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Problemas populares de Cálculo

y^{''}+4y=0,y(0)=1,y^'(0)=4	y^{\prime\:\prime\:}+4y=0,y(0)=1,y^{\prime\:}(0)=4
(dy)/(dx)=32x^3y^3,y(0)=k	\frac{dy}{dx}=32x^{3}y^{3},y(0)=k
integral de [(a^3)/(x^2+a^2)]^2	\int\:[\frac{a^{3}}{x^{2}+a^{2}}]^{2}dx
límite cuando x tiende a 4 de 3x+5	\lim\:_{x\to\:4}(3x+5)
serie de n=1 a infinity de (n/(n+4))^n	\sum\:_{n=1}^{\infty\:}(\frac{n}{n+4})^{n}
integral de cos(4x-3)	\int\:\cos(4x-3)dx
serie de n=1 a infinity de pi^n	\sum\:_{n=1}^{\infty\:}π^{n}
área y=3x-x^2,y=-3x	area\:y=3x-x^{2},y=-3x
(\partial)/(\partial x)(2^2+1^2)	\frac{\partial\:}{\partial\:x}(2^{2}+1^{2})
pendiente (2/7 ,5),(10,39)	slope\:(\frac{2}{7},5),(10,39)
integral de 15 a 35 de (x^2x)	\int\:_{15}^{35}(x^{2}x)dx
(\partial)/(\partial y)(x/y-yz)	\frac{\partial\:}{\partial\:y}(\frac{x}{y}-yz)
integral de (3x-1)/(x^{2/3)}	\int\:\frac{3x-1}{x^{\frac{2}{3}}}dx
integral de ((x-1))/(x^3+x^2+6x)	\int\:\frac{(x-1)}{x^{3}+x^{2}+6x}dx
límite cuando x tiende a 4-de 4x	\lim\:_{x\to\:4-}(4x)
derivada de 1/(3x^2+1)	\frac{d}{dx}(\frac{1}{3x^{2}+1})
integral de x^2e^{4x^3}	\int\:x^{2}e^{4x^{3}}dx
serie de n=0 a infinity de 1^{ln(n)}	\sum\:_{n=0}^{\infty\:}1^{\ln(n)}
derivative y= 1/2 e^{2x}+e^x+1	derivative\:y=\frac{1}{2}e^{2x}+e^{x}+1
derivative 3sin(4x)	derivative\:3\sin(4x)
derivada de x^4+cos(x+1)	\frac{d}{dx}(x^{4}+\cos(x)+1)
integral de ((16-9x^2)^{3/2})/(x^6)	\int\:\frac{(16-9x^{2})^{\frac{3}{2}}}{x^{6}}dx
integral de (16)/((x+2)^2)	\int\:\frac{16}{(x+2)^{2}}dx
y^'=y+xy	y^{\prime\:}=y+xy
serie de n=1 a infinity de (((3n-1))/((3n)))^{n^2}	\sum\:_{n=1}^{\infty\:}(\frac{(3n-1)}{(3n)})^{n^{2}}
tan(x)sin^2(y)dx+cos^2(x)cot(y)dy=0	\tan(x)\sin^{2}(y)dx+\cos^{2}(x)\cot(y)dy=0
serie de n=0 a infinity de 1+1/(n^2)	\sum\:_{n=0}^{\infty\:}1+\frac{1}{n^{2}}
y^'=32x^3y^3	y^{\prime\:}=32x^{3}y^{3}
integral de-2 a 2 de x^2e^{x^3+8}	\int\:_{-2}^{2}x^{2}e^{x^{3}+8}dx
derivative 5ln(x)	derivative\:5\ln(x)
derivative x^2log_{3}(x^3)	derivative\:x^{2}\log_{3}(x^{3})
integral de (8x-7/x)	\int\:(8x-\frac{7}{x})dx
tangent y=cos(x),\at x=(3pi)/2	tangent\:y=\cos(x),\at\:x=\frac{3π}{2}
derivative f(x)= 5/((2x-3)^4)	derivative\:f(x)=\frac{5}{(2x-3)^{4}}
