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Popular Calculus Problems

limit as x approaches infinity of m/n	\lim\:_{x\to\:\infty\:}(\frac{m}{n})
sum from n=0 to infinity of 0.01^n	\sum\:_{n=0}^{\infty\:}0.01^{n}
y+y^'=sin(t),y(pi)=1	y+y^{\prime\:}=\sin(t),y(π)=1
integral from 1 to 3x of (t^2+t)	\int\:_{1}^{3x}(t^{2}+t)dt
tangent of f(x)=2-2x^2,-16,\at x=3	tangent\:f(x)=2-2x^{2},-16,\at\:x=3
limit as x approaches-4 of 10x^2+34x-24	\lim\:_{x\to\:-4}(10x^{2}+34x-24)
sum from n=1 to infinity of 2-5(0.9)^n	\sum\:_{n=1}^{\infty\:}2-5(0.9)^{n}
sum from n=0 to infinity of 1/n-1/(n+1)	\sum\:_{n=0}^{\infty\:}\frac{1}{n}-\frac{1}{n+1}
limit as x approaches-5-of (x+2)/(x+5)	\lim\:_{x\to\:-5-}(\frac{x+2}{x+5})
inverse oflaplace 3/(s+4)	inverselaplace\:\frac{3}{s+4}
integral of (5x^3-18)^715x^2	\int\:(5x^{3}-18)^{7}15x^{2}dx
integral of (4e^x)/(e^{2x)+10e^x+25}	\int\:\frac{4e^{x}}{e^{2x}+10e^{x}+25}dx
(dy)/(dx)+x^2y=2x^2	\frac{dy}{dx}+x^{2}y=2x^{2}
y^'=(y+2t)^2	y^{\prime\:}=(y+2t)^{2}
sqrt(-2y-y^2)dx+(3+2x-x^2)dy=0	\sqrt{-2y-y^{2}}dx+(3+2x-x^{2})dy=0
y^{''}-y^'-2y=cos(x)-sin(2x)	y^{\prime\:\prime\:}-y^{\prime\:}-2y=\cos(x)-\sin(2x)
derivative of-2asin(2x+2bcos(2x))	\frac{d}{dx}(-2a\sin(2x)+2b\cos(2x))
derivative of y=sqrt(2+8e^{6x)}	derivative\:y=\sqrt{2+8e^{6x}}
derivative of ((e^x-2)/((1-e^{-x))^2})	\frac{d}{dx}(\frac{(e^{x}-2)}{(1-e^{-x})^{2}})
integral of 1/((x-1)^2)	\int\:\frac{1}{(x-1)^{2}}dx
(\partial)/(\partial x)(5xy)	\frac{\partial\:}{\partial\:x}(5xy)
derivative of (e^{-x}-e^5(e^x+e^{-3}))	\frac{d}{dx}((e^{-x}-e^{5})(e^{x}+e^{-3}))
derivative of 2^{2x+1}	\frac{d}{dx}(2^{2x+1})
tangent of y= 1/(x-2),\at x=4	tangent\:y=\frac{1}{x-2},\at\:x=4
derivative of y=sqrt(5-3x^2)	derivative\:y=\sqrt{5-3x^{2}}
y^{''}+2y^'+2y=sin(kx)	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=\sin(kx)
integral of sec(2x)tan(2x)-4/(x^2)	\int\:\sec(2x)\tan(2x)-\frac{4}{x^{2}}dx
integral of (cos(y))	\int\:(\cos(y))dy
slope of (-3,5),(7,-9)	slope\:(-3,5),(7,-9)
taylor 8/(1-x)	taylor\:\frac{8}{1-x}
integral of (x^5-x^3+2x)/(x^4)	\int\:\frac{x^{5}-x^{3}+2x}{x^{4}}dx
integral of e^{16x}	\int\:e^{16x}dx
limit as x approaches 5 of x-4	\lim\:_{x\to\:5}(x-4)
