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Popular Calculus Problems

limit as x approaches 2 of (x^3)/3-7x^2	\lim\:_{x\to\:2}(\frac{x^{3}}{3}-7x^{2})
f(y)=y^4	f(y)=y^{4}
(d^2)/(dx^2)(sec(pi/4))	\frac{d^{2}}{dx^{2}}(\sec(\frac{π}{4}))
integral of sec(x)tan(x)-9e^x	\int\:\sec(x)\tan(x)-9e^{x}dx
integral from 1 to 3 of x^2e^x	\int\:_{1}^{3}x^{2}e^{x}dx
tangent of f(x)=x^2,\at x=-1/4	tangent\:f(x)=x^{2},\at\:x=-\frac{1}{4}
y^'-2xy-8=0	y^{\prime\:}-2xy-8=0
laplacetransform e^{3(t+1)}	laplacetransform\:e^{3(t+1)}
derivative of y=x(3x-2)^4	derivative\:y=x(3x-2)^{4}
integral of (e^{2x})/(\sqrt[4]{e^x+1)}	\int\:\frac{e^{2x}}{\sqrt[4]{e^{x}+1}}dx
integral of x^2(sqrt(4+x^3))	\int\:x^{2}(\sqrt{4+x^{3}})dx
xy^'+y=5xy^2	xy^{\prime\:}+y=5xy^{2}
integral of 1/((6-x^2)^{3/2)}	\int\:\frac{1}{(6-x^{2})^{\frac{3}{2}}}dx
derivative of 2x-(2000/(x^2))	\frac{d}{dx}(2x-\frac{2000}{x^{2}})
integral of 6arctan(4y)	\int\:6\arctan(4y)dy
(\partial)/(\partial x)(2y^{4x})	\frac{\partial\:}{\partial\:x}(2y^{4x})
tangent of f(x)=sin(x)+1,\at x=-pi/2	tangent\:f(x)=\sin(x)+1,\at\:x=-\frac{π}{2}
area f(x)=x^2-4,x=-4,x=3	area\:f(x)=x^{2}-4,x=-4,x=3
integral of 1/(x^2sqrt(a^2-x^2))	\int\:\frac{1}{x^{2}\sqrt{a^{2}-x^{2}}}dx
limit as x approaches-3 of \|x\|-2	\lim\:_{x\to\:-3}(\left\|x\right\|-2)
laplacetransform e^t	laplacetransform\:e^{t}
tangent of f(x)=(5x)/(x+3),2,\at x=2	tangent\:f(x)=\frac{5x}{x+3},2,\at\:x=2
derivative of 2^{arctan(x})	\frac{d}{dx}(2^{\arctan(x)})
integral of (x+1)^2e^{-2x}	\int\:(x+1)^{2}e^{-2x}dx
(\partial)/(\partial x)(cos^6(x^2y^9))	\frac{\partial\:}{\partial\:x}(\cos^{6}(x^{2}y^{9}))
derivative of 3x^2+xy+2x+y	\frac{d}{dx}(3x^{2}+xy+2x+y)
taylor cos(x), pi/2	taylor\:\cos(x),\frac{π}{2}
(\partial)/(\partial y)(x^4y-3x^5y^2)	\frac{\partial\:}{\partial\:y}(x^{4}y-3x^{5}y^{2})
limit as x approaches 1 of x+1	\lim\:_{x\to\:1}(x+1)
integral of xln(3x)	\int\:x\ln(3x)dx
derivative of x(x-15^2)	\frac{d}{dx}(x(x-15)^{2})
integral of e^{sin(x)}cos(x)	\int\:e^{\sin(x)}\cos(x)dx
integral of 224sin(7x)\sqrt[3]{cos(7x)}	\int\:224\sin(7x)\sqrt[3]{\cos(7x)}dx
integral of 3sin^3(x)cos^3(x)	\int\:3\sin^{3}(x)\cos^{3}(x)dx
integral from-1 to 2 of (x-8\|x\|)	\int\:_{-1}^{2}(x-8\left\|x\right\|)dx
derivative of x^{4/5}*(x-4^2)	\frac{d}{dx}(x^{\frac{4}{5}}\cdot\:(x-4)^{2})
integral of 1/(w^2)	\int\:\frac{1}{w^{2}}dw
integral of x^4*2^{x^5+7}	\int\:x^{4}\cdot\:2^{x^{5}+7}dx
integral of (19)/((1-x^2)^{3/2)}	\int\:\frac{19}{(1-x^{2})^{\frac{3}{2}}}dx
integral of cos((nx)/2)	\int\:\cos(\frac{nx}{2})dx
integral of 1/((1+e^{-y))}	\int\:\frac{1}{(1+e^{-y})}dy
derivative of \sqrt[7]{x}+2sqrt(x^7)	\frac{d}{dx}(\sqrt[7]{x}+2\sqrt{x^{7}})
integral of x^7e^{-x^4}	\int\:x^{7}e^{-x^{4}}dx
integral of log_{b}(x)	\int\:\log_{b}(x)dx
area y+x=4,36-9x=y^2	area\:y+x=4,36-9x=y^{2}
d/(dt)(A*(cos(ωt+φ)))	\frac{d}{dt}(A\cdot\:(\cos(ωt+φ)))
y^'(x)=(x^2)/(1-y^2),y(4)=2	y^{\prime\:}(x)=\frac{x^{2}}{1-y^{2}},y(4)=2
integral of 2sqrt(x)e^{sqrt(x)}	\int\:2\sqrt{x}e^{\sqrt{x}}dx
derivative of y=(x^2+1)^3	derivative\:y=(x^{2}+1)^{3}
integral of (1+cos(2x))/(sin^2(2x))	\int\:\frac{1+\cos(2x)}{\sin^{2}(2x)}dx
