Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
67001	Integrate By Parts	integral of x^3e^x with respect to x	$\int x^{3} e^{x} d x$
67002	Find the Antiderivative	f(x)=x/2-3x^2+x^-3	$f (x) = \frac{x}{2} - 3 x^{2} + x^{- 3}$
67003	Find the Derivative - d/dx	(d^2)/(dx^2)(sec(x))	$\frac{d^{2}}{d x^{2}} (\sec (x))$
67004	Evaluate the Integral	integral from 0 to 2 of (4/5t^3-3/4t^2+2/5t) with respect to t	$\int_{0}^{2} (\frac{4}{5} t^{3} - \frac{3}{4} t^{2} + \frac{2}{5} t) d t$
67005	Find the Maximum/Minimum Value	f(x) = square root of x	$f (x) = \sqrt{x}$
67006	Find dy/dx	1/x+1/y=1	$\frac{1}{x} + \frac{1}{y} = 1$
67007	Solve the Differential Equation	(dy)/(dx)=x/y	$\frac{d y}{d x} = \frac{x}{y}$
67008	Find dy/dx	x^3+y^3=3xy	$x^{3} + y^{3} = 3 x y$
67009	Find dx/dy	x^2+y^2=9	$x^{2} + y^{2} = 9$
67010	Integrate By Parts	integral of x^2cos(x) with respect to x	$\int x^{2} \cos (x) d x$
67011	Find dy/dx	e^(x/y)=x-y	$e^{\frac{x}{y}} = x - y$
67012	Find dy/dx	y=x	$y = x$
67013	Evaluate the Integral	integral from -2 to 1 of [(2-x)-x^2] with respect to y	$\int_{- 2}^{1} [(2 - x) - x^{2}] d y$
67014	Evaluate the Integral	integral from 0 to pi/4 of (sin(t))/(cos(t)^2) with respect to t	$\int_{0}^{\frac{π}{4}} \frac{\sin (t)}{\cos^{2} (t)} d t$
67015	Find dy/dx	sin(x)+2cos(2y)=1	$\sin (x) + 2 \cos (2 y) = 1$
67016	Determine if Continuous	f(x)=-3x-1 if x<-1; -x+1 if x>=-1	$f (x) = {\begin{cases} - 3 x - 1 & x < - 1 \\ - x + 1 & x \geq - 1 \end{cases}$
67017	Find dy/dx	y = square root of x^2+1	$y = \sqrt{x^{2} + 1}$
67018	Determine if Continuous	f(x)=(x^2-4)/(x-2) if x<2; ax^2-bx+3 if 2<=x<3; 4x-a+b if x>=3	$f (x) = {\begin{cases} \frac{x^{2} - 4}{x - 2} & x < 2 \\ a x^{2} - b x + 3 & 2 \leq x < 3 \\ 4 x - a + b & x \geq 3 \end{cases}$
67019	Solve the Differential Equation	dx+e^(3x)dy=0	$d x + e^{3 x} d y = 0$
67020	Evaluate the Limit	limit as x approaches pi/2 from the right of (cos(x))/(1-sin(x))	$lim_{x \to {(\frac{π}{2})}^{+}} \frac{\cos (x)}{1 - \sin (x)}$
67021	Find dx/dy	y=x^2	$y = x^{2}$
67022	Find dy/dx	y=x^( square root of x)	$y = x^{\sqrt{x}}$
67023	Evaluate the Integral	integral from 0 to 4 of (4/5t^3-3/4t^2+2/5t) with respect to t	$\int_{0}^{4} (\frac{4}{5} t^{3} - \frac{3}{4} t^{2} + \frac{2}{5} t) d t$
67024	Evaluate the Integral	integral of (3x^2-4x+2)^4(3x-2) with respect to x	$\int {(3 x^{2} - 4 x + 2)}^{4} (3 x - 2) d x$
67025	Find dy/dx	y=x^3e^x	$y = x^{3} e^{x}$
67026	Find the Derivative - d/dx	2e^(1/2x)	$2 e^{\frac{1}{2} x}$
67027	Find dy/dx	2xy+x^3-3y^2=5	$2 x y + x^{3} - 3 y^{2} = 5$
67028	Find dy/dx	x^2+6xy+12y^2=28	$x^{2} + 6 x y + 12 y^{2} = 28$
67029	Evaluate the Integral	integral from 0 to 6 of [5(2^(-x/3))-x/5] with respect to x	$\int_{0}^{6} [5 (2^{- \frac{x}{3}}) - \frac{x}{5}] d x$
67030	Evaluate the Integral	integral from negative infinity to infinity of 1/(1+x^2) with respect to x	$\int_{- \infty}^{\infty} \frac{1}{1 + x^{2}} d x$
67031	Solve the Differential Equation	x(dy)/(dx)=4y	$x \frac{d y}{d x} = 4 y$
67032	Find dx/dy	y=x^x	$y = x^{x}$
67033	Find dy/dx	y^2-x^2y+3x^3=4	$y^{2} - x^{2} y + 3 x^{3} = 4$
