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Popular Calculus Problems

limit as x approaches 1 of 1-x-[x]	\lim\:_{x\to\:1}(1-x-[x])
derivative of (2x-3/(x^2-1))	\frac{d}{dx}(\frac{2x-3}{x^{2}-1})
integral of (6x+y)	\int\:(6x+y)dx
xy'+(1+xcot(x))y=0	xy\prime\:+(1+x\cot(x))y=0
tangent of f(x)=tan(3x),\at x= pi/9	tangent\:f(x)=\tan(3x),\at\:x=\frac{π}{9}
integral of sqrt(2+2cos(4x))	\int\:\sqrt{2+2\cos(4x)}dx
(\partial)/(\partial y)(x/((x^2+y^2)))	\frac{\partial\:}{\partial\:y}(\frac{x}{(x^{2}+y^{2})})
integral of (x^2)	\int\:(x^{2})dx
derivative of (2x^{2x})	\frac{d}{dx}((2x)^{2x})
derivative of 4x^3sec(7x)	\frac{d}{dx}(4x^{3}\sec(7x))
tangent of sqrt(x^2+16),\at x=3	tangent\:\sqrt{x^{2}+16},\at\:x=3
integral of 1/3 x^3sqrt(9-x^2)	\int\:\frac{1}{3}x^{3}\sqrt{9-x^{2}}dx
derivative of f(x)=(12)/((3x-4)^5)	\frac{d}{dx}f(x)=\frac{12}{(3x-4)^{5}}
integral of (-2)/(z^3)	\int\:\frac{-2}{z^{3}}dz
y^{''}+4y^'+5y=15x+e^{-x}	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=15x+e^{-x}
derivative of (sin(x)/(1+sin(x)))	\frac{d}{dx}(\frac{\sin(x)}{1+\sin(x)})
integral from 1 to infinity of (1/(x^3))	\int\:_{1}^{\infty\:}(\frac{1}{x^{3}})dx
laplacetransform 4t^2cos(2t)+5te^{-7t}	laplacetransform\:4t^{2}\cos(2t)+5te^{-7t}
derivative of \sqrt[4]{x^9}+2sqrt(x^5)	\frac{d}{dx}(\sqrt[4]{x^{9}}+2\sqrt{x^{5}})
derivative of f(x)=(c^5-x^5)/(c^5+c^5)	derivative\:f(x)=\frac{c^{5}-x^{5}}{c^{5}+c^{5}}
f^'(t)-f(t)=6t	f^{\prime\:}(t)-f(t)=6t
y^2+x^2y^'=xyy^'	y^{2}+x^{2}y^{\prime\:}=xyy^{\prime\:}
area y=x,y=(x-1)^2	area\:y=x,y=(x-1)^{2}
integral of ((9+sqrt(x)+x))/x	\int\:\frac{(9+\sqrt{x}+x)}{x}dx
integral of sec^2(2x)sin(2x)	\int\:\sec^{2}(2x)\sin(2x)dx
limit as x approaches-infinity of g(x)	\lim\:_{x\to\:-\infty\:}(g(x))
integral of sqrt(6x-7)	\int\:\sqrt{6x-7}dx
16y^{''}+3y=0	16y^{\prime\:\prime\:}+3y=0
integral from 0 to N of e^{-st}sin(2t)	\int\:_{0}^{N}e^{-st}\sin(2t)dt
derivative of 1/(sqrt(1+4t^2))	derivative\:\frac{1}{\sqrt{1+4t^{2}}}
slope of 5/(sqrt(x))	slope\:\frac{5}{\sqrt{x}}
integral from 0 to 1 of 3^{-x}	\int\:_{0}^{1}3^{-x}dx
integral from b to 2b of x^6	\int\:_{b}^{2b}x^{6}dx
derivative of-4x+4	\frac{d}{dx}(-4x+4)
limit as x approaches 0 of 1-e^x	\lim\:_{x\to\:0}(1-e^{x})
derivative of asin(3x)	\frac{d}{dx}(a\sin(3x))
limit as x approaches-1-of x/(x^2-1)	\lim\:_{x\to\:-1-}(\frac{x}{x^{2}-1})
derivative of 1/(8x)	derivative\:\frac{1}{8x}
slope of y=sqrt(x),(25,5)	slope\:y=\sqrt{x},(25,5)
(\partial)/(\partial y)(sqrt(4-x^2-y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{4-x^{2}-y^{2}})
integral of sqrt(1+\sqrt{z)}	\int\:\sqrt{1+\sqrt{z}}dz
integral of (x-2)^4	\int\:(x-2)^{4}dx
derivative of e(1/x)	\frac{d}{dx}(e(\frac{1}{x}))
16xy^'-2y=-(x^2)/(y^{15)}	16xy^{\prime\:}-2y=-\frac{x^{2}}{y^{15}}
maclaurin tan(2x)	maclaurin\:\tan(2x)
integral of cos^2(wt)	\int\:\cos^{2}(wt)dt
integral of (sin(8x))/8	\int\:\frac{\sin(8x)}{8}dx
(dy)/(dx)=ye^{-x^2},y(4)=1	\frac{dy}{dx}=ye^{-x^{2}},y(4)=1
y^2(dy)/(dx)=3x^2y^3-6x^2	y^{2}\frac{dy}{dx}=3x^{2}y^{3}-6x^{2}
integral of sin^5(6x)	\int\:\sin^{5}(6x)dx
