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Popular Calculus Problems

limit as x approaches 0 of (7x^2-4x)/x	\lim\:_{x\to\:0}(\frac{7x^{2}-4x}{x})
d/(dt)(asin(t))	\frac{d}{dt}(a\sin(t))
laplacetransform e^2tcos(2t)	laplacetransform\:e^{2}t\cos(2t)
integral of 6/7 x^{-1/7}	\int\:\frac{6}{7}x^{-\frac{1}{7}}dx
limit as x approaches 3-of (x-3)^{-1}	\lim\:_{x\to\:3-}((x-3)^{-1})
(\partial)/(\partial y)(ln(10x^2-7y^2))	\frac{\partial\:}{\partial\:y}(\ln(10x^{2}-7y^{2}))
tangent of 2/(3\sqrt[3]{x)}	tangent\:\frac{2}{3\sqrt[3]{x}}
derivative of f(x)=(4-3x-x^2)/(x^2-1)	derivative\:f(x)=\frac{4-3x-x^{2}}{x^{2}-1}
integral of 10arcsin(x)	\int\:10\arcsin(x)dx
limit as x approaches-2 of (x+1)(x+3)	\lim\:_{x\to\:-2}((x+1)(x+3))
derivative of x^{(2/x)}	derivative\:x^{(\frac{2}{x})}
derivative of y=3x^2+12x+6	derivative\:y=3x^{2}+12x+6
y^{''}+4y^'+4y=8x^2	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=8x^{2}
derivative of xe^xy	\frac{d}{dx}(xe^{x}y)
(d^3)/(dx^3)(cos(x)-sin(x))	\frac{d^{3}}{dx^{3}}(\cos(x)-\sin(x))
integral of 6/(x(x+2))	\int\:\frac{6}{x(x+2)}dx
limit as x approaches 3+of (\|x-2\|)/(x-2)	\lim\:_{x\to\:3+}(\frac{\left\|x-2\right\|}{x-2})
(\partial)/(\partial x)(sqrt(56x^2-8y^2-16x-31)+1-8x)	\frac{\partial\:}{\partial\:x}(\sqrt{56x^{2}-8y^{2}-16x-31}+1-8x)
f(x)=1+x	f(x)=1+x
integral of 1/(x^{1+c)}	\int\:\frac{1}{x^{1+c}}dx
integral of (-5x^2)/(x^4-1)	\int\:\frac{-5x^{2}}{x^{4}-1}dx
(\partial)/(\partial t)(cos^2(t))	\frac{\partial\:}{\partial\:t}(\cos^{2}(t))
limit as x approaches 0-of 2x+c	\lim\:_{x\to\:0-}(2x+c)
(dy)/(dx)=(x^2-1)/(y^2)	\frac{dy}{dx}=\frac{x^{2}-1}{y^{2}}
y^{'''}+4y^{''}-5y^'=0	y^{\prime\:\prime\:\prime\:}+4y^{\prime\:\prime\:}-5y^{\prime\:}=0
integral from 0 to 8 of (8x-x^2)	\int\:_{0}^{8}(8x-x^{2})dx
d/(dy)(e^{2x+y})	\frac{d}{dy}(e^{2x+y})
taylor f(x)=arctan(x)	taylor\:f(x)=\arctan(x)
derivative of x^2*e^{-4x}	\frac{d}{dx}(x^{2}\cdot\:e^{-4x})
derivative of (x-3sqrt(x))	\frac{d}{dx}((x-3)\sqrt{x})
integral of (ln(z))/(z^2)	\int\:\frac{\ln(z)}{z^{2}}dz
integral from-1 to 3 of (4x^2-7)/(2x+3)	\int\:_{-1}^{3}\frac{4x^{2}-7}{2x+3}dx
derivative of In	\frac{d}{dx}(In)