67034	Evaluate the Integral	integral from 0 to 5 of [(x+2)-x/2] with respect to x	$\int_{0}^{5} [(x + 2) - \frac{x}{2}] d x$
67035	Find dy/dx	y = cube root of x	$y = \sqrt[3]{x}$
67036	Evaluate the Limit	limit as x approaches negative infinity of ( square root of x^8-5x^3)/(3x^4+4)	$lim_{x \to - \infty} \frac{\sqrt{x^{8} - 5 x^{3}}}{3 x^{4} + 4}$
67037	Evaluate the Limit	limit as x approaches pi/2 of (3cos(x)^2)/(2-2sin(x))	$lim_{x \to \frac{π}{2}} \frac{3 \cos^{2} (x)}{2 - 2 \sin (x)}$
67038	Find dy/dx	e^(x^2y)=x+y	$e^{x^{2} y} = x + y$
67039	Find dy/dx	y=(cot(x))/(1+cot(x))	$y = \frac{\cot (x)}{1 + \cot (x)}$
67040	Find dy/dx	3x^2+5x^2y^2=2y	$3 x^{2} + 5 x^{2} y^{2} = 2 y$
67041	Evaluate the Integral	integral of (x^2+5)^3*2x with respect to x	$\int {(x^{2} + 5)}^{3} \cdot 2 x d x$
67042	Find dy/dx	x^3+y^3=3xy^2	$x^{3} + y^{3} = 3 x y^{2}$
67043	Find the Maximum/Minimum Value	f(x)=1/x	$f (x) = \frac{1}{x}$
67044	Evaluate the Integral	integral of 5^(x+2) with respect to x	$\int 5^{x + 2} d x$
67045	Evaluate the Limit	limit as x approaches -3 of (x+3)/(4- square root of 2x+22)	$lim_{x \to - 3} \frac{x + 3}{4 - \sqrt{2 x + 22}}$
67046	Evaluate the Integral	integral of (x^4+ square root of x^3) with respect to x	$\int (x^{4} + \sqrt{x^{3}}) d x$
67047	Evaluate the Limit	limit as x approaches pi/4 of (cos(2x))/(cos(x)-sin(x))	$lim_{x \to \frac{π}{4}} \frac{\cos (2 x)}{\cos (x) - \sin (x)}$
67048	Determine if Continuous	f(x)=3x+1 if x<-2; x-3 if x>=-2	$f (x) = {\begin{cases} 3 x + 1 & x < - 2 \\ x - 3 & x \geq - 2 \end{cases}$
67049	Evaluate the Limit	limit as x approaches 0 of (7x^5+5x^2+12x)/(3x^5+4x)	$lim_{x \to 0} \frac{7 x^{5} + 5 x^{2} + 12 x}{3 x^{5} + 4 x}$
67050	Find dy/dx	x^2y^2=36	$x^{2} y^{2} = 36$
67051	Determine if Continuous	f(x)=-x+4 if x<1; 2x+1 if x>=1	$f (x) = {\begin{cases} - x + 4 & x < 1 \\ 2 x + 1 & x \geq 1 \end{cases}$
67052	Integrate By Parts	integral of xsin(x) with respect to x	$\int x \sin (x) d x$
67053	Evaluate the Limit	limit as x approaches negative infinity of ( square root of 4x^4-x)/(2x^2+3)	$lim_{x \to - \infty} \frac{\sqrt{4 x^{4} - x}}{2 x^{2} + 3}$
67054	Evaluate the Limit	limit as x approaches -4 of (7x+28)/(x^2+x-12)	$lim_{x \to - 4} \frac{7 x + 28}{x^{2} + x - 12}$
67055	Find dy/dx	x^3y-2x^2+y^4=8	$x^{3} y - 2 x^{2} + y^{4} = 8$
67056	Find dy/dx	square root of xy=x^2y+1	$\sqrt{x y} = x^{2} y + 1$
67057	Find the Derivative - d/dx	(x^2+1)	$(x^{2} + 1)$
67058	Find dy/dx	x^2-y^2=16	$x^{2} - y^{2} = 16$
67059	Integrate By Parts	integral of e^xcos(x) with respect to x	$\int e^{x} \cos (x) d x$
67060	Find the Slope	-2/3	$- \frac{2}{3}$
67061	Find dy/dx	4x^2+9y^2=36	$4 x^{2} + 9 y^{2} = 36$
67062	Find dy/dx	2x^3-5xy-y^2=3	$2 x^{3} - 5 x y - y^{2} = 3$
67063	Find dy/dx	x=cos(y)	$x = \cos (y)$
67064	Find the Maximum/Minimum Value	f(x)=1/4x^3-1/2x^2-x+2	$f (x) = \frac{1}{4} x^{3} - \frac{1}{2} x^{2} - x + 2$
67065	Find dy/dx	x+tan(xy)=0	$x + \tan (x y) = 0$
67066	Evaluate the Limit	limit as x approaches pi/2 of (sin(2x))/(cos(x))	$lim_{x \to \frac{π}{2}} \frac{\sin (2 x)}{\cos (x)}$
67067	Determine if Continuous	f(x)=-2x+3 if X<2; x-3 if X>=2	$f (x) = {\begin{cases} - 2 x + 3 & X < 2 \\ x - 3 & X \geq 2 \end{cases}$
