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Problemas populares de Cálculo

y^{''}=4y,y^'(0)=1,y(0)=0	y^{\prime\:\prime\:}=4y,y^{\prime\:}(0)=1,y(0)=0
y^{''}-18y^'+81y=t^{-2}e^{9t}	y^{\prime\:\prime\:}-18y^{\prime\:}+81y=t^{-2}e^{9t}
límite cuando x tiende a 1 de sqrt(x^2+3)-2	\lim\:_{x\to\:1}(\sqrt{x^{2}+3}-2)
derivada de (5^x/(cos(x)))	\frac{d}{dx}(\frac{5^{x}}{\cos(x)})
límite cuando x tiende a 5 de 3x-7	\lim\:_{x\to\:5}(3x-7)
área y=x^4-4x^2,y=x^2-4	area\:y=x^{4}-4x^{2},y=x^{2}-4
y^'=(x^4)/(16)(e^{-y})	y^{\prime\:}=\frac{x^{4}}{16}(e^{-y})
integral de 2/(3x-4)	\int\:\frac{2}{3x-4}dx
derivada de x(1-x^3)	\frac{d}{dx}(x(1-x)^{3})
integral de 1 a 3 de (9^x-7^x)	\int\:_{1}^{3}(9^{x}-7^{x})dx
derivada de (x^2-2/(x^2+2))	\frac{d}{dx}(\frac{x^{2}-2}{x^{2}+2})
y^'=7y	y^{\prime\:}=7y
derivada de (2x+1^5+10x(2x+1)^4)	\frac{d}{dx}((2x+1)^{5}+10x(2x+1)^{4})
(\partial)/(\partial s)(2s^2+t^2)	\frac{\partial\:}{\partial\:s}(2s^{2}+t^{2})
(\partial)/(\partial s)(e^{s^3+t^2})	\frac{\partial\:}{\partial\:s}(e^{s^{3}+t^{2}})
1/4 y^{''}+y^'+y=x^2-5x	\frac{1}{4}y^{\prime\:\prime\:}+y^{\prime\:}+y=x^{2}-5x
integral de e^xx+e^x	\int\:e^{x}x+e^{x}dx
derivative f(x)= 3/(2x^5)	derivative\:f(x)=\frac{3}{2x^{5}}
integral de 1/(sqrt(t^2-6t+13))	\int\:\frac{1}{\sqrt{t^{2}-6t+13}}dt
integral de ln(8x+1)	\int\:\ln(8x+1)dx
inversalaplace ((2s+1))/(s^2-6s+7)	inverselaplace\:\frac{(2s+1)}{s^{2}-6s+7}
derivative f(x)=2ax+b	derivative\:f(x)=2ax+b
límite cuando h tiende a 0 de ((5+h)-5)/h	\lim\:_{h\to\:0}(\frac{(5+h)-5}{h})
inversalaplace 1/(s^2+3s+100)	inverselaplace\:\frac{1}{s^{2}+3s+100}
integral de cos^4(x)sin^4(x)	\int\:\cos^{4}(x)\sin^{4}(x)dx
derivative y=tan(4x^2)	derivative\:y=\tan(4x^{2})
implicit sqrt(x)+sqrt(y)=8	implicit\:\sqrt{x}+\sqrt{y}=8
derivative y= 5/(\sqrt[4]{x)}	derivative\:y=\frac{5}{\sqrt[4]{x}}
y^{''}-8y^'+17y=0,y(0)=4,y^'(0)=-1	y^{\prime\:\prime\:}-8y^{\prime\:}+17y=0,y(0)=4,y^{\prime\:}(0)=-1
integral de t/(t^4+3)	\int\:\frac{t}{t^{4}+3}dt
límite cuando x tiende a 1-de arccos(-x^3)	\lim\:_{x\to\:1-}(\arccos(-x^{3}))
derivative ((x^2+2)/(x^2-2))^5	derivative\:(\frac{x^{2}+2}{x^{2}-2})^{5}
