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Popular Calculus Problems

limit as x approaches 2+of (\|x\|+2)/(x-2)	\lim\:_{x\to\:2+}(\frac{\left\|x\right\|+2}{x-2})
x(dy)/(dx)=y-x	x\frac{dy}{dx}=y-x
(x^2-4)(dy)/(dx)+4y=(x+2)2	(x^{2}-4)\frac{dy}{dx}+4y=(x+2)2
limit as x approaches 0 of ((cos(2x)-cos(3x)))/(x^2)	\lim\:_{x\to\:0}(\frac{(\cos(2x)-\cos(3x))}{x^{2}})
integral of ((x+3))/(sqrt(5-4x-x^2))	\int\:\frac{(x+3)}{\sqrt{5-4x-x^{2}}}dx
(\partial)/(\partial x)(sin(3y)+2ze^{-2x})	\frac{\partial\:}{\partial\:x}(\sin(3y)+2ze^{-2x})
(\partial)/(\partial x)(x-1/y)	\frac{\partial\:}{\partial\:x}(x-\frac{1}{y})
integral of (2x+3)sqrt(2x+1)	\int\:(2x+3)\sqrt{2x+1}dx
derivative of sech^2(3x)	\frac{d}{dx}(\sech^{2}(3x))
integral of (2x-3)/(x^2+4x+5)	\int\:\frac{2x-3}{x^{2}+4x+5}dx
sum from n=2 to infinity of (-1)/n	\sum\:_{n=2}^{\infty\:}\frac{-1}{n}
derivative of (x^3-2x^2+2x-4/(x^2+2))	\frac{d}{dx}(\frac{x^{3}-2x^{2}+2x-4}{x^{2}+2})
derivative of f(x)=(c^9-x^9)/(c^9+x^9)	derivative\:f(x)=\frac{c^{9}-x^{9}}{c^{9}+x^{9}}
derivative of sqrt(1+36x)	\frac{d}{dx}(\sqrt{1+36x})
integral of 1/(x^2-12)	\int\:\frac{1}{x^{2}-12}dx
integral of (x+4)/(x^3+3x^2-10x)	\int\:\frac{x+4}{x^{3}+3x^{2}-10x}dx
integral of-3pisin(pi)x	\int\:-3π\sin(π)xdx
tangent of f(x)=-2sin(x),\at x= 3/4 pi	tangent\:f(x)=-2\sin(x),\at\:x=\frac{3}{4}π
x^2y^'+4/3 xy=-2cos(2x)y^{-1/2}	x^{2}y^{\prime\:}+\frac{4}{3}xy=-2\cos(2x)y^{-\frac{1}{2}}
sum from n=1 to infinity of sin(npi)	\sum\:_{n=1}^{\infty\:}\sin(nπ)
integral from-1 to 1 of (e^{2x})/(1+e^x)	\int\:_{-1}^{1}\frac{e^{2x}}{1+e^{x}}dx
derivative of 1/(arccos(x^2+2x+4))	\frac{d}{dx}(\frac{1}{\arccos(x^{2}+2x+4)})
tangent of f(x)=x^2,(-0.8,0.64)	tangent\:f(x)=x^{2},(-0.8,0.64)
integral of (5x)/((x^2+6)^2)	\int\:\frac{5x}{(x^{2}+6)^{2}}dx
integral of 0e^x	\int\:0e^{x}dx
y^{''}sin(x)cos(x)-2y^'=0	y^{\prime\:\prime\:}\sin(x)\cos(x)-2y^{\prime\:}=0
integral of 6e^{-5x}	\int\:6e^{-5x}dx
limit as x approaches 0 of 2/(sin(x))	\lim\:_{x\to\:0}(\frac{2}{\sin(x)})
derivative of y=log_{e}(x)	derivative\:y=\log_{e}(x)
integral of-7/(x^8)	\int\:-\frac{7}{x^{8}}dx
tangent of f(x)=x^2+9x,\at x=-8	tangent\:f(x)=x^{2}+9x,\at\:x=-8
