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Problemas populares de Cálculo

área f(x)=x^3-x^2-x,g(x)=x	area\:f(x)=x^{3}-x^{2}-x,g(x)=x
(2xy^3-3x^2y^2)dx+(xy^3+2x^2y^2)dy=0	(2xy^{3}-3x^{2}y^{2})dx+(xy^{3}+2x^{2}y^{2})dy=0
(dy)/(dt)=0.04y(400-y)	\frac{dy}{dt}=0.04y(400-y)
integral de sqrt(\sqrt{x)-1}	\int\:\sqrt{\sqrt{x}-1}dx
integral de 1/(((x-1)(x^2+1)))	\int\:\frac{1}{((x-1)(x^{2}+1))}dx
y^{''}+225y=sec(15x)	y^{\prime\:\prime\:}+225y=\sec(15x)
inversalaplace (3se^{-2s})/(5s^2+45)	inverselaplace\:\frac{3se^{-2s}}{5s^{2}+45}
integral de 4t^4e^{2t^5}	\int\:4t^{4}e^{2t^{5}}dt
y^{''}+4y=cos(2x)	y^{\prime\:\prime\:}+4y=\cos(2x)
integral de x^2arctan(3x)	\int\:x^{2}\arctan(3x)dx
(\partial)/(\partial x)(4x+5)	\frac{\partial\:}{\partial\:x}(4x+5)
derivative f(x)=x^2-3	derivative\:f(x)=x^{2}-3
x^2y^'=y-xy	x^{2}y^{\prime\:}=y-xy
derivada de 2(sin(x^2+2x^2cos(x^2)))	\frac{d}{dx}(2(\sin(x^{2})+2x^{2}\cos(x^{2})))
integral de (6x)/(\sqrt[5]{(x^2+7)^2)}	\int\:\frac{6x}{\sqrt[5]{(x^{2}+7)^{2}}}dx
derivada de (x^{10}-1^3)	\frac{d}{dx}((x^{10}-1)^{3})
derivative 2000+2x-0.0001x^2	derivative\:2000+2x-0.0001x^{2}
límite cuando h tiende a 0 de (sin(pi+h))/h	\lim\:_{h\to\:0}(\frac{\sin(π+h)}{h})
(\partial)/(\partial x)(y^2)	\frac{\partial\:}{\partial\:x}(y^{2})
integral de xos(8x^2+pi)	\int\:xos(8x^{2}+π)dx
derivada de (x^2+4x+6^5)	\frac{d}{dx}((x^{2}+4x+6)^{5})
integral de 24	\int\:24
derivative y= 1/4 (6t^2+8)	derivative\:y=\frac{1}{4}(6t^{2}+8)
integral de 1/6 (e^{6x})	\int\:\frac{1}{6}(e^{6x})dx
derivative y=cos(e^x)	derivative\:y=\cos(e^{x})
serie de n=0 a infinity de (n^5)/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{n^{5}}{2^{n}}
tangent f(x)= 8/(x^2+4),(2,1)	tangent\:f(x)=\frac{8}{x^{2}+4},(2,1)
límite cuando x tiende a infinity de 2	\lim\:_{x\to\:\infty\:}(2)
integral de 0 a infinity de 8xe^{2x}	\int\:_{0}^{\infty\:}8xe^{2x}dx
(\partial)/(\partial x)(7x^8y^4+9x^7y^6)	\frac{\partial\:}{\partial\:x}(7x^{8}y^{4}+9x^{7}y^{6})
integral de 2e^{3y}	\int\:2e^{3y}dy
(\partial)/(\partial z)(x^2+8z)	\frac{\partial\:}{\partial\:z}(x^{2}+8z)
límite cuando x tiende a 2 de 6/((x-2)^2)	\lim\:_{x\to\:2}(\frac{6}{(x-2)^{2}})
