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Popular Calculus Problems

limit as x approaches-2 of (sin(-pix))/(2+x)	\lim\:_{x\to\:-2}(\frac{\sin(-πx)}{2+x})
integral from 2 to 3 of (22)/(sqrt(3-x))	\int\:_{2}^{3}\frac{22}{\sqrt{3-x}}dx
tangent of f(x)=x^3-4x,\at x=0	tangent\:f(x)=x^{3}-4x,\at\:x=0
inverse oflaplace 2/((s+2))	inverselaplace\:\frac{2}{(s+2)}
derivative of ln(((8x-9)^2)/(-x-1))	derivative\:\ln(\frac{(8x-9)^{2}}{-x-1})
derivative of x^{11/2}	derivative\:x^{\frac{11}{2}}
x^'=-x^2	x^{\prime\:}=-x^{2}
derivative of f(2)=3x^2-2x+5	derivative\:f(2)=3x^{2}-2x+5
integral of (x+2)/(x^3)	\int\:\frac{x+2}{x^{3}}dx
(\partial)/(\partial x)(2xe^{x^2})	\frac{\partial\:}{\partial\:x}(2xe^{x^{2}})
integral of (sec^2(pix)-sqrt(x))	\int\:(\sec^{2}(πx)-\sqrt{x})dx
(\partial)/(\partial x)(((yx)/(zw))^{1/2})	\frac{\partial\:}{\partial\:x}((\frac{yx}{zw})^{\frac{1}{2}})
derivative of (4-xe^x/(x+e^x))	\frac{d}{dx}(\frac{4-xe^{x}}{x+e^{x}})
sum from n=1 to infinity of (cos(npi))/(n^2)	\sum\:_{n=1}^{\infty\:}\frac{\cos(nπ)}{n^{2}}
limit as x approaches 2 of (sqrt(x+47-7))/(5x-10)	\lim\:_{x\to\:2}(\frac{\sqrt{x+47-7}}{5x-10})
(\partial)/(\partial x)(y^5sin(6x))	\frac{\partial\:}{\partial\:x}(y^{5}\sin(6x))
integral from 0 to 1 of integral from 0 to s^5 of cos(s^6)	\int\:_{0}^{1}\int\:_{0}^{s^{5}}\cos(s^{6})dtds
y^'=-ty	y^{\prime\:}=-ty
y^'=((x+2y))/x	y^{\prime\:}=\frac{(x+2y)}{x}
derivative of (1+e^{-x}^{-1})	\frac{d}{dx}((1+e^{-x})^{-1})
(dy)/(dx)=y(1-y)	\frac{dy}{dx}=y(1-y)
limit as x approaches 4 of 5x^2-2x+3	\lim\:_{x\to\:4}(5x^{2}-2x+3)
limit as x approaches 7 of ((x^2-2x-35))/(x-7)	\lim\:_{x\to\:7}(\frac{(x^{2}-2x-35)}{x-7})
limit as x approaches 0 of (1^x-9^x)/x	\lim\:_{x\to\:0}(\frac{1^{x}-9^{x}}{x})
(\partial)/(\partial x)(x^2+2y^2-x^2y)	\frac{\partial\:}{\partial\:x}(x^{2}+2y^{2}-x^{2}y)
integral of (10)/(sqrt(1-x^2))	\int\:\frac{10}{\sqrt{1-x^{2}}}dx
xy^{''}-2y^'=0	xy^{\prime\:\prime\:}-2y^{\prime\:}=0
integral of 6/((9t^2+1)^2)	\int\:\frac{6}{(9t^{2}+1)^{2}}dt
derivative of Ax^2e^x	\frac{d}{dx}(Ax^{2}e^{x})
integral from 0 to 3 of 450.268e^{1.12567t}	\int\:_{0}^{3}450.268e^{1.12567t}dt
limit as x approaches infinity of e^x-x	\lim\:_{x\to\:\infty\:}(e^{x}-x)
integral of (x^2+1)/(x^4+1)	\int\:\frac{x^{2}+1}{x^{4}+1}dx
