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Popular Calculus Problems

limit as x approaches 7-of (2x+1)/(x-7)	\lim\:_{x\to\:7-}(\frac{2x+1}{x-7})
limit as x approaches infinity of 1.07^x	\lim\:_{x\to\:\infty\:}(1.07^{x})
laplacetransform 3sin(t)-3cos(t)	laplacetransform\:3\sin(t)-3\cos(t)
tangent of f(x)=(4+x)/(x-2),\at x=8	tangent\:f(x)=\frac{4+x}{x-2},\at\:x=8
xyy^'=x^2+3y^2	xyy^{\prime\:}=x^{2}+3y^{2}
area 3x,xsqrt(64-x^2)	area\:3x,x\sqrt{64-x^{2}}
integral of x^{7/8}	\int\:x^{\frac{7}{8}}dx
derivative of (4x^2+72x)/(x-2)	derivative\:\frac{4x^{2}+72x}{x-2}
integral of pisin(pi)θ	\int\:π\sin(π)θdθ
limit as x approaches 0 of (tan(4x))^x	\lim\:_{x\to\:0}((\tan(4x))^{x})
y^{''}+4y^'+7y=0	y^{\prime\:\prime\:}+4y^{\prime\:}+7y=0
(\partial)/(\partial x)(xln(y+x))	\frac{\partial\:}{\partial\:x}(x\ln(y+x))
y^'=e(-2t)-y	y^{\prime\:}=e(-2t)-y
derivative of f(x)=(x^3+5x^2-3)sqrt(x)	derivative\:f(x)=(x^{3}+5x^{2}-3)\sqrt{x}
(cos(3x))^'	(\cos(3x))^{\prime\:}
derivative of e^x-1-x	\frac{d}{dx}(e^{x}-1-x)
(dy)/(dx)=e^{-x^2}	\frac{dy}{dx}=e^{-x^{2}}
integral of sech^6(x)tanh(x)	\int\:\sech^{6}(x)\tanh(x)dx
(\partial)/(\partial x)((x-y)/(x^2+y+1))	\frac{\partial\:}{\partial\:x}(\frac{x-y}{x^{2}+y+1})
integral from 0 to 3 of (2-x)e^x	\int\:_{0}^{3}(2-x)e^{x}dx
inverse oflaplace 8/((s+1)^2(s+2))	inverselaplace\:\frac{8}{(s+1)^{2}(s+2)}
integral of 1/((x-4)(x-1))	\int\:\frac{1}{(x-4)(x-1)}dx
integral from 2 to 3 of 7/(sqrt(3-x))	\int\:_{2}^{3}\frac{7}{\sqrt{3-x}}dx
derivative of ((sqrt(x^2-3x-4))/x)	\frac{d}{dx}(\frac{(\sqrt{x^{2}-3x-4})}{x})
limit as x approaches 0 of e^{ax}	\lim\:_{x\to\:0}(e^{ax})
derivative of (sqrt(t))/(2t-9)	derivative\:\frac{\sqrt{t}}{2t-9}
derivative of (6x^2+5)^3	derivative\:(6x^{2}+5)^{3}
derivative of x+2cos(x)	\frac{d}{dx}(x+2\cos(x))
integral of sec(3θ)tan(3θ)	\int\:\sec(3θ)\tan(3θ)dθ
derivative of 3t	derivative\:3t
(\partial)/(\partial y)(-xe^{xy})	\frac{\partial\:}{\partial\:y}(-xe^{xy})
(\partial)/(\partial x)(6x^7y^6+2x^5y^8)	\frac{\partial\:}{\partial\:x}(6x^{7}y^{6}+2x^{5}y^{8})
limit as x approaches 3 of x^2-9	\lim\:_{x\to\:3}(x^{2}-9)
integral of sin(1/2 x)	\int\:\sin(\frac{1}{2}x)dx
