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Recent questions and answers in Calculus
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GATE2017 EC2: 26
The values of the integrals $\int_{0}^{1}\left ( \int_{0}^{1}\frac{xy}{(x+y)^3}dy \right )dx$ and $\int_{0}^{1}\left ( \int_{0}^{1}\frac{xy}{(x+y)^3}dx \right )dy$ are same and equal to 0.5 same and equal to 0.5 0.5 and 0.5, respectively 0.5 and 0.5, respectively
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GATE2017 EC1: 27
A three dimensional region $R$ of finite volume is described by $x^{2}+y^{2}\leq z^{3};0\leq z\leq 1$ where, $x,y,z$ are real.The volume of $R$ (up to two decimal places) is ________.
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Nov 17, 2017
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gate2017ec1
volumeintegrals
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GATE2017 EC1: 26
Let $f(x)=e^{x+x^{2}}$ for real $x$ .From among the following ,choose the Taylor series approximation of $f(x)$ around $x=0$, which includes all powers of $x$ less than or equal to 3. $1 + x + x^{2} + x^{3} $ $1 + x +\frac{3}{2} x^{2} + x^{3} $ $1 + x +\frac{3}{2} x^{2} + \frac{7}{6}x^{3} $ $1 + x +3 x^{2} + 7x^{3} $
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gate2017ec1
taylorseries
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