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Popular Calculus Problems

limit as y approaches 0 of (y^2)/(y^4)	\lim\:_{y\to\:0}(\frac{y^{2}}{y^{4}})
derivative of f(x)=e^x-x^7	derivative\:f(x)=e^{x}-x^{7}
limit as x approaches 1 of (x^2-9)/(x-3)	\lim\:_{x\to\:1}(\frac{x^{2}-9}{x-3})
area y^2=4x+4,y=4x-16	area\:y^{2}=4x+4,y=4x-16
limit as x approaches+0 of e^{4x+2}	\lim\:_{x\to\:+0}(e^{4x+2})
derivative of tan^n(x)	\frac{d}{dx}(\tan^{n}(x))
integral of e^{-x^6}(-6x^5)	\int\:e^{-x^{6}}(-6x^{5})dx
integral of (2x)/((x^2+4)^2)	\int\:\frac{2x}{(x^{2}+4)^{2}}dx
implicit (dy)/(dx),-x+y-x^3=y^3+4x^2	implicit\:\frac{dy}{dx},-x+y-x^{3}=y^{3}+4x^{2}
integral of ((x+1)^2)/(x^2)	\int\:\frac{(x+1)^{2}}{x^{2}}dx
integral of 1/(n(n+1))	\int\:\frac{1}{n(n+1)}
y^{''}-3y^'-18y=0	y^{\prime\:\prime\:}-3y^{\prime\:}-18y=0
area x^3-15x^2+50x,-x^3+15x^2-50x	area\:x^{3}-15x^{2}+50x,-x^{3}+15x^{2}-50x
sum from n=0 to infinity of 1/(2n+3)	\sum\:_{n=0}^{\infty\:}\frac{1}{2n+3}
-2y^'+6x^2=0	-2y^{\prime\:}+6x^{2}=0
integral of (-x^2+x+4)/(x(x-2)^2)	\int\:\frac{-x^{2}+x+4}{x(x-2)^{2}}dx
sum from n=1 to infinity of ln((n+1)/n)	\sum\:_{n=1}^{\infty\:}\ln(\frac{n+1}{n})
9y^{''}-y=(xex)/3	9y^{\prime\:\prime\:}-y=\frac{xex}{3}
integral from 3 to 8 of x^3ln(3x)	\int\:_{3}^{8}x^{3}\ln(3x)dx
y^{''}-8y^'+20y=200x^2-39xe^x	y^{\prime\:\prime\:}-8y^{\prime\:}+20y=200x^{2}-39xe^{x}
integral from 0 to 8 of xe^{-x}	\int\:_{0}^{8}xe^{-x}dx
derivative of-x/(x^2+y^2)	\frac{d}{dx}(-\frac{x}{x^{2}+y^{2}})
integral of 1/(sqrt(2-3x^2))	\int\:\frac{1}{\sqrt{2-3x^{2}}}dx
limit as x approaches pi-of cot(x)	\lim\:_{x\to\:π-}(\cot(x))
derivative of 8e^{4x}	derivative\:8e^{4x}
slope of xy-5y^2=4	slope\:xy-5y^{2}=4
laplacetransform 4te^{3t}sin(2t)	laplacetransform\:4te^{3t}\sin(2t)
integral of sqrt(18-18sin(x))	\int\:\sqrt{18-18\sin(x)}dx
limit as x approaches infinity of 1/(x!)	\lim\:_{x\to\:\infty\:}(\frac{1}{x!})
derivative of-1/(x^{2/3)}	derivative\:-\frac{1}{x^{\frac{2}{3}}}
derivative of sinh^2(3x)	\frac{d}{dx}(\sinh^{2}(3x))
y^{''}+4y=0,y(0)=4,y^'(0)=1	y^{\prime\:\prime\:}+4y=0,y(0)=4,y^{\prime\:}(0)=1
integral of (cos(9x))	\int\:(\cos(9x))dx
