Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
81001	Find the Concavity	f(x)=-1/15x^6+6x^4	$f (x) = - \frac{1}{15} x^{6} + 6 x^{4}$
81002	Find the Derivative - d/dx	y=(11x^2)/(4x)	$y = \frac{11 x^{2}}{4 x}$
81003	Evaluate the Integral	integral of 10/((1+x)^2) with respect to x	$\int \frac{10}{{(1 + x)}^{2}} d x$
81004	Find the Antiderivative	f(x)=12/17	$f (x) = \frac{12}{17}$
81005	Evaluate the Integral	integral from 0 to 1 of (e^t+5e^(5t)) with respect to t	$\int_{0}^{1} (e^{t} + 5 e^{5 t}) d t$
81006	Find Where Increasing/Decreasing	f(x)=5+4x+x^2	$f (x) = 5 + 4 x + x^{2}$
81007	Evaluate the Integral	integral of x^2(2x-1)^2 with respect to x	$\int x^{2} {(2 x - 1)}^{2} d x$
81008	Solve the Differential Equation	y'+y=0	$y' + y = 0$
81009	Find the Maximum/Minimum Value	f(x) = square root of x^3+3x^2	$f (x) = \sqrt{x^{3} + 3 x^{2}}$
81010	Evaluate the Limit	limit as x approaches 5 of (2x-10)/(x^2-2x-15)	$lim_{x \to 5} \frac{2 x - 10}{x^{2} - 2 x - 15}$
81011	Determine if Continuous	f(x)=2x+1 if x>=1; 4-x^2 if x=1	$f (x) = {\begin{cases} 2 x + 1 & x \geq 1 \\ 4 - x^{2} & x = 1 \end{cases}$
81012	Evaluate the Integral	integral of x(x+2)(4x-1) with respect to x	$\int x (x + 2) (4 x - 1) d x$
81013	Use Logarithmic Differentiation to Find the Derivative	y=x^5sin(x)	$y = x^{5} \sin (x)$
81014	Find the Concavity	f(x)=1/6x^4+5x^3+50x^2	$f (x) = \frac{1}{6} x^{4} + 5 x^{3} + 50 x^{2}$
81015	Find the Concavity	f(x)=1/3x^6+3x^5+15/2x^4	$f (x) = \frac{1}{3} x^{6} + 3 x^{5} + \frac{15}{2} x^{4}$
81016	Evaluate the Summation	sum from k=1 to 8 of -1(2/3)k-1	$\sum_{k = 1}^{8} - 1 (\frac{2}{3}) k - 1$
81017	Find the Integral	1/( square root of x+1)	$\frac{1}{\sqrt{x + 1}}$
81018	Find the Inflection Points	f(x)=-1/3x^3-9x^2	$f (x) = - \frac{1}{3} x^{3} - 9 x^{2}$
81019	Evaluate the Integral	integral from -1 to 5 of \|x^3-4x\| with respect to x	$\int_{- 1}^{5} \| x^{3} - 4 x \| d x$
81020	Evaluate the Limit	limit as x approaches 2 of (x^5-32)/(x^4-16)	$lim_{x \to 2} \frac{x^{5} - 32}{x^{4} - 16}$
81021	Find the Integral	2^xdx	$2^{x} d x$
81022	Find the Antiderivative	sin(x/2)^2	$\sin^{2} (\frac{x}{2})$
81023	Evaluate the Integral	integral from -2 to 2 of cube root of 8x+(4x)/(x^3) with respect to x	$\int_{- 2}^{2} \sqrt[3]{8 x} + \frac{4 x}{x^{3}} d x$
81024	Find the Derivative - d/dx	-4x^(1/2)	$- 4 x^{\frac{1}{2}}$
81025	Evaluate the Integral	integral of (4/( square root of x)-( square root of x)/4) with respect to x	$\int (\frac{4}{\sqrt{x}} - \frac{\sqrt{x}}{4}) d x$