laplacetransform sin(6t)	laplacetransform\:\sin(6t)
f(x)=cos(7x)	f(x)=\cos(7x)
expand (x^2)/(5(1-x))	expand\:\frac{x^{2}}{5(1-x)}
derivative of cos(xt)	\frac{d}{dx}(\cos(xt))
limit as x approaches 0.5 of f(x)	\lim\:_{x\to\:0.5}(f(x))
integral from 1 to 5 of 2/(x^3)	\int\:_{1}^{5}\frac{2}{x^{3}}dx
derivative of (2e^x-x^5/(1-3x^5))	\frac{d}{dx}(\frac{2e^{x}-x^{5}}{1-3x^{5}})
integral of (2x-3)/6	\int\:\frac{2x-3}{6}dx
derivative of (x^2/(x^4))	\frac{d}{dx}(\frac{x^{2}}{x^{4}})
derivative of 1/(sqrt(1-x))	\frac{d}{dx}(\frac{1}{\sqrt{1-x}})
integral of coth^2(x)	\int\:\coth^{2}(x)dx
integral of 1/(9-x^2)	\int\:\frac{1}{9-x^{2}}dx
integral of e^{-kNx}	\int\:e^{-kNx}dx
expand 2(x-6)^3	expand\:2(x-6)^{3}
limit as z approaches 0 of z^3cos(1/z)	\lim\:_{z\to\:0}(z^{3}\cos(\frac{1}{z}))
derivative of cos^3(e^{4x})	derivative\:\cos^{3}(e^{4x})
(\partial)/(\partial x)(xy+4/x+2/y)	\frac{\partial\:}{\partial\:x}(xy+\frac{4}{x}+\frac{2}{y})
taylor sqrt(x),16	taylor\:\sqrt{x},16
f(x)=e^{10x}	f(x)=e^{10x}
(\partial)/(\partial y)(x^2y^2e^{2xy})	\frac{\partial\:}{\partial\:y}(x^{2}y^{2}e^{2xy})
(x^{3/2})^'	(x^{\frac{3}{2}})^{\prime\:}
(\partial)/(\partial y)(ln(sqrt(x^2+y^2)))	\frac{\partial\:}{\partial\:y}(\ln(\sqrt{x^{2}+y^{2}}))
maclaurin ln(4+x^2)	maclaurin\:\ln(4+x^{2})
integral from 1 to 2 of 15sqrt(4x^2-3)	\int\:_{1}^{2}15\sqrt{4x^{2}-3}dx
limit as x approaches infinity of 1/8	\lim\:_{x\to\:\infty\:}(\frac{1}{8})
tangent of f(x)= 3/(4x+1),(-1,-1)	tangent\:f(x)=\frac{3}{4x+1},(-1,-1)
derivative of 2x+(200/x)	\frac{d}{dx}(2x+\frac{200}{x})
derivative of f(x)= 32/0	derivative\:f(x)=\frac{32}{0}
(\partial)/(\partial y)(e^{-y}cos(pix))	\frac{\partial\:}{\partial\:y}(e^{-y}\cos(πx))
integral of 4tan^2(x)sec^2(x)	\int\:4\tan^{2}(x)\sec^{2}(x)dx
integral of arcsin(1/x)	\int\:\arcsin(\frac{1}{x})dx
taylor f(x)=8.8sqrt(x)	taylor\:f(x)=8.8\sqrt{x}
derivative of e^{2x}x(acos(x+bsin(x)))	\frac{d}{dx}(e^{2x}x(a\cos(x)+b\sin(x)))
limit as x approaches 8+of 3/(x-8)	\lim\:_{x\to\:8+}(\frac{3}{x-8})
derivative of-(x^2/2)	\frac{d}{dx}(-\frac{x^{2}}{2})
derivative of 2\sqrt[5]{x^3}	derivative\:2\sqrt[5]{x^{3}}
tangent of f(x)=(-8x)/(x^2+1),\at x=0	tangent\:f(x)=\frac{-8x}{x^{2}+1},\at\:x=0
integral of 1/x-3/(x^2+1)	\int\:\frac{1}{x}-\frac{3}{x^{2}+1}dx
integral of (2sin(x))	\int\:(2\sin(x))dx
derivative of (3x^3/2)	\frac{d}{dx}(\frac{3x^{3}}{2})
(ye^{xy}cos(2x)-2e^{xy}sin(2x)+2x)+(xe^{xy}cos(2x)-3)y^'=0	(ye^{xy}\cos(2x)-2e^{xy}\sin(2x)+2x)+(xe^{xy}\cos(2x)-3)y^{\prime\:}=0
limit as x approaches 0 of (1-6x)^{5/x}	\lim\:_{x\to\:0}((1-6x)^{\frac{5}{x}})
(dy)/(dx)-sin(x)y=2sin(x)	\frac{dy}{dx}-\sin(x)y=2\sin(x)
derivative of g(t)=5(cos(pit))^2	derivative\:g(t)=5(\cos(πt))^{2}
(dy)/(dx)=2x-1+2xy-y	\frac{dy}{dx}=2x-1+2xy-y
slope of (-19.7,10.5),(-18.9,3.4)	slope\:(-19.7,10.5),(-18.9,3.4)
derivative of cos(2pix)	\frac{d}{dx}(\cos(2πx))
inverse oflaplace t^6e^{8t}	inverselaplace\:t^{6}e^{8t}
f(x)=3e^{2x}	f(x)=3e^{2x}
integral from 9 to 16 of 1/(9-sqrt(x))	\int\:_{9}^{16}\frac{1}{9-\sqrt{x}}dx

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