integral of sin(ln(7x))	\int\:\sin(\ln(7x))dx
derivative of 4x^8	\frac{d}{dx}(4x^{8})
derivative of-cot(x)csc(x)	derivative\:-\cot(x)\csc(x)
integral from 0 to pi/4 of sin^4(4x)	\int\:_{0}^{\frac{π}{4}}\sin^{4}(4x)dx
limit as x approaches 2 of x^3+4	\lim\:_{x\to\:2}(x^{3}+4)
integral of (x-3)(x+11)^{15}	\int\:(x-3)(x+11)^{15}dx
derivative of y=(x^6)/(f(x))	derivative\:y=\frac{x^{6}}{f(x)}
integral of x^2sqrt(x-1)	\int\:x^{2}\sqrt{x-1}dx
tangent of f(x)=sqrt(x+2)	tangent\:f(x)=\sqrt{x+2}
(\partial)/(\partial x)(3y^2+x^2-3)	\frac{\partial\:}{\partial\:x}(3y^{2}+x^{2}-3)
y^'=cos(2x)	y^{\prime\:}=\cos(2x)
derivative of 25cos((pix)/(50))	derivative\:25\cos(\frac{πx}{50})
integral of cos^3(ax+b)	\int\:\cos^{3}(ax+b)dx
f(x)=2\sqrt[3]{x}	f(x)=2\sqrt[3]{x}
limit as x approaches infinity of e^2	\lim\:_{x\to\:\infty\:}(e^{2})
integral of (x^2-1)/(x+1)	\int\:\frac{x^{2}-1}{x+1}dx
derivative of (x^2/(x-1))	\frac{d}{dx}(\frac{x^{2}}{x-1})
integral of cos(cx)	\int\:\cos(cx)dx
derivative of sin(pi/3)	\frac{d}{dx}(\sin(\frac{π}{3}))
integral of (sqrt(x^2-324))/x	\int\:\frac{\sqrt{x^{2}-324}}{x}dx
derivative of 3cos(x+4x^2)	\frac{d}{dx}(3\cos(x)+4x^{2})
x^4+5y^4sqrt(x^5+4)y^'=0,y(0)=1	x^{4}+5y^{4}\sqrt{x^{5}+4}y^{\prime\:}=0,y(0)=1
integral of (4x^4-5x^2)/((x+3)(x-2))	\int\:\frac{4x^{4}-5x^{2}}{(x+3)(x-2)}dx
integral of xsin(n)x	\int\:x\sin(n)xdx
limit as n approaches 2 of (n-1)/(n^2-1)	\lim\:_{n\to\:2}(\frac{n-1}{n^{2}-1})
derivative of x^3-3x^2-9x+5	\frac{d}{dx}(x^{3}-3x^{2}-9x+5)
integral of (-1)/4 sin(2x)	\int\:\frac{-1}{4}\sin(2x)dx
limit as x approaches 0 of ln(x)+1	\lim\:_{x\to\:0}(\ln(x)+1)
derivative of (log_{e}(x)^2)	\frac{d}{dx}((\log_{e}(x))^{2})
integral of 70sin^4(x)cos^3(x)	\int\:70\sin^{4}(x)\cos^{3}(x)dx
integral from 1 to 2 of 4x^2	\int\:_{1}^{2}4x^{2}dx
limit as x approaches 5-of f(x)	\lim\:_{x\to\:5-}(f(x))
derivative of ln((x^3-4/x))	\frac{d}{dx}(\ln(\frac{x^{3}-4}{x}))
limit as x approaches 0 of (ln(x))/(x+1)	\lim\:_{x\to\:0}(\frac{\ln(x)}{x+1})
tangent of f(x)=(7x)/(x-3),\at x=6	tangent\:f(x)=\frac{7x}{x-3},\at\:x=6
derivative of 2+5tan^{-1}(x/2)	derivative\:2+5\tan^{-1}(\frac{x}{2})