(dy)/(dx)=12x^3y	\frac{dy}{dx}=12x^{3}y
integral of (e^x+1)(e^x+x)	\int\:(e^{x}+1)(e^{x}+x)dx
derivative of x^4(2x-5)^6	derivative\:x^{4}(2x-5)^{6}
y^{''}+40y^'+625y=0	y^{\prime\:\prime\:}+40y^{\prime\:}+625y=0
derivative of sqrt((s^2+1)/(s^2+4))	derivative\:\sqrt{\frac{s^{2}+1}{s^{2}+4}}
integral from 0 to 1 of (17)/(x^5)	\int\:_{0}^{1}\frac{17}{x^{5}}dx
integral of xsqrt(x^2+2x+2)	\int\:x\sqrt{x^{2}+2x+2}dx
integral of xsin(-2x)	\int\:x\sin(-2x)dx
9y^{''}+24y^'+16y=0	9y^{\prime\:\prime\:}+24y^{\prime\:}+16y=0
(1/(1+x^2))^'	(\frac{1}{1+x^{2}})^{\prime\:}
integral from-1 to 5 of 3x^2+6x	\int\:_{-1}^{5}3x^{2}+6xdx
tangent of y=4x^3-4x,(-1,0)	tangent\:y=4x^{3}-4x,(-1,0)
limit as x approaches-2 of-3	\lim\:_{x\to\:-2}(-3)
integral from 0 to 1 of (1/(x^2))	\int\:_{0}^{1}(\frac{1}{x^{2}})dx
integral of cot^3(x/2)csc^2(x/2)	\int\:\cot^{3}(\frac{x}{2})\csc^{2}(\frac{x}{2})dx
derivative of ((x^2-2x^3)/(5x))	\frac{d}{dx}(\frac{(x^{2}-2x)^{3}}{5x})
integral of 8x^3e^{4x}	\int\:8x^{3}e^{4x}dx
tangent of f(x)=-8x^2-7x,\at x=-4	tangent\:f(x)=-8x^{2}-7x,\at\:x=-4
integral of (x^2-3x+12)/((x^2-4x+11)^2)	\int\:\frac{x^{2}-3x+12}{(x^{2}-4x+11)^{2}}dx
derivative of 1/(x^3-2/(x^2))	\frac{d}{dx}(\frac{1}{x^{3}}-\frac{2}{x^{2}})
derivative of (x^4+7x^2-3)^4	derivative\:(x^{4}+7x^{2}-3)^{4}
tangent of f(x)= 5/(x^2),\at x=1	tangent\:f(x)=\frac{5}{x^{2}},\at\:x=1
integral of (x-1)/(x^2+3x+2)	\int\:\frac{x-1}{x^{2}+3x+2}dx
(dy)/(dx)=(3y)^{1/2}e^{x+10}	\frac{dy}{dx}=(3y)^{\frac{1}{2}}e^{x+10}
integral from-1 to 1 of (x^3-9x)	\int\:_{-1}^{1}(x^{3}-9x)dx
limit as x approaches 0 of 1/x sin(x/3)	\lim\:_{x\to\:0}(\frac{1}{x}\sin(\frac{x}{3}))
(dy)/(dx)+7y=5	\frac{dy}{dx}+7y=5
derivative of-2x^2(x+4)	derivative\:-2x^{2}(x+4)
(\partial)/(\partial x)(4(xy)^2)	\frac{\partial\:}{\partial\:x}(4(xy)^{2})
derivative of (1/(x^2-9/(x^4))(x+7x^3))	\frac{d}{dx}((\frac{1}{x^{2}}-\frac{9}{x^{4}})(x+7x^{3}))
integral from-1 to 1 of x^2-2x+3	\int\:_{-1}^{1}x^{2}-2x+3dx
y=(2y^4+2x)(dy)/(dx)	y=(2y^{4}+2x)\frac{dy}{dx}
integral from 0 to pi/4 of 1/(cos(x))	\int\:_{0}^{\frac{π}{4}}\frac{1}{\cos(x)}dx
(\partial)/(\partial x)(cos(x^3))	\frac{\partial\:}{\partial\:x}(\cos(x^{3}))