derivada de sin(xln(5x))	\frac{d}{dx}(\sin(x)\ln(5x))
derivative e^{19}	derivative\:e^{19}
(dy)/(dx)=e^4x+7y	\frac{dy}{dx}=e^{4}x+7y
integral de xsqrt(3x^2-6)	\int\:x\sqrt{3x^{2}-6}dx
integral de 3/(5x^{2/5)}	\int\:\frac{3}{5x^{\frac{2}{5}}}dx
límite cuando x tiende a 2 de (2x^2-5x+2)/(x^3-2x^2)	\lim\:_{x\to\:2}(\frac{2x^{2}-5x+2}{x^{3}-2x^{2}})
derivada de ax^2e^{-3x}	\frac{d}{dx}(ax^{2}e^{-3x})
(\partial)/(\partial x)(x^4-8xy-5y^2)	\frac{\partial\:}{\partial\:x}(x^{4}-8xy-5y^{2})
integral de 5/(\sqrt[4]{x^2)}	\int\:\frac{5}{\sqrt[4]{x^{2}}}dx
(\partial)/(\partial x)(ln(x^2+y^2+z^2))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+y^{2}+z^{2}))
integral de (x)e^{x^2-1}	\int\:(x)e^{x^{2}-1}dx
límite cuando x tiende a 2 de (11x)/(4-x^2)	\lim\:_{x\to\:2}(\frac{11x}{4-x^{2}})
derivative (3x-5)(x^2+4)	derivative\:(3x-5)(x^{2}+4)
integral de (7x+14)/(x^2+5x-6)	\int\:\frac{7x+14}{x^{2}+5x-6}dx
integral de 1/(3x^2-2x+4)	\int\:\frac{1}{3x^{2}-2x+4}dx
y^{''}+y=sec(t)tan(t)	y^{\prime\:\prime\:}+y=\sec(t)\tan(t)
área 2-x^2,x,-2,1	area\:2-x^{2},x,-2,1
serie de n=1 a infinity de (n!)/(n!+1)	\sum\:_{n=1}^{\infty\:}\frac{n!}{n!+1}
integral de 0 a 1 de (x/(x^2+1))	\int\:_{0}^{1}(\frac{x}{x^{2}+1})dx
integral de 3 a 7 de x/(x^2+6x+13)	\int\:_{3}^{7}\frac{x}{x^{2}+6x+13}dx
(\partial)/(\partial y)((x+2y+3z)^{3/2})	\frac{\partial\:}{\partial\:y}((x+2y+3z)^{\frac{3}{2}})
(1+x^2)(dy)/(dx)-2xy=x^2+x^4	(1+x^{2})\frac{dy}{dx}-2xy=x^{2}+x^{4}
(\partial)/(\partial x)(20e^{5x}y)	\frac{\partial\:}{\partial\:x}(20e^{5x}y)
f(x)=ln(x^2-1)	f(x)=\ln(x^{2}-1)
derivada de (x^2-6x/((x-3)^2))	\frac{d}{dx}(\frac{x^{2}-6x}{(x-3)^{2}})
integral de 3/((x-2)^2)	\int\:\frac{3}{(x-2)^{2}}dx
pendienteintercept (12,-16),(-9,8)	slopeintercept\:(12,-16),(-9,8)
integral de (tan(x)(6cos(x)-6sec(x)))	\int\:(\tan(x)(6\cos(x)-6\sec(x)))dx
y^{''}-y^'-6y=-4e^2t,y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}-y^{\prime\:}-6y=-4e^{2}t,y(0)=0,y^{\prime\:}(0)=0
integral de (x^2)/((x-1)(x^2+4x+5))	\int\:\frac{x^{2}}{(x-1)(x^{2}+4x+5)}dx
(dy)/(dx)=(5x)/(3y)	\frac{dy}{dx}=\frac{5x}{3y}
integral de 0 a pi de 13sin^2(2x)	\int\:_{0}^{π}13\sin^{2}(2x)dx
integral de 1 a 9 de sqrt(t)ln(t)	\int\:_{1}^{9}\sqrt{t}\ln(t)dt