integral of (9e^x-9sqrt(x))	\int\:(9e^{x}-9\sqrt{x})dx
derivative of x^3e^{6x^3+8x^2-7}	derivative\:x^{3}e^{6x^{3}+8x^{2}-7}
derivative of arcsin(x^3)	\frac{d}{dx}(\arcsin(x^{3}))
derivative of f(x)=(f(x))/(x^2+2)	derivative\:f(x)=\frac{f(x)}{x^{2}+2}
integral from 1 to 16 of 4/(sqrt(x))	\int\:_{1}^{16}\frac{4}{\sqrt{x}}dx
limit as x approaches 0 of (2x)/(x^2-5x)	\lim\:_{x\to\:0}(\frac{2x}{x^{2}-5x})
(\partial)/(\partial x)(4xln(x)y)	\frac{\partial\:}{\partial\:x}(4x\ln(x)y)
integral of (2x+y)^8	\int\:(2x+y)^{8}dx
limit as x approaches 0+of (x)^{-x^2}	\lim\:_{x\to\:0+}((x)^{-x^{2}})
d/(ds)(s/(s^2+b^2))	\frac{d}{ds}(\frac{s}{s^{2}+b^{2}})
inverse oflaplace te^{2t}	inverselaplace\:te^{2t}
y^{''}+5y^'+4y=sin(3x)	y^{\prime\:\prime\:}+5y^{\prime\:}+4y=\sin(3x)
(\partial)/(\partial x)(xy+x^2)	\frac{\partial\:}{\partial\:x}(xy+x^{2})
9(x^2+y^2)dx+7xydy=0	9(x^{2}+y^{2})dx+7xydy=0
sum from n=1 to infinity of (64)/(n^3)	\sum\:_{n=1}^{\infty\:}\frac{64}{n^{3}}
integral of (6x^2-3x+1)/((4x+1)(x^2+1))	\int\:\frac{6x^{2}-3x+1}{(4x+1)(x^{2}+1)}dx
derivative of y=2^{3x^2}	derivative\:y=2^{3x^{2}}
integral of ((cos^5(t)))/(sqrt(sin(t)))	\int\:\frac{(\cos^{5}(t))}{\sqrt{\sin(t)}}dt
limit as x approaches a of (f(x))/(g(x))	\lim\:_{x\to\:a}(\frac{f(x)}{g(x)})
derivative of 2cos(x/2+pi)	\frac{d}{dx}(2\cos(\frac{x}{2})+π)
sum from n=0 to infinity of (-5/9)^n	\sum\:_{n=0}^{\infty\:}(-\frac{5}{9})^{n}
integral from 2 to 7 of x^2	\int\:_{2}^{7}x^{2}dx
derivative of y=xe^x-e^x	derivative\:y=xe^{x}-e^{x}
integral of x^7sqrt(x^4+5)	\int\:x^{7}\sqrt{x^{4}+5}dx
integral from ln(2) to 3 of 5e^x	\int\:_{\ln(2)}^{3}5e^{x}dx
integral from-pi to pi of \|x\|	\int\:_{-π}^{π}\left\|x\right\|dx
(\partial)/(\partial x)(1/((1+x^2+y^2)))	\frac{\partial\:}{\partial\:x}(\frac{1}{(1+x^{2}+y^{2})})
derivative of f(x)=(2x)/(1+x^2)	derivative\:f(x)=\frac{2x}{1+x^{2}}
(\partial)/(\partial x)((4x^3)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{4x^{3}}{x^{2}+y^{2}})
(dy)/(dx)=sqrt(9y)e^{x+9}	\frac{dy}{dx}=\sqrt{9y}e^{x+9}
(\partial)/(\partial x)(1/(2sqrt(x)))	\frac{\partial\:}{\partial\:x}(\frac{1}{2\sqrt{x}})

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