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Popular Calculus Problems

limit as x approaches 3 of 5(x-3)ln(x-3)	\lim\:_{x\to\:3}(5(x-3)\ln(x-3))
tangent of f(x)= 1/x+3,\at x=-1	tangent\:f(x)=\frac{1}{x}+3,\at\:x=-1
limit as x approaches 5 of-9/(x+5)	\lim\:_{x\to\:5}(-\frac{9}{x+5})
integral from 1 to 3 of 1/(sqrt(3-x))	\int\:_{1}^{3}\frac{1}{\sqrt{3-x}}dx
derivative of (sin(6x))^4	derivative\:(\sin(6x))^{4}
integral from 1 to e of x^3ln(x)	\int\:_{1}^{e}x^{3}\ln(x)dx
derivative of x/(20)	\frac{d}{dx}(\frac{x}{20})
tangent of y=7e^x+x,(0,7)	tangent\:y=7e^{x}+x,(0,7)
inverse oflaplace 4	inverselaplace\:4
integral from 0 to 6 of x^2-6x	\int\:_{0}^{6}x^{2}-6xdx
area x^2,x+5	area\:x^{2},x+5
y^{''}-6y^'+8y=2cos(3t),y(0)=2,y^'(0)=-4	y^{\prime\:\prime\:}-6y^{\prime\:}+8y=2\cos(3t),y(0)=2,y^{\prime\:}(0)=-4
e^yy^'=e^y+4x	e^{y}y^{\prime\:}=e^{y}+4x
derivative of sec^2(2x)	derivative\:\sec^{2}(2x)
ydx+(x^2+4x)dy=0	ydx+(x^{2}+4x)dy=0
(dy)/(dx)=(e^x+7)^2	\frac{dy}{dx}=(e^{x}+7)^{2}
derivative of y=x^2cos(4/x)	derivative\:y=x^{2}\cos(\frac{4}{x})
normal of f(x)=x^4+2e^x,(0,2)	normal\:f(x)=x^{4}+2e^{x},(0,2)
derivative of (sin(x))^2	derivative\:(\sin(x))^{2}
limit as x approaches 0+of-x+5	\lim\:_{x\to\:0+}(-x+5)
taylor e^{-3x}	taylor\:e^{-3x}
limit as x approaches 9-of (x^9)/(x-9)	\lim\:_{x\to\:9-}(\frac{x^{9}}{x-9})
limit as x approaches 0+of xln(x^6)	\lim\:_{x\to\:0+}(x\ln(x^{6}))
tangent of (6x)/((x+1))	tangent\:\frac{6x}{(x+1)}
integral of (7x^2+x+54)/(x^3+9x)	\int\:\frac{7x^{2}+x+54}{x^{3}+9x}dx
derivative of y=sqrt(x+2)	derivative\:y=\sqrt{x+2}
derivative of 5/(25x^2+1)	\frac{d}{dx}(\frac{5}{25x^{2}+1})
integral of (2t^5)/5-(2t^2)/5-(2t)/5	\int\:\frac{2t^{5}}{5}-\frac{2t^{2}}{5}-\frac{2t}{5}dt
derivative of ln(3^{3x})	\frac{d}{dx}(\ln(3^{3x}))
integral from 0 to 1/2 of 5cos(-1(x))	\int\:_{0}^{\frac{1}{2}}5\cos(-1(x))dx
(\partial)/(\partial x)(ysqrt(x))	\frac{\partial\:}{\partial\:x}(y\sqrt{x})
(\partial)/(\partial x)(e^{-pi/2})	\frac{\partial\:}{\partial\:x}(e^{-\frac{π}{2}})
integral of 20te^t	\int\:20te^{t}dt
tangent of f(x)=4x^2+7,(-3,43)	tangent\:f(x)=4x^{2}+7,(-3,43)
slope ofintercept (-4,-6),(4,-2)	slopeintercept\:(-4,-6),(4,-2)
tangent of f(x)=(-4x)/(x^2+1),(1,-2)	tangent\:f(x)=\frac{-4x}{x^{2}+1},(1,-2)
integral of x/(e^{-3x)}	\int\:\frac{x}{e^{-3x}}dx
integral of tan^2(w)	\int\:\tan^{2}(w)dw
(\partial)/(\partial x)(-ae^{kz}wsin(kx-wt))	\frac{\partial\:}{\partial\:x}(-ae^{kz}w\sin(kx-wt))
y^{''}-5y^'=25t,y(0)=5,y^'(0)=0	y^{\prime\:\prime\:}-5y^{\prime\:}=25t,y(0)=5,y^{\prime\:}(0)=0
integral from 0 to 2 of xsqrt(4-x^2)	\int\:_{0}^{2}x\sqrt{4-x^{2}}dx
integral of (arctan(x))/((1+x^2)^{3/2)}	\int\:\frac{\arctan(x)}{(1+x^{2})^{\frac{3}{2}}}dx
integral of 12x^2(x^3+4)^3	\int\:12x^{2}(x^{3}+4)^{3}dx
derivative of xsqrt(2)	\frac{d}{dx}(x\sqrt{2})
derivative of x^{2/3}-1	\frac{d}{dx}(x^{\frac{2}{3}}-1)
area x,x^1,0,1	area\:x,x^{1},0,1
limit as n approaches infinity of n/4	\lim\:_{n\to\:\infty\:}(\frac{n}{4})
limit as x approaches 0+of x^2ln(3x)	\lim\:_{x\to\:0+}(x^{2}\ln(3x))
integral of 10sqrt(tan(x))sec^4(x)	\int\:10\sqrt{\tan(x)}\sec^{4}(x)dx
