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Popular Calculus Problems

limit as x approaches 4-of (\|4-x\|)/(x-4)	\lim\:_{x\to\:4-}(\frac{\left\|4-x\right\|}{x-4})
limit as x approaches 1 of 3	\lim\:_{x\to\:1}(3)
y^'-2xy=6x	y^{\prime\:}-2xy=6x
derivative of 4x^3+2x	derivative\:4x^{3}+2x
y^'=ay-by^3	y^{\prime\:}=ay-by^{3}
area x^3,x^{1/3},[0,2]	area\:x^{3},x^{\frac{1}{3}},[0,2]
(\partial)/(\partial x)((xy^2)/(t+2z))	\frac{\partial\:}{\partial\:x}(\frac{xy^{2}}{t+2z})
limit as x approaches 0 of cot(x)-1/x	\lim\:_{x\to\:0}(\cot(x)-\frac{1}{x})
derivative of (x-1/(x+3))	\frac{d}{dx}(\frac{x-1}{x+3})
11(t+1)(dy)/(dt)-8y=24t,y(0)=16	11(t+1)\frac{dy}{dt}-8y=24t,y(0)=16
integral of 2e^{5x+e^{5x}}	\int\:2e^{5x+e^{5x}}dx
integral of sin(2pix)	\int\:\sin(2πx)dx
derivative of 3x^2-6x+10	\frac{d}{dx}(3x^{2}-6x+10)
sqrt(1-2x)y^'=(4+y^2)	\sqrt{1-2x}y^{\prime\:}=(4+y^{2})
derivative of g(x)=5	derivative\:g(x)=5
derivative of e^{7sqrt(x)}	derivative\:e^{7\sqrt{x}}
derivative of f(x)=ln(324sin^2(x))	derivative\:f(x)=\ln(324\sin^{2}(x))
integral of e^{-9t}	\int\:e^{-9t}dt
tangent of f(x)=(5x)/(x+2),\at x=3	tangent\:f(x)=\frac{5x}{x+2},\at\:x=3
integral from 0 to 1 of e^t	\int\:_{0}^{1}e^{t}dt
integral of p(p+8)^5	\int\:p(p+8)^{5}dp
sum from n=1 to infinity of 0.75*0.5^{n-1}	\sum\:_{n=1}^{\infty\:}0.75\cdot\:0.5^{n-1}
integral of e^{(2x)}	\int\:e^{(2x)}dx
(\partial)/(\partial y)(x^2-2xy+3y^2)	\frac{\partial\:}{\partial\:y}(x^{2}-2xy+3y^{2})
integral of sin^3(2x)cos^6(2x)	\int\:\sin^{3}(2x)\cos^{6}(2x)dx
area x=4sqrt(y),x=0,y=4	area\:x=4\sqrt{y},x=0,y=4
derivative of (e^x)/(2x^2)	derivative\:\frac{e^{x}}{2x^{2}}
derivative of sqrt(x/(x-1))	\frac{d}{dx}(\sqrt{\frac{x}{x-1}})
expand (x^5+2x)*(x^3+x^2+x+7)	expand\:(x^{5}+2x)\cdot\:(x^{3}+x^{2}+x+7)
integral of e^{-x}*cos(wx)	\int\:e^{-x}\cdot\:\cos(wx)dx
y^{''}+y^'+y=0,y(0)=1,y^'(0)=-1	y^{\prime\:\prime\:}+y^{\prime\:}+y=0,y(0)=1,y^{\prime\:}(0)=-1
(\partial)/(\partial x)(ln(x^4+y^3))	\frac{\partial\:}{\partial\:x}(\ln(x^{4}+y^{3}))
derivative of-(2x/((2+x^2)^2))	\frac{d}{dx}(-\frac{2x}{(2+x^{2})^{2}})
limit as x approaches 1 of 2x-x^2-x^3	\lim\:_{x\to\:1}(2x-x^{2}-x^{3})
