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Popular Calculus Problems

tangent of f(x)=x^3-3x+2\at (2.4)	tangent\:f(x)=x^{3}-3x+2\at\:(2.4)
area x=sqrt(y),x= y/2	area\:x=\sqrt{y},x=\frac{y}{2}
limit as x approaches infinity of 2x^2-3	\lim\:_{x\to\:\infty\:}(2x^{2}-3)
area x^2-4,x=-4,x=3,y=0	area\:x^{2}-4,x=-4,x=3,y=0
integral from 0 to 1 of (3x^2-4x+1)	\int\:_{0}^{1}(3x^{2}-4x+1)dx
y^{''}+1/4 y=0	y^{\prime\:\prime\:}+\frac{1}{4}y=0
limit as x approaches-4 of 3	\lim\:_{x\to\:-4}(3)
limit as x approaches infinity of 1/(log_{2)(x)}	\lim\:_{x\to\:\infty\:}(\frac{1}{\log_{2}(x)})
integral from-1 to 0 of 1/(x^2)	\int\:_{-1}^{0}\frac{1}{x^{2}}dx
inverse oflaplace (4se^{-4s})/(2s^2+50)	inverselaplace\:\frac{4se^{-4s}}{2s^{2}+50}
inverse oflaplace (s+1)/(s^2+s+1)	inverselaplace\:\frac{s+1}{s^{2}+s+1}
d/(dt)(ln(sec(t)+tan(t)))	\frac{d}{dt}(\ln(\sec(t)+\tan(t)))
y^'=y(2x-5)	y^{\prime\:}=y(2x-5)
integral of 24(1-x)^5	\int\:24(1-x)^{5}dx
derivative of A(2xe^{2x}+e^{2x}*2x^2)	\frac{d}{dx}(A(2xe^{2x}+e^{2x}\cdot\:2x^{2}))
derivative of f(x)=x(3x^4-sqrt(x))	derivative\:f(x)=x(3x^{4}-\sqrt{x})
derivative of 10log_{10}(x)	derivative\:10\log_{10}(x)
limit as x approaches 9 of 6/9	\lim\:_{x\to\:9}(\frac{6}{9})
(\partial)/(\partial x)(x^2+4y^2+3z^2)	\frac{\partial\:}{\partial\:x}(x^{2}+4y^{2}+3z^{2})
normal of y=4x^2,(-1,4)	normal\:y=4x^{2},(-1,4)
xy^'-2y=2x^2+2x+1	xy^{\prime\:}-2y=2x^{2}+2x+1
slope of (-2,0),(0,1)	slope\:(-2,0),(0,1)
y^'+3/(t^2)y=0	y^{\prime\:}+\frac{3}{t^{2}}y=0
laplacetransform sin(6(t-(3pi)/6))	laplacetransform\:\sin(6(t-\frac{3π}{6}))
derivative of x(e^{-x})	\frac{d}{dx}(x(e^{-x}))
(\partial)/(\partial x)((xy)/(e^{x^2+y^2)})	\frac{\partial\:}{\partial\:x}(\frac{xy}{e^{x^{2}+y^{2}}})
derivative of ln(arctan(2x^3))	derivative\:\ln(\arctan(2x^{3}))
integral of 3/x+2e^x	\int\:\frac{3}{x}+2e^{x}dx
derivative of 3x-x^2	\frac{d}{dx}(3x-x^{2})
derivative of (4-x^2/(4+x^2))	\frac{d}{dx}(\frac{4-x^{2}}{4+x^{2}})
integral of (x+1/(x^4sqrt(x)))	\int\:(x+\frac{1}{x^{4}\sqrt{x}})dx
integral of sec^8(x)	\int\:\sec^{8}(x)dx
(\partial)/(\partial x)(40xy*e^{5x^2-2y})	\frac{\partial\:}{\partial\:x}(40xy\cdot\:e^{5x^{2}-2y})
integral of 1/4 x^3	\int\:\frac{1}{4}x^{3}dx