(\partial)/(\partial y)(e^{xz})	\frac{\partial\:}{\partial\:y}(e^{xz})
integral of sec^2(5x)	\int\:\sec^{2}(5x)dx
derivative of y=e^{10-7x}	derivative\:y=e^{10-7x}
maclaurin e^{3x}	maclaurin\:e^{3x}
(\partial)/(\partial x)(2xe^{xy^3})	\frac{\partial\:}{\partial\:x}(2xe^{xy^{3}})
derivative of sqrt(36-y^2)	derivative\:\sqrt{36-y^{2}}
y^{''}-5y^'+6y=cos(2x)+1	y^{\prime\:\prime\:}-5y^{\prime\:}+6y=\cos(2x)+1
limit as x approaches+(-1)-of 2	\lim\:_{x\to\:+(-1)-}(2)
derivative of-(2sec^2(x)/((1+tan(x))^3))	\frac{d}{dx}(-\frac{2\sec^{2}(x)}{(1+\tan(x))^{3}})
tangent of f(x)= 7/(sqrt(x)),\at x=1	tangent\:f(x)=\frac{7}{\sqrt{x}},\at\:x=1
(\partial)/(\partial u)(u+2v)	\frac{\partial\:}{\partial\:u}(u+2v)
derivative of x-2pi	\frac{d}{dx}(x-2π)
derivative of y=x^2+2x-2	derivative\:y=x^{2}+2x-2
y^'=e^{9y-x}	y^{\prime\:}=e^{9y-x}
tangent of f(x)=x^3,\at x=-5	tangent\:f(x)=x^{3},\at\:x=-5
limit as x approaches 0 of 1-cos(3x)	\lim\:_{x\to\:0}(1-\cos(3x))
limit as x approaches infinity of log_{2}(log_{2}(x)-1)	\lim\:_{x\to\:\infty\:}(\log_{2}(\log_{2}(x)-1))
integral from 0 to pi/2 of sin^5(x)	\int\:_{0}^{\frac{π}{2}}\sin^{5}(x)dx
integral from 0 to 2 of 8000te^{-0.6t}	\int\:_{0}^{2}8000te^{-0.6t}dt
integral of (6x^2+3x+10)/(x^3+2x^2+5x)	\int\:\frac{6x^{2}+3x+10}{x^{3}+2x^{2}+5x}dx
tangent of sqrt(x^2+40)	tangent\:\sqrt{x^{2}+40}
derivative of (x^5-2x/(-5))	\frac{d}{dx}(\frac{x^{5}-2x}{-5})
derivative of 7u^e	derivative\:7u^{e}
maclaurin e^{-x^2}	maclaurin\:e^{-x^{2}}
integral of (2x)/((x^2+1)^2)	\int\:\frac{2x}{(x^{2}+1)^{2}}dx
integral from pi/6 to pi/4 of cos(x)	\int\:_{\frac{π}{6}}^{\frac{π}{4}}\cos(x)dx
taylor s(t)=5^t	taylor\:s(t)=5^{t}
derivative of-3tan(x)	\frac{d}{dx}(-3\tan(x))
integral from 7 to 8 of (7/(x^2)-1)	\int\:_{7}^{8}(\frac{7}{x^{2}}-1)dx
integral of ((x^2+1)/(x^2))	\int\:(\frac{x^{2}+1}{x^{2}})dx
derivative of ((x-4)/x)	\frac{d}{dx}(\frac{(x-4)}{x})
(\partial)/(\partial x)(6xsin(8x^2y))	\frac{\partial\:}{\partial\:x}(6x\sin(8x^{2}y))
derivative of-(2x)/((1+x^2)^2)	derivative\:-\frac{2x}{(1+x^{2})^{2}}
derivative of (x^2+2x^5)	\frac{d}{dx}((x^{2}+2x)^{5})
area y=x^2,y=x,y=2	area\:y=x^{2},y=x,y=2
derivative of (1^2/(2^1))	\frac{d}{dx}(\frac{1^{2}}{2^{1}})
sum from n=0 to infinity of (1/2)^{2n}	\sum\:_{n=0}^{\infty\:}(\frac{1}{2})^{2n}
derivative of y= 1/3 e^{3x}	derivative\:y=\frac{1}{3}e^{3x}
integral from 0 to 1 of (2x+1)^4	\int\:_{0}^{1}(2x+1)^{4}dx
derivative of f(x)=-8sin(x)	derivative\:f(x)=-8\sin(x)
integral of (z^2)	\int\:(z^{2})dz
(\partial)/(\partial x)(1/x+1/(1-x))	\frac{\partial\:}{\partial\:x}(\frac{1}{x}+\frac{1}{1-x})
integral of (-2cos(x))	\int\:(-2\cos(x))dx
integral of sin(t/2)t	\int\:\sin(\frac{t}{2})tdt
area 1-x^2,-1,1	area\:1-x^{2},-1,1
d/(da)(tan(a)*cot(a))	\frac{d}{da}(\tan(a)\cdot\:\cot(a))
(d^2y)/(dx^2)-6(dy)/(dx)+9y=sec(3x)	\frac{d^{2}y}{dx^{2}}-6\frac{dy}{dx}+9y=\sec(3x)
derivative of arcsin(e^{3x})	\frac{d}{dx}(\arcsin(e^{3x}))
integral of 6xcos(3x^2)	\int\:6x\cos(3x^{2})dx
(\partial)/(\partial x)((x+y)^z)	\frac{\partial\:}{\partial\:x}((x+y)^{z})
limit as x approaches pi of x	\lim\:_{x\to\:π}(x)

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