(\partial)/(\partial y)(x+3y)	\frac{\partial\:}{\partial\:y}(x+3y)
slope of (-1.3)(3.5)	slope\:(-1.3)(3.5)
derivative of g(x)=ln^3(x)	derivative\:g(x)=\ln^{3}(x)
tangent of y=(5x)/(2^x),\at x=2	tangent\:y=\frac{5x}{2^{x}},\at\:x=2
(\partial)/(\partial y)(ln(x^2+3y))	\frac{\partial\:}{\partial\:y}(\ln(x^{2}+3y))
derivative of (6x^5-7x/(x^4-8))	\frac{d}{dx}(\frac{6x^{5}-7x}{x^{4}-8})
integral of (6e^{-0.2x})	\int\:(6e^{-0.2x})dx
area 5-x,25-x^2	area\:5-x,25-x^{2}
integral of 1/(x^2)arctan(x)	\int\:\frac{1}{x^{2}}\arctan(x)dx
limit as x approaches 4+of sqrt(x-4)	\lim\:_{x\to\:4+}(\sqrt{x-4})
derivative of f(x)=0.6x^{1.5}	derivative\:f(x)=0.6x^{1.5}
(dy)/(dx)=9.8-0.196y	\frac{dy}{dx}=9.8-0.196y
y^{''}-4y^'-21y=0	y^{\prime\:\prime\:}-4y^{\prime\:}-21y=0
integral of sec^4(u)tan(u)	\int\:\sec^{4}(u)\tan(u)du
2x(y+1)dx-ydy=0	2x(y+1)dx-ydy=0
limit as x approaches 0 of arccos(x)	\lim\:_{x\to\:0}(\arccos(x))
limit as x approaches infinity of 6x	\lim\:_{x\to\:\infty\:}(6x)
integral of 5sin^3(x)cos^2(x)	\int\:5\sin^{3}(x)\cos^{2}(x)dx
derivative of f(x)=arcsin(6x+1)	derivative\:f(x)=\arcsin(6x+1)
integral of y^2z^3	\int\:y^{2}z^{3}dx
(\partial)/(\partial x)(4ln((3xy)/(7z)))	\frac{\partial\:}{\partial\:x}(4\ln(\frac{3xy}{7z}))
integral of-cos(2y)	\int\:-\cos(2y)dy
derivative of 4sqrt(x)-3/(x^6)	derivative\:4\sqrt{x}-\frac{3}{x^{6}}
integral of 2x^2-4	\int\:2x^{2}-4dx
integral of 4/(sqrt(x+4)+\sqrt{x)}	\int\:\frac{4}{\sqrt{x+4}+\sqrt{x}}dx
limit as x approaches-1 of 4x^3-2m	\lim\:_{x\to\:-1}(4x^{3}-2m)
limit as x approaches 0-of (x^2)/2-1/x	\lim\:_{x\to\:0-}(\frac{x^{2}}{2}-\frac{1}{x})
integral of 1/(sec(x)+1)	\int\:\frac{1}{\sec(x)+1}dx
tangent of y=sqrt(x),(49,7)	tangent\:y=\sqrt{x},(49,7)
integral of (25)/(x^{3/2)}	\int\:\frac{25}{x^{\frac{3}{2}}}dx
integral of x*2^{x^2}	\int\:x\cdot\:2^{x^{2}}dx
f'(x)	f\prime\:(x)
integral of xsec^2(4x)	\int\:x\sec^{2}(4x)dx
tangent of f(x)=(x^2-15)^7,\at x=4	tangent\:f(x)=(x^{2}-15)^{7},\at\:x=4
x(dy)/(dx)+2y=6x^2sqrt(y)	x\frac{dy}{dx}+2y=6x^{2}\sqrt{y}
derivative of acos^3(x)	\frac{d}{dx}(a\cos^{3}(x))
derivative of y=x^2ln(3x)	derivative\:y=x^{2}\ln(3x)
y^'=((1-y)^2)/(x+1),y(0)=5	y^{\prime\:}=\frac{(1-y)^{2}}{x+1},y(0)=5
derivative of ln(ln(sec(x)))	\frac{d}{dx}(\ln(\ln(\sec(x))))
sum from n=1 to infinity of 1-7/(4^n)	\sum\:_{n=1}^{\infty\:}1-\frac{7}{4^{n}}
(\partial)/(\partial x)(8-x^2-y^2)	\frac{\partial\:}{\partial\:x}(8-x^{2}-y^{2})
24y^{''}-2y^'-15y=0	24y^{\prime\:\prime\:}-2y^{\prime\:}-15y=0
d/(dt)(cos^2(e^{cos^2(t)}))	\frac{d}{dt}(\cos^{2}(e^{\cos^{2}(t)}))
limit as x approaches-2 of 5x^2	\lim\:_{x\to\:-2}(5x^{2})
(dy)/(dx)=(cos(16x))/(e^{16y)}	\frac{dy}{dx}=\frac{\cos(16x)}{e^{16y}}
derivative of tan(xsec^2(x))	\frac{d}{dx}(\tan(x)\sec^{2}(x))
integral from 2 to 3 of (31)/(sqrt(3-x))	\int\:_{2}^{3}\frac{31}{\sqrt{3-x}}dx
(tsin(t))^'	(t\sin(t))^{\prime\:}
(\partial)/(\partial x)(e^{xz}y^3-ln(x))	\frac{\partial\:}{\partial\:x}(e^{xz}y^{3}-\ln(x))
derivative of arctan(11x)	\frac{d}{dx}(\arctan(11x))

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