81026	Find dy/dx	y = cube root of (1+x^2)/(x-4)	$y = \sqrt[3]{\frac{1 + x^{2}}{x - 4}}$
81027	Find the Inflection Points	f(x)=-1/3x^6-3x^5-15/2x^4	$f (x) = - \frac{1}{3} x^{6} - 3 x^{5} - \frac{15}{2} x^{4}$
81028	Integrate By Parts	integral of e^(8theta)sin(9theta) with respect to theta	$\int e^{8 θ} \sin (9 θ) d θ$
81029	Evaluate the Integral	integral of 3/(x^3)+5 square root of x with respect to x	$\int \frac{3}{x^{3}} + 5 \sqrt{x} d x$
81030	Find the Integral	( square root of x)/x	$\frac{\sqrt{x}}{x}$
81031	Evaluate the Limit	limit as x approaches 0 of (x+cos(-7x)-1)/(-2x)	$lim_{x \to 0} \frac{x + \cos (- 7 x) - 1}{- 2 x}$
81032	Find the Derivative - d/dx	x^3-2x^2-6x+pi	$x^{3} - 2 x^{2} - 6 x + π$
81033	Find the Maximum/Minimum Value	f(x)=(x^2)/((x-1)^2)	$f (x) = \frac{x^{2}}{{(x - 1)}^{2}}$
81034	Find the Derivative - d/dx	(dy)/(dx)=(y^2)/(x^2)	$\frac{d y}{d x} = \frac{y^{2}}{x^{2}}$
81035	Evaluate the Limit	limit as x approaches pi/3 of cot(-(2 square root of 3x)/pi+csc(x)-pi/4)	$lim_{x \to \frac{π}{3}} \cot (- \frac{2 \sqrt{3} x}{π} + \csc (x) - \frac{π}{4})$
81036	Evaluate the Limit	limit as x approaches - square root of 3 of (8(x^4-9))/(x^2-3)	$lim_{x \to - \sqrt{3}} \frac{8 (x^{4} - 9)}{x^{2} - 3}$
81037	Find the Tangent Line at (1,0)	x^2y^2-2xy+x^2=1 , (1,0)	$x^{2} y^{2} - 2 x y + x^{2} = 1$ , $(1, 0)$
81038	Find the Antiderivative	x^2-3^x+1/x	$x^{2} - 3^{x} + \frac{1}{x}$
81039	Evaluate the Limit	limit as x approaches infinity of (x^4-10)/(4x^3+x)	$lim_{x \to \infty} \frac{x^{4} - 10}{4 x^{3} + x}$
81040	Find the Derivative - d/dx	(sin(x))e^(-x)	$(\sin (x)) e^{- x}$
81041	Integrate By Parts	integral of (x^2+2x)cos(x) with respect to x	$\int (x^{2} + 2 x) \cos (x) d x$
81042	Find the Antiderivative	((x^2+1)/x)^2	${(\frac{x^{2} + 1}{x})}^{2}$
81043	Find the Antiderivative	e^x(2+(e^(-x))/(cos(x)^2))	$e^{x} (2 + \frac{e^{- x}}{\cos^{2} (x)})$
81044	Find the Antiderivative	f(x)=4e^x+x^3	$f (x) = 4 e^{x} + x^{3}$
81045	Find the Antiderivative	f(x)=x^8+3x^7-5x+2	$f (x) = x^{8} + 3 x^{7} - 5 x + 2$
81046	Evaluate the Integral	integral of x(x^2+3/(x^4)) with respect to x	$\int x (x^{2} + \frac{3}{x^{4}}) d x$
81047	Find the Maximum/Minimum Value	f(x)=x^2e^(-x^2)	$f (x) = x^{2} e^{- x^{2}}$
81048	Find the Inflection Points	f(x)=-1/15x^6+x^5-4x^4	$f (x) = - \frac{1}{15} x^{6} + x^{5} - 4 x^{4}$
81049	Integrate By Parts	integral of x natural log of 1+x with respect to x	$\int x \ln (1 + x) d x$
81050	Find the Maximum/Minimum Value	y=xe^(-x)	$y = x e^{- x}$