integral of x(ln(x)+e^x)	\int\:x(\ln(x)+e^{x})dx
tangent of f(x)=1-x^2,\at x=2	tangent\:f(x)=1-x^{2},\at\:x=2
integral of (21)/(25+4r^2)	\int\:\frac{21}{25+4r^{2}}dr
taylor 1/x-1	taylor\:\frac{1}{x}-1
(\partial)/(\partial x)(2y-3x+5)	\frac{\partial\:}{\partial\:x}(2y-3x+5)
integral of (e^{6x}+e^{-9x})	\int\:(e^{6x}+e^{-9x})dx
integral of x^2*cos(nx)	\int\:x^{2}\cdot\:\cos(nx)dx
derivative of (2x/(x-4))	\frac{d}{dx}(\frac{2x}{x-4})
derivative of (2x/(sqrt(x^2+9)))	\frac{d}{dx}(\frac{2x}{\sqrt{x^{2}+9}})
inverse oflaplace (3s-15)/(2s^2-4s+10)	inverselaplace\:\frac{3s-15}{2s^{2}-4s+10}
derivative of (x^2+1/(x^2-4x+3))	\frac{d}{dx}(\frac{x^{2}+1}{x^{2}-4x+3})
derivative of cos(x+sin(x)+x)	\frac{d}{dx}(\cos(x)+\sin(x)+x)
integral of x/(sqrt(25+x^4))	\int\:\frac{x}{\sqrt{25+x^{4}}}dx
derivative of e^{x^3}*3x^2	\frac{d}{dx}(e^{x^{3}}\cdot\:3x^{2})
derivative of 2x^3e^{-0.6x}	\frac{d}{dx}(2x^{3}e^{-0.6x})
integral of v/(v^2+1)	\int\:\frac{v}{v^{2}+1}dv
integral of (x^2+6)/(x^3+x^2-2x)	\int\:\frac{x^{2}+6}{x^{3}+x^{2}-2x}dx
tangent of f(x)= 2/(x+7),(-8,-2)	tangent\:f(x)=\frac{2}{x+7},(-8,-2)
derivative of e^xarctan(x)	\frac{d}{dx}(e^{x}\arctan(x))
x((dy)/(dx))= 1/(y^3)	x(\frac{dy}{dx})=\frac{1}{y^{3}}
(dy)/(dx)=(x+y+4)^2	\frac{dy}{dx}=(x+y+4)^{2}
derivative of (e^x)/(5+5x)	derivative\:\frac{e^{x}}{5+5x}
(\partial)/(\partial y)(e^{2y}-ycos(x)y)	\frac{\partial\:}{\partial\:y}(e^{2y}-y\cos(x)y)
sum from n=1 to infinity of (sin(8))^n	\sum\:_{n=1}^{\infty\:}(\sin(8))^{n}
integral of x^2sqrt(25-x^2)	\int\:x^{2}\sqrt{25-x^{2}}dx
area 19-x^2,-2x+16,-5,0	area\:19-x^{2},-2x+16,-5,0
area (12x-x^3+1),x^2+29,{0,7}	area\:(12x-x^{3}+1),x^{2}+29,\left\{0,7\right\}
limit as x approaches 0+of 4+ln(x)	\lim\:_{x\to\:0+}(4+\ln(x))
e^xy(dy)/(dx)=e^{-y}+e^{-5x-y}	e^{x}y\frac{dy}{dx}=e^{-y}+e^{-5x-y}
derivative of sqrt((x^2+8))	derivative\:\sqrt{(x^{2}+8)}
derivative of f(x)=(x^2)/(x^2+x-2)	derivative\:f(x)=\frac{x^{2}}{x^{2}+x-2}
integral of (x^2-3)sin(2x)	\int\:(x^{2}-3)\sin(2x)dx
derivative of sin(x+sin(y)+sin(x+y))	\frac{d}{dx}(\sin(x)+\sin(y)+\sin(x+y))
slope of 1/((x-2))	slope\:\frac{1}{(x-2)}
derivative of sqrt((cos(x-1)/(sin(x))))	\frac{d}{dx}(\sqrt{\frac{\cos(x)-1}{\sin(x)}})