derivada de 1/(sqrt(3x^2-1))	\frac{d}{dx}(\frac{1}{\sqrt{3x^{2}-1}})
derivative 20x-16x^2	derivative\:20x-16x^{2}
y^{''}+16y=3csc^2(4t)	y^{\prime\:\prime\:}+16y=3\csc^{2}(4t)
integral de 2/((x+1)(x-1))	\int\:\frac{2}{(x+1)(x-1)}dx
(dy)/(dx)=1+y+x^2+yx^2	\frac{dy}{dx}=1+y+x^{2}+yx^{2}
derivative ln(1+e^{x+1})	derivative\:\ln(1+e^{x+1})
derivada de 1/(x^{20})	\frac{d}{dx}(\frac{1}{x^{20}})
derivada de-(12/(x^3))	\frac{d}{dx}(-\frac{12}{x^{3}})
integral de 1/2 tcos(4)t^2	\int\:\frac{1}{2}t\cos(4)t^{2}dt
d/(dy)(y+1)	\frac{d}{dy}(y+1)
integral de 6x+5	\int\:6x+5dx
inversalaplace 4/s+6/(s^5)-1/(s+8)	inverselaplace\:\frac{4}{s}+\frac{6}{s^{5}}-\frac{1}{s+8}
área y=2x^2-x,(-1,2)	area\:y=2x^{2}-x,(-1,2)
derivative x(ln(3x))^2	derivative\:x(\ln(3x))^{2}
y^'= y/(1+x)	y^{\prime\:}=\frac{y}{1+x}
integral de x^3-x^2-6x	\int\:x^{3}-x^{2}-6xdx
derivative f(x)=ln(x^5)	derivative\:f(x)=\ln(x^{5})
derivada de sqrt(2+5x)	\frac{d}{dx}(\sqrt{2+5x})
integral de 4 a 5 de xsqrt(x^2-16)	\int\:_{4}^{5}x\sqrt{x^{2}-16}dx
(\partial)/(\partial x)(1/3 (x^2+2)^{3/2})	\frac{\partial\:}{\partial\:x}(\frac{1}{3}(x^{2}+2)^{\frac{3}{2}})
límite cuando x tiende a infinity de sqrt(9x^2+x)-3	\lim\:_{x\to\:\infty\:}(\sqrt{9x^{2}+x}-3)
integral de 1/(y^3+y)	\int\:\frac{1}{y^{3}+y}dy
integral de 1/(x(x^2+1)^2)	\int\:\frac{1}{x(x^{2}+1)^{2}}dx
integral de 1/((x+1)sqrt(x^2+2x-8))	\int\:\frac{1}{(x+1)\sqrt{x^{2}+2x-8}}dx
derivative (x^3-1)/(x^2)	derivative\:\frac{x^{3}-1}{x^{2}}
integral de (3x-1)/(x^2+9)	\int\:\frac{3x-1}{x^{2}+9}dx
derivada de ln({g}(x))	\frac{d}{dx}(\ln({g}(x)))
integral de x/((x^2+9)^2)	\int\:\frac{x}{(x^{2}+9)^{2}}dx
integral de a/(x^2+a^2)	\int\:\frac{a}{x^{2}+a^{2}}dx
derivative (x^3+2)e^x	derivative\:(x^{3}+2)e^{x}
integral de 9x^8e^{5x^9}	\int\:9x^{8}e^{5x^{9}}dx
derivative sqrt(3/(x-1))	derivative\:\sqrt{\frac{3}{x-1}}
y^'-2y=-3y^2	y^{\prime\:}-2y=-3y^{2}
integral de arctan(t^2)	\int\:\arctan(t^{2})dt
tangent y= 5/x	tangent\:y=\frac{5}{x}
y^'+sin(x)y=-sin(x)	y^{\prime\:}+\sin(x)y=-\sin(x)
integral de x*sin(x)	\int\:x\cdot\:\sin(x)dx
tangent f(x)=-0.5x^2,\at x=10	tangent\:f(x)=-0.5x^{2},\at\:x=10
