pi	$36 π$
68784	Find the Maximum/Minimum Value	f(x)=3-4sin(2x+pi/4)	$f (x) = 3 - 4 \sin (2 x + \frac{π}{4})$
68785	Find the Absolute Max and Min over the Interval	f(x)=7sin(x)+7cos(x) , 0<=x<=2pi	$f (x) = 7 \sin (x) + 7 \cos (x)$ , $0 \leq x \leq 2 π$
68786	Find the Arc Length	y=(x^3)/3+1/(4x) , 1<=x<=3	$y = \frac{x^{3}}{3} + \frac{1}{4 x}$ , $1 \leq x \leq 3$
68787	Find Where Increasing/Decreasing	f(x)=x^2e^x	$f (x) = x^{2} e^{x}$
68788	Evaluate the Limit	limit as x approaches 0 of (x^4+2x^3-x^2)/(x^2)	$lim_{x \to 0} \frac{x^{4} + 2 x^{3} - x^{2}}{x^{2}}$
68789	Evaluate the Integral	integral from 1 to infinity of 1/(x^p) with respect to x	$\int_{1}^{\infty} \frac{1}{x^{p}} d x$
68790	Evaluate the Integral	integral of a^x with respect to a	$\int a^{x} d a$
68791	Find the Domain and Range	f(x)=-2x+3 if x<1; 4x-3 if x>=1	$f (x) = {\begin{cases} - 2 x + 3 & x < 1 \\ 4 x - 3 & x \geq 1 \end{cases}$
68792	Find dy/dx	4y-2x=3x^2	$4 y - 2 x = 3 x^{2}$
68793	Find the Derivative - d/dx	e^x-x-1	$e^{x} - x - 1$
68794	Find the Slope	f(x)=3	$f (x) = 3$
68795	Find the Derivative - d/dθ	cos(theta)^3	$\cos^{3} (θ)$
68796	Integrate Using u-Substitution	integral of (sin( square root of x))/( square root of x) with respect to x	$\int \frac{\sin (\sqrt{x})}{\sqrt{x}} d x$
68797	Evaluate the Limit	limit as x approaches infinity of (1+x)^(1/x)	$lim_{x \to \infty} {(1 + x)}^{\frac{1}{x}}$
68798	Find the Derivative - d/dx	y=(x/3+6 square root of x)^3	$y = {(\frac{x}{3} + 6 \sqrt{x})}^{3}$
68799	Find dy/dx	x^3+y^3=xy	$x^{3} + y^{3} = x y$
68800	Evaluate the Integral	integral of (1+tan(x)^2) with respect to x	$\int (1 + \tan^{2} (x)) d x$