derivative of 2e^xcos(x)	derivative\:2e^{x}\cos(x)
(\partial)/(\partial x)(ln(x^3))	\frac{\partial\:}{\partial\:x}(\ln(x^{3}))
integral of 1/((1-y))	\int\:\frac{1}{(1-y)}dy
integral of (3/x)	\int\:(\frac{3}{x})dx
(\partial)/(\partial z)(5sin^2(z))	\frac{\partial\:}{\partial\:z}(5\sin^{2}(z))
sum from n=1 to infinity of 4+(-1)^n	\sum\:_{n=1}^{\infty\:}4+(-1)^{n}
integral of 5(tan(x))(ln(cos(x)))	\int\:5(\tan(x))(\ln(\cos(x)))dx
integral from 2 to infinity of 1/(3x+2)	\int\:_{2}^{\infty\:}\frac{1}{3x+2}dx
derivative of 5x+1	derivative\:5x+1
integral of e^xsin(6e^x+3)	\int\:e^{x}\sin(6e^{x}+3)dx
slope of sqrt(sin(cos^2(x))),\at x=pi	slope\:\sqrt{\sin(\cos^{2}(x))},\at\:x=π
derivative of (6+x)/(1-6x)	derivative\:\frac{6+x}{1-6x}
inverse oflaplace 6/(s^2)	inverselaplace\:\frac{6}{s^{2}}
(dx)/(dt)=3x^2+2x	\frac{dx}{dt}=3x^{2}+2x
integral of 5/(\sqrt[3]{x)}	\int\:\frac{5}{\sqrt[3]{x}}dx
derivative of (arcsin(x)/(sqrt(1-x^2)))	\frac{d}{dx}(\frac{\arcsin(x)}{\sqrt{1-x^{2}}})
limit as x approaches 8-of (sqrt(64-x^2))/(x-8)	\lim\:_{x\to\:8-}(\frac{\sqrt{64-x^{2}}}{x-8})
derivative of xsqrt(64-x^2)	\frac{d}{dx}(x\sqrt{64-x^{2}})
derivative of \sqrt[3]{(3x/(x+2)})	\frac{d}{dx}(\sqrt[3]{\frac{3x}{x+2}})
derivative of f(t)=(\sqrt[3]{t})/(t-3)	derivative\:f(t)=\frac{\sqrt[3]{t}}{t-3}
integral from 0 to 5 of pi(25-x^2)	\int\:_{0}^{5}π(25-x^{2})dx
limit as x approaches 4 of (x+3)^2	\lim\:_{x\to\:4}((x+3)^{2})
(d^2}{dx^2}(e^{-\frac{x^2)/2})	\frac{d^{2}}{dx^{2}}(e^{-\frac{x^{2}}{2}})
(d^3)/(dx^3)(sin(x))	\frac{d^{3}}{dx^{3}}(\sin(x))
limit as x approaches 0+of tan(4x)	\lim\:_{x\to\:0+}(\tan(4x))
derivative of 4/(x^7)	derivative\:\frac{4}{x^{7}}
derivative of sqrt(18-2x)	derivative\:\sqrt{18-2x}
taylor f(x)=2^x	taylor\:f(x)=2^{x}
limit as x approaches-infinity of 6/((1+e^{-x))}	\lim\:_{x\to\:-\infty\:}(\frac{6}{(1+e^{-x})})
limit as x approaches 7 of (x^3-4x^2-19x-14)/(x^2-8x-7)	\lim\:_{x\to\:7}(\frac{x^{3}-4x^{2}-19x-14}{x^{2}-8x-7})
y^{''}+2y^'+y=x^2-2x+1	y^{\prime\:\prime\:}+2y^{\prime\:}+y=x^{2}-2x+1
derivative of (x^4ln(x)^5)	\frac{d}{dx}((x^{4}\ln(x))^{5})
limit as x approaches 6 of ln(6-x)	\lim\:_{x\to\:6}(\ln(6-x))
limit as x approaches 0 of x-1/x	\lim\:_{x\to\:0}(x-\frac{1}{x})
limit as x approaches 0+of 4sin(x)ln(x)	\lim\:_{x\to\:0+}(4\sin(x)\ln(x))