derivative of 2xe^x+3sec(x)	\frac{d}{dx}(2xe^{x}+3\sec(x))
derivative of ln((ax^n))	\frac{d}{dx}(\ln((ax)^{n}))
(dy)/(dx)=y(1-y),y(0)=8	\frac{dy}{dx}=y(1-y),y(0)=8
limit as x approaches 4-of 3x-5	\lim\:_{x\to\:4-}(3x-5)
derivative of 4x^3-56x^2+196x	derivative\:4x^{3}-56x^{2}+196x
integral of 1/((sin(x)+cos(x))^2)	\int\:\frac{1}{(\sin(x)+\cos(x))^{2}}dx
integral of 2x^3e^{-2x}	\int\:2x^{3}e^{-2x}dx
limit as x approaches pi/4 of (cos(2x))/(sqrt(2)cos(x)-1)	\lim\:_{x\to\:\frac{π}{4}}(\frac{\cos(2x)}{\sqrt{2}\cos(x)-1})
cos^2(x)sin(x)dy+(ycos^3(x)-1)dx=0	\cos^{2}(x)\sin(x)dy+(y\cos^{3}(x)-1)dx=0
x^2(dy)/(dx)+2xy=5y^3	x^{2}\frac{dy}{dx}+2xy=5y^{3}
derivative of 6ln(x^2)	\frac{d}{dx}(6\ln(x^{2}))
integral of x*tan^2(x)	\int\:x\cdot\:\tan^{2}(x)dx
limit as x approaches 0 of sqrt(3x+1)	\lim\:_{x\to\:0}(\sqrt{3x+1})
(y^'-e^{-t}+3)/y =-3	\frac{y^{\prime\:}-e^{-t}+3}{y}=-3
limit as n approaches infinity of \sum_{i=1}^n(1+(2i)/n)^3(2/n)	\lim\:_{n\to\:\infty\:}(\sum\:_{i=1}^{n}(1+\frac{2i}{n})^{3}(\frac{2}{n}))
derivative of (x^3+x-2/(x-x^2))	\frac{d}{dx}(\frac{x^{3}+x-2}{x-x^{2}})
derivative of e^{(1-x^2-(y^2/4)})	\frac{d}{dx}(e^{(1-x^{2}-\frac{y^{2}}{4})})
derivative of e^{3e^x}	derivative\:e^{3e^{x}}
tangent of f(x)=2x^2,\at x=-1	tangent\:f(x)=2x^{2},\at\:x=-1
derivative of (-10/(\sqrt[3]{x)})	\frac{d}{dx}(\frac{-10}{\sqrt[3]{x}})
integral from 2 to 6 of (1/(sqrt(x-2)))	\int\:_{2}^{6}(\frac{1}{\sqrt{x-2}})dx
limit as x approaches 1 of ln\|ln(x)\|	\lim\:_{x\to\:1}(\ln\left\|\ln(x)\right\|)
(dy)/(dt)=8y	\frac{dy}{dt}=8y
(dy)/(dx)=x^3+2x+pi	\frac{dy}{dx}=x^{3}+2x+π
integral from-1 to 2 of (-x^2+x+2)	\int\:_{-1}^{2}(-x^{2}+x+2)dx
derivative of tan(x^3)	\frac{d}{dx}(\tan(x^{3}))
derivative of (sin^2(x))/(cos^2(x))	derivative\:\frac{\sin^{2}(x)}{\cos^{2}(x)}
limit as x approaches 4+of 2x-7	\lim\:_{x\to\:4+}(2x-7)
slope of sqrt(x)+1/(sqrt(x^3))	slope\:\sqrt{x}+\frac{1}{\sqrt{x^{3}}}
integral of ((x-2)/(x(x^2+2)))	\int\:(\frac{x-2}{x(x^{2}+2)})dx
integral of 1/((u+1)^2)	\int\:\frac{1}{(u+1)^{2}}du
x^2y^'=1-x^2+y^2-x^2y^2	x^{2}y^{\prime\:}=1-x^{2}+y^{2}-x^{2}y^{2}
integral of x^2cos(1/3 x)	\int\:x^{2}\cos(\frac{1}{3}x)dx