(\partial)/(\partial x)(xe^y-1)	\frac{\partial\:}{\partial\:x}(xe^{y}-1)
slope of x^2+y^2=27	slope\:x^{2}+y^{2}=27
integral from 1 to x of (e^{-3t})/t	\int\:_{1}^{x}\frac{e^{-3t}}{t}dt
area 3x^2,(5,75)	area\:3x^{2},(5,75)
integral of (2-3sin(2x))/(cos(2x))	\int\:\frac{2-3\sin(2x)}{\cos(2x)}dx
integral of 4/(x-5)	\int\:\frac{4}{x-5}dx
(\partial)/(\partial x)(((2x-y))/(2x+y))	\frac{\partial\:}{\partial\:x}(\frac{(2x-y)}{2x+y})
(dy)/(dx)+y/x =8x^7y^2	\frac{dy}{dx}+\frac{y}{x}=8x^{7}y^{2}
(\partial)/(\partial x)(4y-4x^3)	\frac{\partial\:}{\partial\:x}(4y-4x^{3})
slope of (1.5)(-1.7)	slope\:(1.5)(-1.7)
integral of 5x^2-6x	\int\:5x^{2}-6xdx
(dx)/(dt)= 6/(t+4)	\frac{dx}{dt}=\frac{6}{t+4}
integral from-1 to 2 of (x+2)-x^2	\int\:_{-1}^{2}(x+2)-x^{2}dx
limit as x approaches 30 of ((sin(x)))/x	\lim\:_{x\to\:30}(\frac{(\sin(x))}{x})
integral from 0 to 1 of 1/(x^4)	\int\:_{0}^{1}\frac{1}{x^{4}}dx
derivative of (2x^2+8x+2/(sqrt(x)))	\frac{d}{dx}(\frac{2x^{2}+8x+2}{\sqrt{x}})
(dy)/(dx)=2-sqrt(2x-y+3)	\frac{dy}{dx}=2-\sqrt{2x-y+3}
(\partial)/(\partial x)(x^3*y^2)	\frac{\partial\:}{\partial\:x}(x^{3}\cdot\:y^{2})
integral from 1 to 0 of (-9sqrt(x))	\int\:_{1}^{0}(-9\sqrt{x})dx
(\partial)/(\partial t)(ln(x+2ct))	\frac{\partial\:}{\partial\:t}(\ln(x+2ct))
integral from-1 to 2 of \|2x-3\|	\int\:_{-1}^{2}\left\|2x-3\right\|dx
y^{''}+36y=0	y^{\prime\:\prime\:}+36y=0
integral of (cos(x)sin^2(x))	\int\:(\cos(x)\sin^{2}(x))dx
derivative of (2x^2-1/(x^2-3))	\frac{d}{dx}(\frac{2x^{2}-1}{x^{2}-3})
integral of 20x^3+12x^2+4	\int\:20x^{3}+12x^{2}+4dx
(\partial)/(\partial x)(y^2x+y)	\frac{\partial\:}{\partial\:x}(y^{2}x+y)
(dy)/(dx)+y^3x+5y=0	\frac{dy}{dx}+y^{3}x+5y=0
6x((dy)/(dx))=2xe^x-6y+6x^2	6x(\frac{dy}{dx})=2xe^{x}-6y+6x^{2}
integral of (sin(6e^{-5x}))/(e^{5x)}	\int\:\frac{\sin(6e^{-5x})}{e^{5x}}dx
sum from n=1 to infinity of n^4(1+n^5)^2	\sum\:_{n=1}^{\infty\:}n^{4}(1+n^{5})^{2}
derivative of f(x)= 3/(x+3)	derivative\:f(x)=\frac{3}{x+3}
integral from 0 to 3 of-x^2+9	\int\:_{0}^{3}-x^{2}+9dx
y^'=((y^2-1))/(2x),y(1)=-2	y^{\prime\:}=\frac{(y^{2}-1)}{2x},y(1)=-2

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