3y^{''}+11y^'+6y=3x^2+7x+3	3y^{\prime\:\prime\:}+11y^{\prime\:}+6y=3x^{2}+7x+3
integral from 1 to 3 of (3x^2-7)/(x^3)	\int\:_{1}^{3}\frac{3x^{2}-7}{x^{3}}dx
(dP)/(dt)=kP^{1.01},P(0)=10	\frac{dP}{dt}=kP^{1.01},P(0)=10
y^{''}+2y^'+5y=6sin(2t)	y^{\prime\:\prime\:}+2y^{\prime\:}+5y=6\sin(2t)
(d^2)/(dx^2)(cos(5x))	\frac{d^{2}}{dx^{2}}(\cos(5x))
limit as x approaches 0 of (a^x-b^x)/x	\lim\:_{x\to\:0}(\frac{a^{x}-b^{x}}{x})
normal of y=2x^2,(-2,8)	normal\:y=2x^{2},(-2,8)
integral from 0 to 5 of (t^2+2t-15)	\int\:_{0}^{5}(t^{2}+2t-15)dt
limit as t approaches 0 of 5/t-5/(e^t-1)	\lim\:_{t\to\:0}(\frac{5}{t}-\frac{5}{e^{t}-1})
area y=x^2-1,x=-2,x=1	area\:y=x^{2}-1,x=-2,x=1
integral of sqrt(1+(4/(\sqrt[3]{x)))^2}	\int\:\sqrt{1+(\frac{4}{\sqrt[3]{x}})^{2}}dx
derivative of 3(4-9x^4)	\frac{d}{dx}(3(4-9x)^{4})
integral of (7e^{7x})/(1+e^{7x)}	\int\:\frac{7e^{7x}}{1+e^{7x}}dx
limit as x approaches 0 of (tan(12x))/(sin(4x))	\lim\:_{x\to\:0}(\frac{\tan(12x)}{\sin(4x)})
(\partial)/(\partial x)(ye^x-x^2y^{-3})	\frac{\partial\:}{\partial\:x}(ye^{x}-x^{2}y^{-3})
tangent of y=(4x)/(x^2+1),(0,0)	tangent\:y=\frac{4x}{x^{2}+1},(0,0)
limit as x approaches-1 of x^2-2x+3	\lim\:_{x\to\:-1}(x^{2}-2x+3)
derivative of-(cos^4(x)/4)	\frac{d}{dx}(-\frac{\cos^{4}(x)}{4})
integral of 1-e^{-2x}	\int\:1-e^{-2x}dx
sin(x)sec(y)dx=dy	\sin(x)\sec(y)dx=dy
integral of (-1)/(sqrt(1-x^2))	\int\:\frac{-1}{\sqrt{1-x^{2}}}dx
derivative of (1+x/x)	\frac{d}{dx}(\frac{1+x}{x})
derivative of (a-b/x ^2)	\frac{d}{dx}((a-\frac{b}{x})^{2})
derivative of (2.4)/(sqrt(5+1x))	derivative\:\frac{2.4}{\sqrt{5+1x}}
integral of x/(4-x)	\int\:\frac{x}{4-x}dx
derivative of y=ln(ln(8x))	derivative\:y=\ln(\ln(8x))
derivative of e^{(e^x)}	derivative\:e^{(e^{x})}
derivative of y=((x^2+4)/(x^2-4))^3	derivative\:y=(\frac{x^{2}+4}{x^{2}-4})^{3}
limit as x approaches 6-of x/(x-6)	\lim\:_{x\to\:6-}(\frac{x}{x-6})
integral of 1/((x+2)(x+2))	\int\:\frac{1}{(x+2)(x+2)}dx
derivative of f(x)=sin^5(x)	derivative\:f(x)=\sin^{5}(x)
d/(dt)(arcsin(sqrt(2t)))	\frac{d}{dt}(\arcsin(\sqrt{2t}))
derivative of (x^4/5)	\frac{d}{dx}(\frac{x^{4}}{5})
