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Popular Calculus Problems

limit as x approaches 2+of 4/((x-2)^3)	\lim\:_{x\to\:2+}(\frac{4}{(x-2)^{3}})
derivative of 3x^{1/3}+2x^2	\frac{d}{dx}(3x^{\frac{1}{3}}+2x^{2})
integral of e^{3x}sin(e^x)	\int\:e^{3x}\sin(e^{x})dx
derivative of sqrt(x)+1/(\sqrt[3]{x})	\frac{d}{dx}(\sqrt{x}+\frac{1}{\sqrt[3]{x}})
limit as x approaches-infinity of 2^x	\lim\:_{x\to\:-\infty\:}(2^{x})
limit as n approaches infinity of ((-1)^{n+1})/((n+3)*n!)	\lim\:_{n\to\:\infty\:}(\frac{(-1)^{n+1}}{(n+3)\cdot\:n!})
integral of x^3sqrt(x^2-8)	\int\:x^{3}\sqrt{x^{2}-8}dx
integral of e^{3x}sin(2x)	\int\:e^{3x}\sin(2x)dx
sum from n=3 to infinity of e^{3-6n}	\sum\:_{n=3}^{\infty\:}e^{3-6n}
(\partial)/(\partial x)(e^{x+y}-1)	\frac{\partial\:}{\partial\:x}(e^{x+y}-1)
integral of (e^{-2x})/(e^x)	\int\:\frac{e^{-2x}}{e^{x}}dx
limit as x approaches-2 of (2+\|x\|)/(2+x)	\lim\:_{x\to\:-2}(\frac{2+\left\|x\right\|}{2+x})
limit as x approaches 0 of (x^4)/x	\lim\:_{x\to\:0}(\frac{x^{4}}{x})
limit as x approaches 3/7 of (\|3-7x\|)/(21x^2-9x)	\lim\:_{x\to\:\frac{3}{7}}(\frac{\left\|3-7x\right\|}{21x^{2}-9x})
area y=sin^2(x),y=sin^3(x),[0,pi]	area\:y=\sin^{2}(x),y=\sin^{3}(x),[0,π]
derivative of 1/(\sqrt[4]{x})	\frac{d}{dx}(\frac{1}{\sqrt[4]{x}})
sum from n=0 to infinity of (x+1)^n	\sum\:_{n=0}^{\infty\:}(x+1)^{n}
derivative of 2xy^4-3	\frac{d}{dx}(2xy^{4}-3)
(\partial)/(\partial x)(2x^3y+sin(x^3))	\frac{\partial\:}{\partial\:x}(2x^{3}y+\sin(x^{3}))
integral of (2x^2+3x)^3	\int\:(2x^{2}+3x)^{3}dx
derivative of y=(f(x))/(x^5)	derivative\:y=\frac{f(x)}{x^{5}}
derivative of 2tan^2(7x)	derivative\:2\tan^{2}(7x)
(2xy+3)dx+(x^2-1)dy=0	(2xy+3)dx+(x^{2}-1)dy=0
3xy^'+7y=0	3xy^{\prime\:}+7y=0
derivative of (e^{10x}+e^{-10x})/x	derivative\:\frac{e^{10x}+e^{-10x}}{x}
derivative of 2(ln(x))	\frac{d}{dx}(2(\ln(x)))
integral from 0 to 1.5 of (3/2-x)^2	\int\:_{0}^{1.5}(\frac{3}{2}-x)^{2}dx
y^{''}-8y^'+16y=t^{-8}e^{4t}	y^{\prime\:\prime\:}-8y^{\prime\:}+16y=t^{-8}e^{4t}
integral of (cos^4(x)sin(x))	\int\:(\cos^{4}(x)\sin(x))dx
integral of (x^2+1)(x^3+3x)^4	\int\:(x^{2}+1)(x^{3}+3x)^{4}dx
integral of (2x+5)/(sqrt(x^2+5x))	\int\:\frac{2x+5}{\sqrt{x^{2}+5x}}dx