integral of ((sqrt(x)-x^3e^x+x^2)/(x^3))	\int\:(\frac{\sqrt{x}-x^{3}e^{x}+x^{2}}{x^{3}})dx
y^'=sqrt((1-y^2)/(e^x))	y^{\prime\:}=\sqrt{\frac{1-y^{2}}{e^{x}}}
sum from n=0 to infinity of p^n	\sum\:_{n=0}^{\infty\:}p^{n}
limit as x approaches 3 of 6x	\lim\:_{x\to\:3}(6x)
integral of q/(pi(-0.125x+0.03125)^2)	\int\:\frac{q}{π(-0.125x+0.03125)^{2}}dx
integral of 1/(2-2x)	\int\:\frac{1}{2-2x}dx
d/(dt)(t/(10)sin(5t))	\frac{d}{dt}(\frac{t}{10}\sin(5t))
derivative of sqrt(x^2-4x)	\frac{d}{dx}(\sqrt{x^{2}-4x})
(1+x^2)dy+(xy+x^3+x)dx=0	(1+x^{2})dy+(xy+x^{3}+x)dx=0
(dy)/(dx)=((6x-2xy^3))/(y^2)	\frac{dy}{dx}=\frac{(6x-2xy^{3})}{y^{2}}
tangent of 2x^2+3x-2	tangent\:2x^{2}+3x-2
derivative of f(t)=(6t+38)/(t+9)	derivative\:f(t)=\frac{6t+38}{t+9}
integral from 1 to 6 of (x^2+1)/(7x-x^2)	\int\:_{1}^{6}\frac{x^{2}+1}{7x-x^{2}}dx
derivative of sqrt(pix)	\frac{d}{dx}(\sqrt{πx})
(dy)/(dx)+4/x y=-3x	\frac{dy}{dx}+\frac{4}{x}y=-3x
inverse oflaplace 1/((s^2+2s+1))	inverselaplace\:\frac{1}{(s^{2}+2s+1)}
derivative of (e^x/((1-e^x)^2))	\frac{d}{dx}(\frac{e^{x}}{(1-e^{x})^{2}})
laplacetransform f(t)=-2	laplacetransform\:f(t)=-2
limit as x approaches 0 of 0/(x^6)	\lim\:_{x\to\:0}(\frac{0}{x^{6}})
derivative of y=x^2+2x	derivative\:y=x^{2}+2x
limit as x approaches 0 of xln(x^2)	\lim\:_{x\to\:0}(x\ln(x^{2}))
limit as x approaches infinity of e^{ax}	\lim\:_{x\to\:\infty\:}(e^{ax})
derivative of ln(x^2+7)	\frac{d}{dx}(\ln(x^{2}+7))
(x^{-1})^'	(x^{-1})^{\prime\:}
derivative of (x-1)^2(x-1.05)^2	derivative\:(x-1)^{2}(x-1.05)^{2}
integral of x/(x^2-7x+12)	\int\:\frac{x}{x^{2}-7x+12}dx
limit as x approaches 1/2 of-4x+2	\lim\:_{x\to\:\frac{1}{2}}(-4x+2)
derivative of sqrt(3x-x^2)	\frac{d}{dx}(\sqrt{3x-x^{2}})
integral from 0 to pi/(26) of tan(13x)	\int\:_{0}^{\frac{π}{26}}\tan(13x)dx
5x^2y^'=y^'+2xe^{-y}	5x^{2}y^{\prime\:}=y^{\prime\:}+2xe^{-y}
y^{''}+4y^'+13y=0,y(0)=7,y(0)=7,y^'(0)=7	y^{\prime\:\prime\:}+4y^{\prime\:}+13y=0,y(0)=7,y(0)=7,y^{\prime\:}(0)=7
(\partial)/(\partial x)(2y(y^2+e^{2x}))	\frac{\partial\:}{\partial\:x}(2y(y^{2}+e^{2x}))
integral from 0 to N of e^{(-st)}sin(2t)	\int\:_{0}^{N}e^{(-st)}\sin(2t)dt
limit as h approaches 3 of (3(x+h)^3-3x^3)/h	\lim\:_{h\to\:3}(\frac{3(x+h)^{3}-3x^{3}}{h})