tangent of f(x)=-x^3-3x^2-3,\at x=-3	tangent\:f(x)=-x^{3}-3x^{2}-3,\at\:x=-3
limit as x approaches-1 of (x+2)/(x^2+x)	\lim\:_{x\to\:-1}(\frac{x+2}{x^{2}+x})
integral of (2.286x-2.5(x-3)-3(x-5))	\int\:(2.286x-2.5(x-3)-3(x-5))dx
derivative of-6e^{-x^2}x	derivative\:-6e^{-x^{2}}x
integral of sqrt(1/x)	\int\:\sqrt{\frac{1}{x}}dx
area y=x^2+4,y=7-2x^2	area\:y=x^{2}+4,y=7-2x^{2}
integral from 1/2 to 1 of (2y+3)/(y^2+y)	\int\:_{\frac{1}{2}}^{1}\frac{2y+3}{y^{2}+y}dy
y^{''}+9y=cos(3t)	y^{\prime\:\prime\:}+9y=\cos(3t)
derivative of ln(x^6+x^3-6)	\frac{d}{dx}(\ln(x^{6}+x^{3}-6))
integral of x^2*sqrt(1+x)	\int\:x^{2}\cdot\:\sqrt{1+x}dx
(\partial)/(\partial x)(-e^{8y}cos(8x)*8)	\frac{\partial\:}{\partial\:x}(-e^{8y}\cos(8x)\cdot\:8)
derivative of y=tan(pix)	derivative\:y=\tan(πx)
derivative of 2xe^{2y}-xcos(xy+2y)	\frac{d}{dx}(2xe^{2y}-x\cos(xy)+2y)
limit as x approaches-2 of sqrt(6-3x)-3	\lim\:_{x\to\:-2}(\sqrt{6-3x}-3)
integral of (x^3)/(xln(x))	\int\:\frac{x^{3}}{x\ln(x)}dx
limit as x approaches 0+of e^{1/x}	\lim\:_{x\to\:0+}(e^{\frac{1}{x}})
integral of e^{-3t}	\int\:e^{-3t}dt
(\partial)/(\partial x)(z*e^{xyz})	\frac{\partial\:}{\partial\:x}(z\cdot\:e^{xyz})
y^'=6xy^2	y^{\prime\:}=6xy^{2}
derivative of x^3(x-5^2)	\frac{d}{dx}(x^{3}(x-5)^{2})
5yy^'=x	5yy^{\prime\:}=x
limit as h approaches infinity of (5h^4-2h^2+3)/(3h^3+2h^2+h)	\lim\:_{h\to\:\infty\:}(\frac{5h^{4}-2h^{2}+3}{3h^{3}+2h^{2}+h})
integral of (x^2+y^2)^{(-3/2)}	\int\:(x^{2}+y^{2})^{(-\frac{3}{2})}dy
(dy)/(dx)=2x(1+y)e^{x^2}	\frac{dy}{dx}=2x(1+y)e^{x^{2}}
derivative of y=2x^2+1	derivative\:y=2x^{2}+1
derivative of ((x+1^3)/3+1/(4x+4))	\frac{d}{dx}(\frac{(x+1)^{3}}{3}+\frac{1}{4x+4})
derivative of 3x^2e^x	derivative\:3x^{2}e^{x}
integral of 2sin(x)+x	\int\:2\sin(x)+xdx
derivative of 5x+3/x	\frac{d}{dx}(5x+\frac{3}{x})
limit as x approaches 0 of sin(x)ln(3x)	\lim\:_{x\to\:0}(\sin(x)\ln(3x))
(1/4 x^8-3e^x+100ln(x))^'	(\frac{1}{4}x^{8}-3e^{x}+100\ln(x))^{\prime\:}
derivative of 0.0125x^2-1.15x+22.85	\frac{d}{dx}(0.0125x^{2}-1.15x+22.85)
limit as x approaches 0 of (e^{5x}-1)/(x^2)	\lim\:_{x\to\:0}(\frac{e^{5x}-1}{x^{2}})

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