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Popular Calculus Problems

limit as x approaches 8 of sqrt(x+1)	\lim\:_{x\to\:8}(\sqrt{x+1})
derivative of f(x)=8x^2+sqrt(x^3)	derivative\:f(x)=8x^{2}+\sqrt{x^{3}}
derivative of (e^x/(5x^2+8))	\frac{d}{dx}(\frac{e^{x}}{5x^{2}+8})
integral of 30sqrt(t)-(12)/(sqrt(t))	\int\:30\sqrt{t}-\frac{12}{\sqrt{t}}dt
area 3cos(pix),8x^2-2,-0.5,0.5	area\:3\cos(πx),8x^{2}-2,-0.5,0.5
derivative of 4/3 (x+1^{3/2})	\frac{d}{dx}(\frac{4}{3}(x+1)^{\frac{3}{2}})
limit as x approaches infinity of n/x	\lim\:_{x\to\:\infty\:}(\frac{n}{x})
integral from 0 to 1 of e^{-(1+j^2pin)t}	\int\:_{0}^{1}e^{-(1+j^{2}πn)t}dt
derivative of sin(3xcos(3x))	\frac{d}{dx}(\sin(3x)\cos(3x))
integral of 2sqrt(cos(2x))sin(2x)	\int\:2\sqrt{\cos(2x)}\sin(2x)dx
integral of 1/((x^2+3x+5)^3)	\int\:\frac{1}{(x^{2}+3x+5)^{3}}dx
integral of 2/(sqrt(3x-7))	\int\:\frac{2}{\sqrt{3x-7}}dx
limit as x approaches-6+of (2x)/(6+x)	\lim\:_{x\to\:-6+}(\frac{2x}{6+x})
(\partial)/(\partial x)(((1+y))/((1+x)))	\frac{\partial\:}{\partial\:x}(\frac{(1+y)}{(1+x)})
derivative of 2e^t	derivative\:2e^{t}
limit as x approaches 1+of (x^2)/(1-x)	\lim\:_{x\to\:1+}(\frac{x^{2}}{1-x})
integral of sqrt(x)e^{-x}	\int\:\sqrt{x}e^{-x}dx
integral of cos(x)e^{-x}	\int\:\cos(x)e^{-x}dx
area y=3x,y=5x^2	area\:y=3x,y=5x^{2}
(d^2)/(dx^2)(sqrt(x)e^{7x})	\frac{d^{2}}{dx^{2}}(\sqrt{x}e^{7x})
integral of (5x^2)/(sqrt(x^2-4))	\int\:\frac{5x^{2}}{\sqrt{x^{2}-4}}dx
integral of (2s+2)/((s^2+1)(s-1)^3)	\int\:\frac{2s+2}{(s^{2}+1)(s-1)^{3}}ds
sum from n=1 to infinity of 0.45^n	\sum\:_{n=1}^{\infty\:}0.45^{n}
area-2x^2+20,3x-15	area\:-2x^{2}+20,3x-15
limit as x approaches+2 of 2x-2	\lim\:_{x\to\:+2}(2x-2)
derivative of arcsin(2x)	derivative\:\arcsin(2x)
(\partial)/(\partial y)(xy^2-x^3y)	\frac{\partial\:}{\partial\:y}(xy^{2}-x^{3}y)
integral of sqrt(36-t^2)	\int\:\sqrt{36-t^{2}}dt
integral of x2^x	\int\:x2^{x}dx
derivative of f(x)=2x^9ex	derivative\:f(x)=2x^{9}ex
derivative of 4sqrt(x)+1/x	\frac{d}{dx}(4\sqrt{x}+\frac{1}{x})
sum from n=1 to infinity of 1/(n*ln(n))	\sum\:_{n=1}^{\infty\:}\frac{1}{n\cdot\:\ln(n)}
integral of 4x*e^{x^2}	\int\:4x\cdot\:e^{x^{2}}dx