(\partial)/(\partial x)(2x^2-4)	\frac{\partial\:}{\partial\:x}(2x^{2}-4)
(\partial)/(\partial x)(sqrt(1+xy))	\frac{\partial\:}{\partial\:x}(\sqrt{1+xy})
slope of (5.12)(-3.4)	slope\:(5.12)(-3.4)
((dy)/(dx))=(x-y^2)/(2xy+y)	(\frac{dy}{dx})=\frac{x-y^{2}}{2xy+y}
tangent of 2/(x-2)	tangent\:\frac{2}{x-2}
y^'+e^{-x}y=e^{e-x}	y^{\prime\:}+e^{-x}y=e^{e-x}
integral from 0 to 4 of sqrt(x)-1/2 x	\int\:_{0}^{4}\sqrt{x}-\frac{1}{2}xdx
tangent of f(x)=4x-x^2,\at x=0	tangent\:f(x)=4x-x^{2},\at\:x=0
derivative of 1-cos(x/2)	\frac{d}{dx}(1-\cos(\frac{x}{2}))
derivative of 261e^{0,5x}+27.464	\frac{d}{dx}(261e^{0,5x}+27.464)
derivative of e^{x{f}(x})	\frac{d}{dx}(e^{x{f}(x)})
derivative of e^{-4x}cos^4(3x)	\frac{d}{dx}(e^{-4x}\cos^{4}(3x))
integral of sec(t)(4sec(t)+3tan(t))	\int\:\sec(t)(4\sec(t)+3\tan(t))dt
integral of 3/(y-3)	\int\:\frac{3}{y-3}dy
(\partial)/(\partial y)(yln(x^2+y^3+5))	\frac{\partial\:}{\partial\:y}(y\ln(x^{2}+y^{3}+5))
integral of (4-32x)/(sqrt(9-16x^2))	\int\:\frac{4-32x}{\sqrt{9-16x^{2}}}dx
derivative of sqrt(5+cot^2(x))	\frac{d}{dx}(\sqrt{5+\cot^{2}(x)})
integral of \sqrt{x	\int\:\sqrt{d}xdx
integral from 0 to 2 of pi(4-x^2)^2	\int\:_{0}^{2}π(4-x^{2})^{2}dx
derivative of ((x^2+4x+3)/(sqrt(x)))	\frac{d}{dx}(\frac{(x^{2}+4x+3)}{\sqrt{x}})
integral of (1/(x^2)+sqrt(x))	\int\:(\frac{1}{x^{2}}+\sqrt{x})dx
sum from n=1 to infinity of 8(-1)^nnx^n	\sum\:_{n=1}^{\infty\:}8(-1)^{n}nx^{n}
integral of x/((1+x^2))	\int\:\frac{x}{(1+x^{2})}dx
integral of (x+3)/(x^2+6x^4)	\int\:\frac{x+3}{x^{2}+6x^{4}}dx
integral of 10xln(3x)	\int\:10x\ln(3x)dx
integral of cos(θ)sin(θ)	\int\:\cos(θ)\sin(θ)dθ
integral from-infinity to infinity of 57cos(pit)	\int\:_{-\infty\:}^{\infty\:}57\cos(πt)dt
y^'=2xy^2+3x^2y^2,y(1)=-1	y^{\prime\:}=2xy^{2}+3x^{2}y^{2},y(1)=-1
taylor ((x^2-x+1))/(x+1)	taylor\:\frac{(x^{2}-x+1)}{x+1}
integral of 2sqrt(a)sqrt(x)	\int\:2\sqrt{a}\sqrt{x}dx
(\partial)/(\partial x)(e^{-x^8-x^4})	\frac{\partial\:}{\partial\:x}(e^{-x^{8}-x^{4}})
limit as x approaches-2 of (x+2)/(4-x^2)	\lim\:_{x\to\:-2}(\frac{x+2}{4-x^{2}})
(\partial)/(\partial x)(((3x-y))/((x+2y)))	\frac{\partial\:}{\partial\:x}(\frac{(3x-y)}{(x+2y)})