integral de 0 a 1 de 4(1+sqrt(x))^5	\int\:_{0}^{1}4(1+\sqrt{x})^{5}dx
integral de ((2x^2+x+2))/((x^2+1)^2)	\int\:\frac{(2x^{2}+x+2)}{(x^{2}+1)^{2}}dx
(\partial)/(\partial x)(x^6y-4x^3y^2)	\frac{\partial\:}{\partial\:x}(x^{6}y-4x^{3}y^{2})
y^{''}+y=3csc^2(t)	y^{\prime\:\prime\:}+y=3\csc^{2}(t)
límite cuando x tiende a 0 de-1/(x-1)	\lim\:_{x\to\:0}(-\frac{1}{x-1})
(dy)/(dx)=3sqrt(yx)	\frac{dy}{dx}=3\sqrt{yx}
(\partial)/(\partial x)((6y)/(x^2+y^2+5))	\frac{\partial\:}{\partial\:x}(\frac{6y}{x^{2}+y^{2}+5})
límite cuando x tiende a 0-de log_{3}(x)	\lim\:_{x\to\:0-}(\log_{3}(x))
integral de (x^3+2)^23x^2	\int\:(x^{3}+2)^{2}3x^{2}dx
límite cuando x tiende a infinity de (4^{x-1})/(n^2+2n)*2^x	\lim\:_{x\to\:\infty\:}(\frac{4^{x-1}}{n^{2}+2n}\cdot\:2^{x})
integral de 2/(x^{3/2)}	\int\:\frac{2}{x^{\frac{3}{2}}}dx
integral de tan^2(x)cos^3(x)	\int\:\tan^{2}(x)\cos^{3}(x)dx
integral de 0 a 1 de 1/(x^p)	\int\:_{0}^{1}\frac{1}{x^{p}}dx
(\partial)/(\partial t)(-(sqrt(s^2+t^2)))	\frac{\partial\:}{\partial\:t}(-(\sqrt{s^{2}+t^{2}}))
derivada de (4x-5^3)	\frac{d}{dx}((4x-5)^{3})
integral de 1/(e^{-3x)}	\int\:\frac{1}{e^{-3x}}dx
d/(dy)(cos(x)y)	\frac{d}{dy}(\cos(x)y)
integral de (x^3-1)/(x^3+2x^2+x)	\int\:\frac{x^{3}-1}{x^{3}+2x^{2}+x}dx
(\partial)/(\partial x)(x^2-5xy+3y^2)	\frac{\partial\:}{\partial\:x}(x^{2}-5xy+3y^{2})
integral de 25arctan(sqrt(x))	\int\:25\arctan(\sqrt{x})dx
(d^2y)/(dx^2)+20(dy)/(dx)+200y=300	\frac{d^{2}y}{dx^{2}}+20\frac{dy}{dx}+200y=300
integral de 1 a infinity de 3e^{-x}	\int\:_{1}^{\infty\:}3e^{-x}dx
tangent 7x^2-3x	tangent\:7x^{2}-3x
integral de-infinity a 0 de 1/(6-8x)	\int\:_{-\infty\:}^{0}\frac{1}{6-8x}dx
integral de 12t+12	\int\:12t+12dt
y^{''}-6y^'+9y=((13.5e^{(3t)}))/(t^2+1)	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=\frac{(13.5e^{(3t)})}{t^{2}+1}
derivada de cosh(ln(e^{x^3}))	\frac{d}{dx}(\cosh(\ln(e^{x^{3}})))
integral de 9/((1-x^2)^{3/2)}	\int\:\frac{9}{(1-x^{2})^{\frac{3}{2}}}dx
integral de 9/(sqrt(x))	\int\:\frac{9}{\sqrt{x}}dx
x^2dy=(5y^3-2xy)dx	x^{2}dy=(5y^{3}-2xy)dx

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