integral of 3xsec(x)tan(x)	\int\:3x\sec(x)\tan(x)dx
(\partial)/(\partial x)(sqrt(x+y))	\frac{\partial\:}{\partial\:x}(\sqrt{x+y})
integral of xe^{-4x^2}	\int\:xe^{-4x^{2}}dx
derivative of f(x)=(sin(x))^x	derivative\:f(x)=(\sin(x))^{x}
integral of e^{2sqrt(x)}	\int\:e^{2\sqrt{x}}dx
(\partial)/(\partial y)((x^2)/(4y^4))	\frac{\partial\:}{\partial\:y}(\frac{x^{2}}{4y^{4}})
integral of-1/2 tan(2x)	\int\:-\frac{1}{2}\tan(2x)dx
integral of 1/(z^2+4)	\int\:\frac{1}{z^{2}+4}dz
area y=x,y=12x,x=16	area\:y=x,y=12x,x=16
y^{''}+y=cot(x)	y^{\prime\:\prime\:}+y=\cot(x)
(\partial)/(\partial y)(ln(3+x^2y^2))	\frac{\partial\:}{\partial\:y}(\ln(3+x^{2}y^{2}))
derivative of (sin(x)/(1+2cos(x)))	\frac{d}{dx}(\frac{\sin(x)}{1+2\cos(x)})
derivative of y=e^xcos(x)	derivative\:y=e^{x}\cos(x)
integral of x^2sqrt(x+1)	\int\:x^{2}\sqrt{x+1}dx
derivative of sin(x+x)	\frac{d}{dx}(\sin(x)+x)
integral of (2x)/(sqrt(1-4x^4))	\int\:\frac{2x}{\sqrt{1-4x^{4}}}dx
integral of (z^2)/(z^3+1)	\int\:\frac{z^{2}}{z^{3}+1}dz
derivative of-9(5x^2+4)^{-6}	derivative\:-9(5x^{2}+4)^{-6}
implicit sqrt(x+y)=x^3+y^2	implicit\:\sqrt{x+y}=x^{3}+y^{2}
integral of e^{tan(x)}sec^2(x)	\int\:e^{\tan(x)}\sec^{2}(x)dx
derivative of y=4x^2	derivative\:y=4x^{2}
derivative of f(x)=ln(7)	derivative\:f(x)=\ln(7)
integral from 0 to 2 of x^3e^{-x^2}	\int\:_{0}^{2}x^{3}e^{-x^{2}}dx
limit as x approaches 0 of (1+x)/(x^2)	\lim\:_{x\to\:0}(\frac{1+x}{x^{2}})
tangent of 4(x-(1/x)^4)	tangent\:4(x-(\frac{1}{x})^{4})
derivative of f(x)= x/3	derivative\:f(x)=\frac{x}{3}
derivative of arccos(cos^2(x))	\frac{d}{dx}(\arccos(\cos^{2}(x)))
derivative of 12sin(x)	\frac{d}{dx}(12\sin(x))
tangent of f(x)=-4x^2-2x+3,\at x=-3	tangent\:f(x)=-4x^{2}-2x+3,\at\:x=-3
limit as t approaches 1 of sqrt(t+5)	\lim\:_{t\to\:1}(\sqrt{t+5})
d/(dt)(3^t)	\frac{d}{dt}(3^{t})
(dy)/(dx)=1-(10x-y+4)^2	\frac{dy}{dx}=1-(10x-y+4)^{2}
3y^{''}+3y^'-2y=0	3y^{\prime\:\prime\:}+3y^{\prime\:}-2y=0
taylor e^{(x^2)}	taylor\:e^{(x^{2})}
limit as x approaches 1+of (2x+1)/(x-1)	\lim\:_{x\to\:1+}(\frac{2x+1}{x-1})
y^{''}+12y^'+37y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+12y^{\prime\:}+37y=0,y(0)=1,y^{\prime\:}(0)=0