integral of (7x^2+2x-7)/(x^3-x)	\int\:\frac{7x^{2}+2x-7}{x^{3}-x}dx
tangent of f(x)=2x^2+x-1,\at x=-1	tangent\:f(x)=2x^{2}+x-1,\at\:x=-1
(dy)/(dx)+y=y^2	\frac{dy}{dx}+y=y^{2}
integral of x*e^{1-x^2}	\int\:x\cdot\:e^{1-x^{2}}dx
integral of ((e^x+1)^2)/(e^x)	\int\:\frac{(e^{x}+1)^{2}}{e^{x}}dx
derivative of x^{ln(x)}	derivative\:x^{\ln(x)}
sum from n=1 to infinity of 3/(n^2+1)	\sum\:_{n=1}^{\infty\:}\frac{3}{n^{2}+1}
derivative of (sqrt(1-x)/(sqrt(x)))	\frac{d}{dx}(\frac{\sqrt{1-x}}{\sqrt{x}})
inverse oflaplace {(s+1)/(s^2+2)}	inverselaplace\:\left\{\frac{s+1}{s^{2}+2}\right\}
integral from 1 to 3 of ln(x-1)	\int\:_{1}^{3}\ln(x-1)dx
sum from n=1 to infinity of cos(2n)	\sum\:_{n=1}^{\infty\:}\cos(2n)
area y=x^2-1,y=x+2,x=0,x+1	area\:y=x^{2}-1,y=x+2,x=0,x+1
limit as x approaches-1 of 5-3x-x^2	\lim\:_{x\to\:-1}(5-3x-x^{2})
slope ofintercept (3.1)(0)	slopeintercept\:(3.1)(0)
derivative of (x^3+1^2)	\frac{d}{dx}((x^{3}+1)^{2})
derivative of y=(4-3x^2)^3	derivative\:y=(4-3x^{2})^{3}
y^'+2y=10	y^{\prime\:}+2y=10
derivative of 1/27 (2x-1^3(6-3x)+1)	\frac{d}{dx}(\frac{1}{27}(2x-1)^{3}(6-3x)+1)
integral from 0 to pi/4 of sin(4x)	\int\:_{0}^{\frac{π}{4}}\sin(4x)dx
inverse oflaplace (-3)/((s-1)^2)	inverselaplace\:\frac{-3}{(s-1)^{2}}
derivative of f(x)=(x^3)/3+4x^2+12x+19	derivative\:f(x)=\frac{x^{3}}{3}+4x^{2}+12x+19
integral of-xcos(x)	\int\:-x\cos(x)dx
(\partial)/(\partial x)(Ae^{-3x})	\frac{\partial\:}{\partial\:x}(Ae^{-3x})
y^{''}-4y^'+13y=0,y(0)=-1,y^'(0)=-5	y^{\prime\:\prime\:}-4y^{\prime\:}+13y=0,y(0)=-1,y^{\prime\:}(0)=-5
derivative of f(x)=arccos(e^{2x})	derivative\:f(x)=\arccos(e^{2x})
area x^3-8x^2+12x,-x^3+8x^2-12x	area\:x^{3}-8x^{2}+12x,-x^{3}+8x^{2}-12x
derivative of y= 7/(sqrt((1-x^2)^3))	derivative\:y=\frac{7}{\sqrt{(1-x^{2})^{3}}}
(\partial)/(\partial x)(1/(x^4))	\frac{\partial\:}{\partial\:x}(\frac{1}{x^{4}})
e^x(y-1)dx+2(e^x+4)dy=0	e^{x}(y-1)dx+2(e^{x}+4)dy=0
taylor sqrt(x),4	taylor\:\sqrt{x},4
derivative of 3/(x^4+7x+1)	derivative\:\frac{3}{x^{4}+7x+1}
y^'=3sqrt(xy)	y^{\prime\:}=3\sqrt{xy}
derivative of (7+2x)/(1-6x)	derivative\:\frac{7+2x}{1-6x}

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