derivada de (cos(x)/(1+cot(x)))	\frac{d}{dx}(\frac{\cos(x)}{1+\cot(x)})
integral de 0 a pi/4 de sin(3x)	\int\:_{0}^{\frac{π}{4}}\sin(3x)dx
derivada de (2(-x^2-4)/((x^2-4)^2))	\frac{d}{dx}(\frac{2(-x^{2}-4)}{(x^{2}-4)^{2}})
derivada de ((x^2-2sqrt(x))/x)	\frac{d}{dx}(\frac{(x^{2}-2\sqrt{x})}{x})
límite cuando x tiende a 0 de (tan(4x))/(3x)	\lim\:_{x\to\:0}(\frac{\tan(4x)}{3x})
límite cuando x tiende a 2 de (3x+4)^5	\lim\:_{x\to\:2}((3x+4)^{5})
derivative 3*\sqrt[3]{x^2+2}	derivative\:3\cdot\:\sqrt[3]{x^{2}+2}
integral de 1/(cos(x))	\int\:\frac{1}{\cos(x)}dx
integral de 1 a 3 de (x^2+1)/(4x-x^2)	\int\:_{1}^{3}\frac{x^{2}+1}{4x-x^{2}}dx
xy^'-y=3xln(x)	xy^{\prime\:}-y=3x\ln(x)
derivative 1/10 x^5-3x^3	derivative\:\frac{1}{10}x^{5}-3x^{3}
integral de (3x-11)/(x^3-5x^2)	\int\:\frac{3x-11}{x^{3}-5x^{2}}dx
integral de-8y^3	\int\:-8y^{3}dy
(\partial)/(\partial x)(x^2+2y^2+9xz)	\frac{\partial\:}{\partial\:x}(x^{2}+2y^{2}+9xz)
límite cuando t tiende a 0-de t^2+1	\lim\:_{t\to\:0-}(t^{2}+1)
integral de e^{2x}cos(e^x)	\int\:e^{2x}\cos(e^{x})dx
(\partial)/(\partial x)(cos^3(x^4y^3))	\frac{\partial\:}{\partial\:x}(\cos^{3}(x^{4}y^{3}))
y^{''}+9y=27	y^{\prime\:\prime\:}+9y=27
límite cuando x tiende a 2+de x^2-4	\lim\:_{x\to\:2+}(x^{2}-4)
derivada de 8/(cos(x^2-2x))	\frac{d}{dx}(\frac{8}{\cos(x^{2}-2x)})
derivative xcos(x)+2tan(x)	derivative\:x\cos(x)+2\tan(x)
integral de 5 a 7 de x/(x^2+6x+13)	\int\:_{5}^{7}\frac{x}{x^{2}+6x+13}dx
derivative (2x^2+2)^3(x^2-1)^2	derivative\:(2x^{2}+2)^{3}(x^{2}-1)^{2}
(2x^{3/2})^'	(2x^{\frac{3}{2}})^{\prime\:}
t^2(dy)/(dt)-t=1+y+ty,y(1)=7	t^{2}\frac{dy}{dt}-t=1+y+ty,y(1)=7
(\partial)/(\partial x)(x^2-y^3-x^2y+y)	\frac{\partial\:}{\partial\:x}(x^{2}-y^{3}-x^{2}y+y)
(\partial)/(\partial x)(-2(1-x)-40x(y-x^2))	\frac{\partial\:}{\partial\:x}(-2(1-x)-40x(y-x^{2}))
derivada de e(-x)	\frac{d}{dx}(e(-x))
integral de 0.2 a 0.4 de 300x	\int\:_{0.2}^{0.4}300xdx
integral de (sqrt(x^2-4))/x	\int\:\frac{\sqrt{x^{2}-4}}{x}dx
derivative (4+ln(x))^7	derivative\:(4+\ln(x))^{7}
(dy)/(dt)+e^ty=-6e^t	\frac{dy}{dt}+e^{t}y=-6e^{t}
tangent f(x)=(4x)/(x+1),(3,3)	tangent\:f(x)=\frac{4x}{x+1},(3,3)

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