Recent questions and answers in Calculus - GO Mechanical

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GATE2019 ME-2: 4
An analytic function $f(z)$ of complex variable $z=x+iy$ may be written as $f(z)=u(x,y)+iv(x,y)$. Then $u(x,y)$ and $v(x,y)$ ...

answered May 24, 2019 in Calculus by ankitgupta.1729 (410 points)

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GATE2019 ME-2: 2
The directional derivative of the function $f(x,y)=x^2+y^2$ along a line directed from $(0,0)$ to $(1,1)$, evaluated at the point $x=1, y=1$ is $\sqrt{2}$ $2$ $2 \sqrt{2}$ $4 \sqrt{2}$

asked Feb 9, 2019 in Calculus by Arjun (21.2k points)

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GATE2018-2-28
For a position vector $\overrightarrow{r} = x \hat{i}+y \hat{j} + z\hat{k}$ the norm of the vector can be defined as $\mid \overrightarrow{r} \mid = \sqrt{x^2+y^2+z^2}$. Given a function $\phi =\text{ln} \mid \overrightarrow{r} \mid$, its ... $\frac{\overrightarrow{r}}{\overrightarrow{r} \cdot \overrightarrow{r} } \\ $ $\frac{\overrightarrow{r}}{\mid \overrightarrow{r} \mid^3} $

asked Feb 17, 2018 in Calculus by Arjun (21.2k points)

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GATE2018-2-2
The divergence of the vector field $\overrightarrow{u}=e^x(\cos \: y\hat{i}+\sin \: y \hat{j})$ is $0$ $e^x \cos y + e^x \sin y$ $2e^x \cos y$ $2e^x \sin y$

asked Feb 17, 2018 in Calculus by Arjun (21.2k points)

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GATE2018-2-1
The Fourier cosine series for an even function $f(x)$ is given by $ f(x)=a_0 + \Sigma_{n=1}^\infty a_n \cos (nx).$ The value of the coefficient $a_2$ for the function $f(x)=\cos ^2 (x)$ in $[0, \pi]$ is $-0.5$ $0.0$ $0.5$ $1.0$

asked Feb 17, 2018 in Calculus by Arjun (21.2k points)

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GATE2018-1-3
According to the Mean Value Theorem, for a continuous function $f(x)$ in the interval $[a,b]$, there exists a value $\xi$ in this interval such that $\int_a^b f(x) dx = $ $f(\xi)(b-a)$ $f(b)(\xi-a)$ $f(a)(b-\xi)$ $0$

asked Feb 17, 2018 in Calculus by Arjun (21.2k points)

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GATE2018-1-4
$F(z)$ is a function of the complex variable $z=x+iy$ given by $F(z)+ i \: z + k \: Re(z) + i \: Im(z)$. For what value of $k$ will $F(z)$ satisfy the Cauchy-Riemann equations? $0$ $1$ $-1$ $y$

asked Feb 17, 2018 in Calculus by Arjun (21.2k points)

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GATE2017 ME-2: 5
The Laplace transform of $te^{t}$ is $\frac{s}{(s+1)^{2}}$ $\frac{1}{(s-1)^{2}}$ $\frac{1}{(s+1)^{2}}$ $\frac{s}{(s-1)}$

asked Feb 27, 2017 in Calculus by Arjun (21.2k points)

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GATE2017 ME-1: 2
The value of $\lim_{x \rightarrow 0}\frac{x^{3}-\sin(x)}{x}$ is $0$ $3$ $1$ $-1$

asked Feb 27, 2017 in Calculus by Arjun (21.2k points)

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