derivative of f(x)=sqrt(7+\sqrt{5x)}	derivative\:f(x)=\sqrt{7+\sqrt{5x}}
y^'=k*y	y^{\prime\:}=k\cdot\:y
derivative of ((3t-1))/(sqrt(t)-2)	derivative\:\frac{(3t-1)}{\sqrt{t}-2}
tangent of y=(4x)/(x+2)	tangent\:y=\frac{4x}{x+2}
derivative of ln(4xy)	\frac{d}{dx}(\ln(4xy))
derivative of (18)/(x^4)	derivative\:\frac{18}{x^{4}}
f(x)= x/((1+x^2))	f(x)=\frac{x}{(1+x^{2})}
derivative of (x^2-3x+2)^5	derivative\:(x^{2}-3x+2)^{5}
integral of x^{12}e^{x^{13}}	\int\:x^{12}e^{x^{13}}dx
tangent of f(x)=x^2-9,(-2,-5)	tangent\:f(x)=x^{2}-9,(-2,-5)
integral of (x^3)/(x^4+5)	\int\:\frac{x^{3}}{x^{4}+5}dx
derivative of 1/(x(8+ln(x)))	\frac{d}{dx}(\frac{1}{x(8+\ln(x))})
limit as x approaches-3 of (x+2)/(x+3)	\lim\:_{x\to\:-3}(\frac{x+2}{x+3})
limit as x approaches-3 of (x-2)/(x+5)	\lim\:_{x\to\:-3}(\frac{x-2}{x+5})
derivative of x^{1/2}y^{1/2}	\frac{d}{dx}(x^{\frac{1}{2}}y^{\frac{1}{2}})
limit as x approaches 8 of x^3-6x+5	\lim\:_{x\to\:8}(x^{3}-6x+5)
tangent of 1/(x^2),\at x=3	tangent\:\frac{1}{x^{2}},\at\:x=3
(dy)/(dx)3x^3+3y^3-5xy=0	\frac{dy}{dx}3x^{3}+3y^{3}-5xy=0
integral of t/(sqrt(at^2+b))	\int\:\frac{t}{\sqrt{at^{2}+b}}dt
(d^2)/(dx^2)(3e^xcos(x))	\frac{d^{2}}{dx^{2}}(3e^{x}\cos(x))
slope of (-3,2),(6,3)	slope\:(-3,2),(6,3)
integral of 30arctan(sqrt(x))	\int\:30\arctan(\sqrt{x})dx
laplacetransform 2sin(3t)	laplacetransform\:2\sin(3t)
limit as x approaches 1 of ax+b	\lim\:_{x\to\:1}(ax+b)
integral of 1/(xe^{-x)}	\int\:\frac{1}{xe^{-x}}dx
derivative of (5x^3+3(x^4-2x))	\frac{d}{dx}((5x^{3}+3)(x^{4}-2x))
laplacetransform te^{2t}sin(t)	laplacetransform\:te^{2t}\sin(t)
(dy)/(dx)+2y=e^{-x}	\frac{dy}{dx}+2y=e^{-x}
taylor X^3-X^2+4X+5	taylor\:X^{3}-X^{2}+4X+5
tangent of f(x)=(125)/(x^2+24),\at x=-1	tangent\:f(x)=\frac{125}{x^{2}+24},\at\:x=-1
integral of 1/(2x^2-4x+20)	\int\:\frac{1}{2x^{2}-4x+20}dx
(\partial)/(\partial x)(x^2e^{yz^2})	\frac{\partial\:}{\partial\:x}(x^{2}e^{yz^{2}})
limit as x approaches-3.1 of x^2	\lim\:_{x\to\:-3.1}(x^{2})
(dy)/(dx)=(xsqrt(x^2-y^2)+y^2)/(xy)	\frac{dy}{dx}=\frac{x\sqrt{x^{2}-y^{2}}+y^{2}}{xy}
integral of sin((xy)/2)	\int\:\sin(\frac{xy}{2})dy
limit as x approaches 0 of (cos(x))/(5x)	\lim\:_{x\to\:0}(\frac{\cos(x)}{5x})