integral from 0 to 1 of (23)/(4y-1)	\int\:_{0}^{1}\frac{23}{4y-1}dy
derivative of f(x)=cos^3(pix)	derivative\:f(x)=\cos^{3}(πx)
integral of (sqrt(x^2-400))/x	\int\:\frac{\sqrt{x^{2}-400}}{x}dx
integral of 0/(x+1)	\int\:\frac{0}{x+1}dx
limit as x approaches 0 of e^{2x}	\lim\:_{x\to\:0}(e^{2x})
(\partial)/(\partial x)(-e^ysin(x)+4y+7yx)	\frac{\partial\:}{\partial\:x}(-e^{y}\sin(x)+4y+7yx)
derivative of r/(sqrt(r^2+8))	derivative\:\frac{r}{\sqrt{r^{2}+8}}
y^{''}-3y^'-4y=0,y(0)=a,y^'(0)=5	y^{\prime\:\prime\:}-3y^{\prime\:}-4y=0,y(0)=a,y^{\prime\:}(0)=5
derivative of 4/(2-4)+(27)/(4+2)	derivative\:\frac{4}{2-4}+\frac{27}{4+2}
integral of 7e^{3x+e^{3x}}	\int\:7e^{3x+e^{3x}}dx
(\partial)/(\partial y)(((x+y))/((x-y)))	\frac{\partial\:}{\partial\:y}(\frac{(x+y)}{(x-y)})
integral of e^{(-1-sqrt(13)i)t}	\int\:e^{(-1-\sqrt{13}i)t}dt
integral of 1/(2u+1)	\int\:\frac{1}{2u+1}du
limit as x approaches 1+of ln(3x^2-x-2)	\lim\:_{x\to\:1+}(\ln(3x^{2}-x-2))
tangent of f(x)=x^2+1,\at x=3	tangent\:f(x)=x^{2}+1,\at\:x=3
limit as x approaches 3 of 5/((x-3)^2)	\lim\:_{x\to\:3}(\frac{5}{(x-3)^{2}})
(dy)/(dx)= 1/x (y^2+y),y(1)=0.5	\frac{dy}{dx}=\frac{1}{x}(y^{2}+y),y(1)=0.5
integral of x^3ln(x)	\int\:x^{3}\ln(x)dx
integral of (x^3+1)^2x^2	\int\:(x^{3}+1)^{2}x^{2}dx
(x+1)y^'+(x+2)y=2xe^{-x}	(x+1)y^{\prime\:}+(x+2)y=2xe^{-x}
tangent of x^{2/3}+y^{2/3}=10,(27,1)	tangent\:x^{\frac{2}{3}}+y^{\frac{2}{3}}=10,(27,1)
derivative of 2x^3-3x^2+2x	\frac{d}{dx}(2x^{3}-3x^{2}+2x)
tangent of 6x^4-9xy-7y^2=104,(-2,2)	tangent\:6x^{4}-9xy-7y^{2}=104,(-2,2)
sum from n=1 to infinity of (-n)/(n^2+1)	\sum\:_{n=1}^{\infty\:}\frac{-n}{n^{2}+1}
limit as x approaches 2 of 3x^2-5x+2	\lim\:_{x\to\:2}(3x^{2}-5x+2)
e^ydx-e^{-x}dy=0,y(0)=0	e^{y}dx-e^{-x}dy=0,y(0)=0
(d^2)/(d{r)^2}(pi{r}^2)	\frac{d^{2}}{d{r}^{2}}(π{r}^{2})
derivative of f(x)=(x+6)/(e^x)	derivative\:f(x)=\frac{x+6}{e^{x}}
sum from n=0 to infinity of sec(n)	\sum\:_{n=0}^{\infty\:}\sec(n)
integral of x^3(2x+5-3sqrt(x))	\int\:x^{3}(2x+5-3\sqrt{x})dx
sum from n=1 to infinity of e^{2n}	\sum\:_{n=1}^{\infty\:}e^{2n}

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