(\partial)/(\partial y)((x-z)/(y+z))	\frac{\partial\:}{\partial\:y}(\frac{x-z}{y+z})
derivada de (2x/(x+5))	\frac{d}{dx}(\frac{2x}{x+5})
laplacetransformación 100x	laplacetransform\:100x
integral de ((4x+3))/(x^2+1)	\int\:\frac{(4x+3)}{x^{2}+1}dx
límite cuando x tiende a infinity de 5+4/x	\lim\:_{x\to\:\infty\:}(5+\frac{4}{x})
derivative y=(5t-1)(2t-3)^{-1}	derivative\:y=(5t-1)(2t-3)^{-1}
serie de n=1 a infinity de 2/(n(n+1))	\sum\:_{n=1}^{\infty\:}\frac{2}{n(n+1)}
derivada de tan(5/x)	\frac{d}{dx}(\tan(\frac{5}{x}))
área y=7x,y=44-x^2	area\:y=7x,y=44-x^{2}
integral de (18)/(x^2-1)	\int\:\frac{18}{x^{2}-1}dx
serie de n=2 a infinity de 1/(ln(n))	\sum\:_{n=2}^{\infty\:}\frac{1}{\ln(n)}
derivative csc^2(x)	derivative\:\csc^{2}(x)
tangent f(x)=3x^2+5x-4,\at x=-0.6667	tangent\:f(x)=3x^{2}+5x-4,\at\:x=-0.6667
y=u+2/u ,u=(2x+1)^3,x=0	y=u+\frac{2}{u},u=(2x+1)^{3},x=0
y^{''}+y=(t^2+t)*sin(t)	y^{\prime\:\prime\:}+y=(t^{2}+t)\cdot\:\sin(t)
tangent f(x)=0.5x^2+2x-3,\at x=-3	tangent\:f(x)=0.5x^{2}+2x-3,\at\:x=-3
integral de 1/(z^3sqrt(z^2-4))	\int\:\frac{1}{z^{3}\sqrt{z^{2}-4}}dz
y^'+3y=2e^{-3t},y(0)=2	y^{\prime\:}+3y=2e^{-3t},y(0)=2
integral de 3x(x-4)	\int\:3x(x-4)dx
derivada de x^2{z}(x)	\frac{d}{dx}(x^{2}{z}(x))
límite cuando x tiende a e de x^2*e^{x^2}	\lim\:_{x\to\:e}(x^{2}\cdot\:e^{x^{2}})
derivative f(x)=2e^x*(x^2+3x-9)^2	derivative\:f(x)=2e^{x}\cdot\:(x^{2}+3x-9)^{2}
d/(dθ)((cos(θ))/(sin(θ)))	\frac{d}{dθ}(\frac{\cos(θ)}{\sin(θ)})
límite cuando x tiende a+0 de sqrt(x-3)	\lim\:_{x\to\:+0}(\sqrt{x-3})
derivative 2^{4x}	derivative\:2^{4x}
integral de 2xsqrt(4x^2+1)	\int\:2x\sqrt{4x^{2}+1}dx
serie de n=0 a infinity de 2/(n^2+4n+3)	\sum\:_{n=0}^{\infty\:}\frac{2}{n^{2}+4n+3}
integral de x-x^2	\int\:x-x^{2}dx
derivada de (-4x^6+4x^5-3x^3/(3x^2))	\frac{d}{dx}(\frac{-4x^{6}+4x^{5}-3x^{3}}{3x^{2}})
integral de e^{2sin^2(x)}sin(2x)	\int\:e^{2\sin^{2}(x)}\sin(2x)dx
derivative (50)/x	derivative\:\frac{50}{x}
integral de (20)/(1-cos(4x))	\int\:\frac{20}{1-\cos(4x)}dx
límite cuando x tiende a 4 de (x+5)/(x-4)	\lim\:_{x\to\:4}(\frac{x+5}{x-4})
límite cuando x tiende a 9/2 de sqrt(2x-7)	\lim\:_{x\to\:\frac{9}{2}}(\sqrt{2x-7})