67068	Evaluate the Integral	integral of (3x^2)/( square root of x^3+8) with respect to x	$\int \frac{3 x^{2}}{\sqrt{x^{3} + 8}} d x$
67069	Find the Derivative - d/dx	y = square root of x+ square root of x+ square root of x	$y = \sqrt{x + \sqrt{x + \sqrt{x}}}$
67070	Find the Antiderivative	f(x)=x^3-3/(x^2)+2x-1	$f (x) = x^{3} - \frac{3}{x^{2}} + 2 x - 1$
67071	Integrate By Parts	integral of x^3e^(x^2) with respect to x	$\int x^{3} e^{x^{2}} d x$
67072	Use Logarithmic Differentiation to Find the Derivative	y=x^(2x)	$y = x^{2 x}$
67073	Find dy/dx	y=x^(sin(x))	$y = x^{\sin (x)}$
67074	Determine if Continuous	f(x)=x-4 if x<2; -2x+2 if x>=2	$f (x) = {\begin{cases} x - 4 & x < 2 \\ - 2 x + 2 & x \geq 2 \end{cases}$
67075	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^(ax)+x)^(1/x)	$lim_{x \to 0} {(e^{a x} + x)}^{\frac{1}{x}}$
67076	Determine if Continuous	f(x)=x-2 if x<-2; 3x+2 if x>=-2	$f (x) = {\begin{cases} x - 2 & x < - 2 \\ 3 x + 2 & x \geq - 2 \end{cases}$
67077	Find the Antiderivative	xe^(-x)	$x e^{- x}$
67078	Find dx/dy	y=x^3	$y = x^{3}$
67079	Find the Derivative - d/dθ	thetacos(theta)sin(theta)	$θ \cos (θ) \sin (θ)$
67080	Find the Antiderivative	f(x)=x(4-x)	$f (x) = x (4 - x)$
67081	Find the Maximum/Minimum Value	f(x)=1/25x^3-1/5x^2-x+5	$f (x) = \frac{1}{25} x^{3} - \frac{1}{5} x^{2} - x + 5$
67082	Find the Maximum/Minimum Value	y=x^3-3x	$y = x^{3} - 3 x$
67083	Find dy/dx	sin(x)+cos(y)=sin(x)cos(y)	$\sin (x) + \cos (y) = \sin (x) \cos (y)$
67084	Evaluate the Integral	integral of (e^(arcsin(x)))/( square root of 1-x^2) with respect to x	$\int \frac{e^{\arcsin (x)}}{\sqrt{1 - x^{2}}} d x$
67085	Evaluate the Limit	limit as theta approaches pi/2 of tan(theta)^2(1-sin(theta))	$lim_{θ \to \frac{π}{2}} \tan^{2} (θ) (1 - \sin (θ))$
67086	Find the Derivative - d/dx	y=tan(5^x)	$y = \tan (5^{x})$
67087	Evaluate the Limit	limit as x approaches -1 of (12x^3+12x^2)/(x^4-x^2)	$lim_{x \to - 1} \frac{12 x^{3} + 12 x^{2}}{x^{4} - x^{2}}$
67088	Find the Derivative - d/dx	-cos(x)^2	$- \cos^{2} (x)$
67089	Find dy/dx	y=e^( square root of x)	$y = e^{\sqrt{x}}$
67090	Find dy/dx	y=2x	$y = 2 x$
67091	Find the Derivative - d/dx	f(x)+g(x)	$f (x) + g (x)$
67092	Evaluate the Limit	limit as x approaches 1 of (x^4+2x^3-3x^2)/(x^3-x^2)	$lim_{x \to 1} \frac{x^{4} + 2 x^{3} - 3 x^{2}}{x^{3} - x^{2}}$
67093	Integrate By Parts	integral of ( natural log of x)/(x^2) with respect to x	$\int \frac{\ln (x)}{x^{2}} d x$
67094	Evaluate the Limit	limit as x approaches negative infinity of ( square root of 16x^6-x^2)/(6x^3+x^2)	$lim_{x \to - \infty} \frac{\sqrt{16 x^{6} - x^{2}}}{6 x^{3} + x^{2}}$
67095	Find the Derivative - d/dx	d/(dx)e^(2x)	$\frac{d}{d x} e^{2 x}$
67096	Find dy/dx	x^3-3x^2y+2xy^2=12	$x^{3} - 3 x^{2} y + 2 x y^{2} = 12$
67097	Evaluate the Limit	limit as x approaches negative infinity of (6x^2-x)/( square root of 9x^4+7x^3)	$lim_{x \to - \infty} \frac{6 x^{2} - x}{\sqrt{9 x^{4} + 7 x^{3}}}$
67098	Find dy/dx	y=sin(x)^3	$y = \sin^{3} (x)$
67099	Use Logarithmic Differentiation to Find the Derivative	y=x^(3x)	$y = x^{3 x}$
67100	Find the Derivative - d/dx	d/(dx)sin(x)^2	$\frac{d}{d x} \sin^{2} (x)$