integral from-1 to 2 of (2x-7)/(x^3)	\int\:_{-1}^{2}\frac{2x-7}{x^{3}}dx
maclaurin 1/(1-x),3	maclaurin\:\frac{1}{1-x},3
integral from 0 to 1 of 2/(x-2)	\int\:_{0}^{1}\frac{2}{x-2}dx
derivative of 1/(1+2x)	\frac{d}{dx}(\frac{1}{1+2x})
derivative of sqrt(9+5x)	\frac{d}{dx}(\sqrt{9+5x})
derivative of 2x^{-7\sqrt[3]{x}}	\frac{d}{dx}(2x^{-7\sqrt[3]{x}})
sum from n=1 to infinity of n!2^nn^{-n}	\sum\:_{n=1}^{\infty\:}n!2^{n}n^{-n}
derivative of sqrt(1+4x^2)	derivative\:\sqrt{1+4x^{2}}
laplacetransform 5(t-4)	laplacetransform\:5(t-4)
integral of (x^2+sqrt(2+x))/(\sqrt[3]{2+x)}	\int\:\frac{x^{2}+\sqrt{2+x}}{\sqrt[3]{2+x}}dx
derivative of x^2*2	derivative\:x^{2}\cdot\:2
limit as x approaches infinity of-2e^{-x}+2	\lim\:_{x\to\:\infty\:}(-2e^{-x}+2)
integral of 3xsqrt(y)	\int\:3x\sqrt{y}dy
implicit (dy)/(dx),y=(sin(x))^{6x}	implicit\:\frac{dy}{dx},y=(\sin(x))^{6x}
(\partial)/(\partial x)(x^2+y^2-9)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}-9)
integral of sec^2(2xta)n^62x	\int\:\sec^{2}(2xta)n^{6}2xdx
derivative of 3/x+e^{2x}*2	\frac{d}{dx}(\frac{3}{x}+e^{2x}\cdot\:2)
tangent of f(x)=x^2-3,(2,1)	tangent\:f(x)=x^{2}-3,(2,1)
sum from n=0 to infinity of (n+1)/3	\sum\:_{n=0}^{\infty\:}\frac{n+1}{3}
derivative of f(x)=2sin(x)	derivative\:f(x)=2\sin(x)
laplacetransform e^{-2t}(t^2+4t+5)	laplacetransform\:e^{-2t}(t^{2}+4t+5)
integral from a to 2a of (a-(a^3)/(x^2))	\int\:_{a}^{2a}(a-\frac{a^{3}}{x^{2}})dx
derivative of 2/(sqrt(x^2+5))	\frac{d}{dx}(\frac{2}{\sqrt{x^{2}+5}})
integral of cos(x)cos(sin(x))	\int\:\cos(x)\cos(\sin(x))dx
limit as x approaches+5-of 5/((x-5)^3)	\lim\:_{x\to\:+5-}(\frac{5}{(x-5)^{3}})
integral of ((3x+5)^3)/(10)	\int\:\frac{(3x+5)^{3}}{10}dx
d/(du)(u^3-5u^2+7/(3u^2)+6)	\frac{d}{du}(u^{3}-5u^{2}+\frac{7}{3u^{2}}+6)
(\partial)/(\partial x)(10990+1120x+873y)	\frac{\partial\:}{\partial\:x}(10990+1120x+873y)
tangent of sqrt(5x+1)	tangent\:\sqrt{5x+1}
integral of (4+3x)/(1+x^2)	\int\:\frac{4+3x}{1+x^{2}}dx
integral of (e^{-2x})/(x^2)	\int\:\frac{e^{-2x}}{x^{2}}dx
integral from 0 to pi/3 of sec^4(x)	\int\:_{0}^{\frac{π}{3}}\sec^{4}(x)dx

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