(\partial)/(\partial y)(y^2sin(2x))	\frac{\partial\:}{\partial\:y}(y^{2}\sin(2x))
derivative 1-2^x	derivative\:1-2^{x}
derivative y=x^2(2x+3)^5	derivative\:y=x^{2}(2x+3)^{5}
integral de (e^{2x})/(25+e^{4x)}	\int\:\frac{e^{2x}}{25+e^{4x}}dx
derivative y=x^2sqrt(4x-7)	derivative\:y=x^{2}\sqrt{4x-7}
tangent f(x)=6sec(x),\at x= pi/6	tangent\:f(x)=6\sec(x),\at\:x=\frac{π}{6}
serie de n=1 a infinity de ne^{4n}	\sum\:_{n=1}^{\infty\:}ne^{4n}
límite cuando x tiende a-3+de f(x)	\lim\:_{x\to\:-3+}(f(x))
tangent f(x)=3x^2-x+7,\at x=2	tangent\:f(x)=3x^{2}-x+7,\at\:x=2
derivada de tan(5x^4)	\frac{d}{dx}(\tan(5x^{4}))
integral de (sin(θ))/(cos^3(θ))	\int\:\frac{\sin(θ)}{\cos^{3}(θ)}dθ
derivada de (3x^2-2^3)	\frac{d}{dx}((3x^{2}-2)^{3})
(dy)/(dx)=6x(x-3)	\frac{dy}{dx}=6x(x-3)
integral de (x+2)/((x^2+4x)^2)	\int\:\frac{x+2}{(x^{2}+4x)^{2}}dx
derivative sqrt(4x-8)	derivative\:\sqrt{4x-8}
tangent sqrt(9-4x),\at x=-1	tangent\:\sqrt{9-4x},\at\:x=-1
integral de 1 a 4 de-4e^{sqrt(x)}	\int\:_{1}^{4}-4e^{\sqrt{x}}dx
derivada de (x-8/(7x^2e^x))	\frac{d}{dx}(\frac{x-8}{7x^{2}e^{x}})
derivative f(x)=(x-2)(x-1)(x+1)(x+2)	derivative\:f(x)=(x-2)(x-1)(x+1)(x+2)
derivada de x^4+1/(x^4)	\frac{d}{dx}(x^{4}+\frac{1}{x^{4}})
derivative (sqrt(s)-4)/(sqrt(s)+2)	derivative\:\frac{\sqrt{s}-4}{\sqrt{s}+2}
derivada de arccos(1/2 x)	\frac{d}{dx}(\arccos(\frac{1}{2}x))
implicit e^{xy}+y^3=2arcsin(x)+ln(y)	implicit\:e^{xy}+y^{3}=2\arcsin(x)+\ln(y)
integral de (ln(x))^5 1/x	\int\:(\ln(x))^{5}\frac{1}{x}dx
(dy)/(dx)+xy=x	\frac{dy}{dx}+xy=x
derivative f(x)= 1/(4x^2+3x)	derivative\:f(x)=\frac{1}{4x^{2}+3x}
integral de (2x+1)e^{-x}	\int\:(2x+1)e^{-x}dx
límite cuando x tiende a 3 de x(x-3)	\lim\:_{x\to\:3}(x(x-3))
y^{'''}-2y^'-4y=0	y^{\prime\:\prime\:\prime\:}-2y^{\prime\:}-4y=0
laplacetransformación t+1^2	laplacetransform\:t+1^{2}
integral de 0 a 11 de 2piy((y^2)/2)	\int\:_{0}^{11}2πy(\frac{y^{2}}{2})dy
inversalaplace s/((s+4))	inverselaplace\:\frac{s}{(s+4)}
(\partial)/(\partial x)(x^3y^5-2x^2y+x)	\frac{\partial\:}{\partial\:x}(x^{3}y^{5}-2x^{2}y+x)

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