derivative of 1/(sqrt(1+x^2))	derivative\:\frac{1}{\sqrt{1+x^{2}}}
limit as x approaches 3 of (-4)/(2x-5)	\lim\:_{x\to\:3}(\frac{-4}{2x-5})
derivative of x+6x^{2/3}	\frac{d}{dx}(x+6x^{\frac{2}{3}})
xy^'=xsqrt(y)+2sqrt(y)	xy^{\prime\:}=x\sqrt{y}+2\sqrt{y}
(d^2)/(dx^2)(sqrt(x+2))	\frac{d^{2}}{dx^{2}}(\sqrt{x+2})
integral of (x^2+1)/(sqrt(x))	\int\:\frac{x^{2}+1}{\sqrt{x}}dx
tangent of y=-1/4 x^2,(-2,-1)	tangent\:y=-\frac{1}{4}x^{2},(-2,-1)
tangent of (1+2x)^2	tangent\:(1+2x)^{2}
y^{''}-8y^'+41y=0	y^{\prime\:\prime\:}-8y^{\prime\:}+41y=0
derivative of (x^2-x+1^{-7})	\frac{d}{dx}((x^{2}-x+1)^{-7})
integral of (x-1)/(x(x^2-5x+6))	\int\:\frac{x-1}{x(x^{2}-5x+6)}dx
integral of (3-5x)^2	\int\:(3-5x)^{2}dx
(dy)/(dx)=2ycos(x)	\frac{dy}{dx}=2y\cos(x)
limit as x approaches 4 of-x^2-9x-8	\lim\:_{x\to\:4}(-x^{2}-9x-8)
derivative of (5sqrt(x)/(2x^{-2)})	\frac{d}{dx}(\frac{5\sqrt{x}}{2x^{-2}})
limit as x approaches infinity of 3+x^2	\lim\:_{x\to\:\infty\:}(3+x^{2})
area 2y=3sqrt(x),y=4,2y+3x=6	area\:2y=3\sqrt{x},y=4,2y+3x=6
integral of ((x-1))/(((x-2)(x^2-2x+2)^2))	\int\:\frac{(x-1)}{((x-2)(x^{2}-2x+2)^{2})}dx
limit as x approaches 0+of (3x)^{sin(x)}	\lim\:_{x\to\:0+}((3x)^{\sin(x)})
25y^{''}-40y^'+16y=0,y(0)=2,y^'(0)=-3	25y^{\prime\:\prime\:}-40y^{\prime\:}+16y=0,y(0)=2,y^{\prime\:}(0)=-3
integral of 5sin^3(x)cos^7(x)	\int\:5\sin^{3}(x)\cos^{7}(x)dx
integral from 1 to 2 of ln\|x^2+1\|	\int\:_{1}^{2}\ln\left\|x^{2}+1\right\|dx
derivative of ln(4x-1)	\frac{d}{dx}(\ln(4x-1))
integral from 4 to 5 of 1/(5x-1)	\int\:_{4}^{5}\frac{1}{5x-1}dx
xy^'+3y=(4e^{2x})/(x^2)	xy^{\prime\:}+3y=\frac{4e^{2x}}{x^{2}}
limit as x approaches 1 of (2x)/(x-1)	\lim\:_{x\to\:1}(\frac{2x}{x-1})
derivative of f(x)=9x^5(x^3-2x)	derivative\:f(x)=9x^{5}(x^{3}-2x)
y^{''}-2y^'-63y=0	y^{\prime\:\prime\:}-2y^{\prime\:}-63y=0
sum from n=1 to infinity of 1/(n^{-1)}	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{-1}}
(d^2y)/(d^2x)+(4dy)/(dx)+3y=0	\frac{d^{2}y}{d^{2}x}+\frac{4dy}{dx}+3y=0
limit as x approaches 0 of x/(x^2-4)	\lim\:_{x\to\:0}(\frac{x}{x^{2}-4})
t^3(dy)/(dt)+3t^2y=2cos(t)	t^{3}\frac{dy}{dt}+3t^{2}y=2\cos(t)
integral of x^{15}e^{-x^{16}}	\int\:x^{15}e^{-x^{16}}dx

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