d/(dt)(3cos(2t))	\frac{d}{dt}(3\cos(2t))
integral of (x^3-(x-1)^2)/x	\int\:\frac{x^{3}-(x-1)^{2}}{x}dx
limit as x approaches 1 of 4x-1	\lim\:_{x\to\:1}(4x-1)
derivative of 100x^2-26xe^x	\frac{d}{dx}(100x^{2}-26xe^{x})
derivative of log_{10}(3x+4)	\frac{d}{dx}(\log_{10}(3x+4))
(\partial)/(\partial x)(tan(xy)+ye^{3x})	\frac{\partial\:}{\partial\:x}(\tan(xy)+ye^{3x})
y^'+y=e^{-t}sin(t)	y^{\prime\:}+y=e^{-t}\sin(t)
derivative of cos(t)	derivative\:\cos(t)
(\partial)/(\partial x)((4x^4y^2+9)^2)	\frac{\partial\:}{\partial\:x}((4x^{4}y^{2}+9)^{2})
integral of (1+e^x)/(1-e^x)	\int\:\frac{1+e^{x}}{1-e^{x}}dx
limit as h approaches 0 of ((7+h)-7)/h	\lim\:_{h\to\:0}(\frac{(7+h)-7}{h})
integral of (x+1)/(sqrt(x+1))	\int\:\frac{x+1}{\sqrt{x+1}}dx
laplacetransform t^2(8e^{2t}-6sin(t))	laplacetransform\:t^{2}(8e^{2t}-6\sin(t))
limit as x approaches 0 of (1+4x)^{4/x}	\lim\:_{x\to\:0}((1+4x)^{\frac{4}{x}})
(\partial}{\partial x}((2t)/((1-\frac{0.5(x))/L)^2))	\frac{\partial\:}{\partial\:x}(\frac{2t}{(1-\frac{0.5(x)}{L})^{2}})
derivative of 1/(csc(x+cot(x)))	\frac{d}{dx}(\frac{1}{\csc(x)+\cot(x)})
derivative of 2arcsin(x^3)	derivative\:2\arcsin(x^{3})
derivative of 10e^{-2x}	\frac{d}{dx}(10e^{-2x})
derivative of h(t)=(t+5)^{2/3}(3t^2-5)^3	derivative\:h(t)=(t+5)^{\frac{2}{3}}(3t^{2}-5)^{3}
limit as x approaches 9 of 5/((x-9))	\lim\:_{x\to\:9}(\frac{5}{(x-9)})
7yy^'=x	7yy^{\prime\:}=x
limit as x approaches (a+1) of x^2-1	\lim\:_{x\to\:(a+1)}(x^{2}-1)
derivative of 3/2 x	\frac{d}{dx}(\frac{3}{2}x)
laplacetransform cos(3t-1)	laplacetransform\:\cos(3t-1)
y^{''}+7y^'+10y=-11te^{2t}	y^{\prime\:\prime\:}+7y^{\prime\:}+10y=-11te^{2t}
integral of (4x+1)^3	\int\:(4x+1)^{3}dx
derivative of-sec(1/x+7x)	derivative\:-\sec(\frac{1}{x}+7x)
(\partial)/(\partial x)(7e^{xy})	\frac{\partial\:}{\partial\:x}(7e^{xy})
derivative of \sqrt[3]{x}tan(5x)	\frac{d}{dx}(\sqrt[3]{x}\tan(5x))
derivative of (sqrt(x)/(ln(x)))	\frac{d}{dx}(\frac{\sqrt{x}}{\ln(x)})
integral of (\sqrt[3]{x^4})	\int\:(\sqrt[3]{x^{4}})dx
4t((dy)/(dt))-y=sqrt(t)	4t(\frac{dy}{dt})-y=\sqrt{t}
integral of 1/(sqrt(144+x^2))	\int\:\frac{1}{\sqrt{144+x^{2}}}dx

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