81051	Find the Antiderivative	3^(2x+1)	$3^{2 x + 1}$
81052	Evaluate the Limit	limit as x approaches 4 of (x^2+7x+y)/(x^2-6x+8)=15/2	$lim_{x \to 4} \frac{x^{2} + 7 x + y}{x^{2} - 6 x + 8} = \frac{15}{2}$
81053	Find the Maximum/Minimum Value	f(x)=6x^4+3x^2	$f (x) = 6 x^{4} + 3 x^{2}$
81054	Evaluate the Limit	limit as x approaches infinity of ((2x+1)^40(4x-1)^5)/((2x+3)^45)	$lim_{x \to \infty} \frac{{(2 x + 1)}^{40} {(4 x - 1)}^{5}}{{(2 x + 3)}^{45}}$
81055	Find the Antiderivative	4 cube root of x-6 square root of x	$4 \sqrt[3]{x} - 6 \sqrt{x}$
81056	Find the Derivative - d/dy	2ye^x-ycos(2xy)	$2 y e^{x} - y \cos (2 x y)$
81057	Integrate Using u-Substitution	integral of (e^u)/((1-e^u)^2) with respect to u	$\int \frac{e^{u}}{{(1 - e^{u})}^{2}} d u$
81058	Find dy/dx	4x^3=y+y^2	$4 x^{3} = y + y^{2}$
81059	Find Where Increasing/Decreasing	f(x) = square root of x-3	$f (x) = \sqrt{x} - 3$
81060	Evaluate the Integral	integral of (x^4-2x^3-12x^2+9x-16)/(x+3) with respect to x	$\int \frac{x^{4} - 2 x^{3} - 12 x^{2} + 9 x - 16}{x + 3} d x$
81061	Find the Inflection Points	f(x)=3/10x^5+x^4+x^3	$f (x) = \frac{3}{10} x^{5} + x^{4} + x^{3}$
81062	Evaluate the Limit	limit as x approaches negative infinity of (x^3-1)/(x^3+7)	$lim_{x \to - \infty} \frac{x^{3} - 1}{x^{3} + 7}$
81063	Evaluate the Integral	integral from 1 to infinity of 1/(2x^2) with respect to x	$\int_{1}^{\infty} \frac{1}{2 x^{2}} d x$
81064	Evaluate the Integral	integral of (4x-2)/((2x-1)^2) with respect to x	$\int \frac{4 x - 2}{{(2 x - 1)}^{2}} d x$
81065	Find dy/dx	y=((3x-1)/(x^2+3))^2	$y = {(\frac{3 x - 1}{x^{2} + 3})}^{2}$
81066	Find the Antiderivative	8x^4+(x^-2)/2	$8 x^{4} + \frac{x^{- 2}}{2}$
81067	Evaluate the Limit	limit as x approaches 3 of (x^3-3x^2)/(5x-15)	$lim_{x \to 3} \frac{x^{3} - 3 x^{2}}{5 x - 15}$
81068	Find dy/dx	y=(x^4)/((6x+1)^3)	$y = \frac{x^{4}}{{(6 x + 1)}^{3}}$
81069	Integrate Using u-Substitution	integral of xsin(x) with respect to x	$\int x \sin (x) d x$
81070	Find the Antiderivative	(2+e^(3x))^2	${(2 + e^{3 x})}^{2}$
81071	Evaluate the Integral	integral from 1 to 2 of (x^2-x-5)/(x+2) with respect to x	$\int_{1}^{2} \frac{x^{2} - x - 5}{x + 2} d x$
81072	Evaluate the Limit	limit as x approaches 1 of ( square root of x-x^2)/( natural log of x)	$lim_{x \to 1} \frac{\sqrt{x} - x^{2}}{\ln (x)}$
81073	Find dy/dx	-3y-2y^3-1+4x^3-2y^2=0	$- 3 y - 2 y^{3} - 1 + 4 x^{3} - 2 y^{2} = 0$
81074	Find the Maximum/Minimum Value	f(x) = square root of 3sin(x)+cos(x)	$f (x) = \sqrt{3} \sin (x) + \cos (x)$