(dy)/(dx)=-sin^2(x+y)	\frac{dy}{dx}=-\sin^{2}(x+y)
integral from-1 to 1 of sqrt(x+2)	\int\:_{-1}^{1}\sqrt{x+2}dx
derivative of sqrt(r)+\sqrt[7]{r}	derivative\:\sqrt{r}+\sqrt[7]{r}
limit as x approaches 2 of (2-x)/(2x^2-4)	\lim\:_{x\to\:2}(\frac{2-x}{2x^{2}-4})
area y=9x^2,y=x^2+6	area\:y=9x^{2},y=x^{2}+6
integral of cos^7(y)	\int\:\cos^{7}(y)dy
derivative of-5cot(x)	\frac{d}{dx}(-5\cot(x))
integral of y/((y+2)(3y-1))	\int\:\frac{y}{(y+2)(3y-1)}dy
(dx)/(dt)-0.06x=200	\frac{dx}{dt}-0.06x=200
derivative of 2+8/x+6/(x^2)	derivative\:2+\frac{8}{x}+\frac{6}{x^{2}}
(-sin(x))^'	(-\sin(x))^{\prime\:}
implicit (dy)/(dx),sqrt(x)+sqrt(y)=5	implicit\:\frac{dy}{dx},\sqrt{x}+\sqrt{y}=5
d/(ds)(sqrt(3)(s^3-s^2))	\frac{d}{ds}(\sqrt{3}(s^{3}-s^{2}))
integral of 9e^{-3x}	\int\:9e^{-3x}dx
derivative of 1/(1-x^2)	derivative\:\frac{1}{1-x^{2}}
y^{''}=-y+0.1y^'	y^{\prime\:\prime\:}=-y+0.1y^{\prime\:}
limit as x approaches 0 of 81x^4-216x^3+216x^2-96x+16	\lim\:_{x\to\:0}(81x^{4}-216x^{3}+216x^{2}-96x+16)
y^'-y=11te^{2t}	y^{\prime\:}-y=11te^{2t}
limit as n approaches infinity of 1/(4n)	\lim\:_{n\to\:\infty\:}(\frac{1}{4n})
integral of e^{(-x)/4}	\int\:e^{\frac{-x}{4}}dx
limit as x approaches (5pi)/6 of cos(x)	\lim\:_{x\to\:\frac{5π}{6}}(\cos(x))
d/(dy)(x/(y^2))	\frac{d}{dy}(\frac{x}{y^{2}})
sum from n=1 to infinity of 5/(n(n+6))	\sum\:_{n=1}^{\infty\:}\frac{5}{n(n+6)}
tangent of 2x^2+3xy+1y^3=-10,(-3,-4)	tangent\:2x^{2}+3xy+1y^{3}=-10,(-3,-4)
x^2y^{''}+xy^'+y=sec(ln(x))	x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}+y=\sec(\ln(x))
derivative of (x+2/(x-3))	\frac{d}{dx}(\frac{x+2}{x-3})
derivative of ln^3(3x^2-5)	\frac{d}{dx}(\ln^{3}(3x^{2}-5))
integral of (x^2+2)^3	\int\:(x^{2}+2)^{3}dx
limit as x approaches 0 of (x-4)^3	\lim\:_{x\to\:0}((x-4)^{3})
y^'=((y^2+1))/x	y^{\prime\:}=\frac{(y^{2}+1)}{x}
limit as x approaches 1 of (1-(2ln(1+x))/x)/(x)	\lim\:_{x\to\:1}(\frac{1-\frac{2\ln(1+x)}{x}}{x})
integral of (12)/(sqrt(x))+12sqrt(x)	\int\:\frac{12}{\sqrt{x}}+12\sqrt{x}dx
area y= 1/(x^2),y=9,x=8	area\:y=\frac{1}{x^{2}},y=9,x=8
derivative of arcsec(2^x)	\frac{d}{dx}(\arcsec(2^{x}))

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