laplacetransform (2e^{-t})(cos(4t))(1(t))	laplacetransform\:(2e^{-t})(\cos(4t))(1(t))
tangent of f(x)=2x^3+3x^2+4x+2,\at x=-1	tangent\:f(x)=2x^{3}+3x^{2}+4x+2,\at\:x=-1
y^{''}+3y^'=9x	y^{\prime\:\prime\:}+3y^{\prime\:}=9x
derivative of e^{(-5x^2-2x^2})	\frac{d}{dx}(e^{(-5x^{2}-2x^{2})})
d/(d{y)}(({y}-2({u)/y)}{{y}})	\frac{d}{d{y}}(\frac{{y}-2({u}{y})}{{y}})
y^{''}+2y=18	y^{\prime\:\prime\:}+2y=18
inverse oflaplace 1/(s(s^2+s+5))	inverselaplace\:\frac{1}{s(s^{2}+s+5)}
tangent of 3/(x^2),\at x=1	tangent\:\frac{3}{x^{2}},\at\:x=1
derivative of 11x	\frac{d}{dx}(11x)
integral from-1 to 1 of ((27)/(x^4)-3)	\int\:_{-1}^{1}(\frac{27}{x^{4}}-3)dx
integral of 5x-7	\int\:5x-7dx
y^'=ky*(100-y)	y^{\prime\:}=ky\cdot\:(100-y)
tangent of f(x) 1/(2sqrt(x+1)),\at x=7	tangent\:f(x)\frac{1}{2\sqrt{x+1}},\at\:x=7
derivative of (e^x+e^{-x}/x)	\frac{d}{dx}(\frac{e^{x}+e^{-x}}{x})
integral of (8+3x)/(1+x^2)	\int\:\frac{8+3x}{1+x^{2}}dx
derivative of y=2x^2+4x-10	derivative\:y=2x^{2}+4x-10
integral of (sqrt(x^2-64))/(x^3)	\int\:\frac{\sqrt{x^{2}-64}}{x^{3}}dx
integral of ln(7x)	\int\:\ln(7x)dx
derivative of y=x^{0.1}(1+x)	\frac{d}{dx}y=x^{0.1}(1+x)
derivative of x^4+5cos(x)	\frac{d}{dx}(x^{4}+5\cos(x))
sum from k=2 to infinity of k/(k^2+3)	\sum\:_{k=2}^{\infty\:}\frac{k}{k^{2}+3}
integral from 0 to pi/4 of (sin(x))^2	\int\:_{0}^{\frac{π}{4}}(\sin(x))^{2}dx
derivative of 5log_{10}(4x^2)	\frac{d}{dx}(5\log_{10}(4x^{2}))
integral of csc^3(4x)	\int\:\csc^{3}(4x)dx
y^'=y(xy^2+3)	y^{\prime\:}=y(xy^{2}+3)
derivative of (ln(x^3)/(ln(x^2)))	\frac{d}{dx}(\frac{\ln(x^{3})}{\ln(x^{2})})
slope ofintercept (3,-8),(-6,-3)	slopeintercept\:(3,-8),(-6,-3)
derivative of 2sqrt(x)-3/(\sqrt[3]{x})	\frac{d}{dx}(2\sqrt{x}-\frac{3}{\sqrt[3]{x}})
integral of (3x+11)/(x^2-x-6)	\int\:\frac{3x+11}{x^{2}-x-6}dx
slope of y=-5x^{1/2}+x^{3/2}	slope\:y=-5x^{\frac{1}{2}}+x^{\frac{3}{2}}
(dy)/(dx)=(y^2-1)x	\frac{dy}{dx}=(y^{2}-1)x
derivative of (x^2+3x-1e^x)	\frac{d}{dx}((x^{2}+3x-1)e^{x})
integral of 2/3 x^{3/2}-6sin(x)+C	\int\:\frac{2}{3}x^{\frac{3}{2}}-6\sin(x)+Cdx
y^'=x^2-1,y(0)=1	y^{\prime\:}=x^{2}-1,y(0)=1

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