81075	Find the Derivative - d/dx	y/(3y^2-x)	$\frac{y}{3 y^{2} - x}$
81076	Find the Derivative - d/dθ	tan(2theta)	$\tan (2 θ)$
81077	Evaluate the Integral	integral from pi to 2pi of theta with respect to theta	$\int_{π}^{2 π} θ d θ$
81078	Evaluate the Integral	integral of (9x^7)/(x^8+9) with respect to x	$\int \frac{9 x^{7}}{x^{8} + 9} d x$
81079	Find Where Increasing/Decreasing	y=12(17/10)^x	$y = 12 {(\frac{17}{10})}^{x}$
81080	Evaluate the Integral	integral from 0 to 2 of (3x^2-sin(x)) with respect to x	$\int_{0}^{2} (3 x^{2} - \sin (x)) d x$
81081	Evaluate the Limit	limit as x approaches infinity of ( square root of 9x^2+4+5x)/(4x+3)	$lim_{x \to \infty} \frac{\sqrt{9 x^{2} + 4} + 5 x}{4 x + 3}$
81082	Evaluate the Integral	integral of ((x^3-2x)^3)/(x^3) with respect to x	$\int \frac{{(x^{3} - 2 x)}^{3}}{x^{3}} d x$
81083	Find the Absolute Max and Min over the Interval	f(x)=(4x^3)/3-4x+1 on -3 , 1	$f (x) = \frac{4 x^{3}}{3} - 4 x + 1$ on $- 3$ , $1$
81084	Evaluate the Limit	limit as x approaches 4 of ( square root of x^2+1- square root of x+13)/(x-4)	$lim_{x \to 4} \frac{\sqrt{x^{2} + 1} - \sqrt{x + 13}}{x - 4}$
81085	Evaluate the Limit	limit as x approaches c of -4*f(x)	$lim_{x \to c} - 4 \cdot f (x)$
81086	Integrate Using u-Substitution	integral of x^3cos(x^4) with respect to x	$\int x^{3} \cos (x^{4}) d x$
81087	Find the Derivative - d/dx	e^(x-e)	$e^{x - e}$
81088	Evaluate the Integral	integral of 1/(a^2+x^2) with respect to x	$\int \frac{1}{a^{2} + x^{2}} d x$
81089	Find the Inflection Points	f(x)=-1/10x^5-2x^4-12x^3	$f (x) = - \frac{1}{10} x^{5} - 2 x^{4} - 12 x^{3}$
81090	Evaluate the Summation	2 sum from m=0 to 5 of 2m^2-7	$2 \sum_{m = 0}^{5} 2 m^{2} - 7$
81091	Find the Third Derivative	y=(x-6)/(4x)	$y = \frac{x - 6}{4 x}$
81092	Find the Area Between the Curves	y=4/3x , y=4 , y=1/16x^2	$y = \frac{4}{3} x$ , $y = 4$ , $y = \frac{1}{16} x^{2}$
81093	Find the Second Derivative	y=(x-6)/(4x)	$y = \frac{x - 6}{4 x}$
81094	Evaluate the Limit	limit as x approaches 1 of (x^3+13x^2+24x-108)/(x^2+12x+35)	$lim_{x \to 1} \frac{x^{3} + 13 x^{2} + 24 x - 108}{x^{2} + 12 x + 35}$
81095	Find the Inflection Points	-1/6x^6-x^5+5x^4	$- \frac{1}{6} x^{6} - x^{5} + 5 x^{4}$
81096	Find the Slope	2/1	$\frac{2}{1}$
81097	Integrate By Parts	integral of e^(-2x) with respect to x	$\int e^{- 2 x} d x$
81098	Find the Concavity	f(x)=-x^3+30x^2+63x	$f (x) = - x^{3} + 30 x^{2} + 63 x$
81099	Find dy/dx	x-y=xy	$x - y = x y$
81100	Find the Antiderivative	1/3cos(6x)-4sin(4x)	$\frac{1}{3} \cos (6 x) - 4 \sin (4 x)$