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Recent questions and answers in Calculus
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votes
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GATE2019 ME2: 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
(
390
points)
gate2019me2
0
votes
0
answers
GATE2019 ME2: 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 $\sqrt{2}$ $2$ $2 \sqrt{2}$ $2 \sqrt{2}$
asked
Feb 9, 2019
in
Calculus
by
Arjun
(
21.2k
points)
gate2019me2
0
votes
0
answers
GATE2018228
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)
gate2018me2
0
votes
0
answers
GATE201822
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)
gate2018me2
0
votes
0
answers
GATE201821
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)
gate2018me2
0
votes
0
answers
GATE201813
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 = $ $f(\xi)(ba)$ $f(b)(\xia)$ $f(a)(b\xi)$ $0$
asked
Feb 17, 2018
in
Calculus
by
Arjun
(
21.2k
points)
gate2018me1
0
votes
0
answers
GATE201814
$F(z)$ 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 CauchyRiemann equations? $0$ $1$ $1$ $y$
asked
Feb 17, 2018
in
Calculus
by
Arjun
(
21.2k
points)
gate2018me1
0
votes
0
answers
GATE2017 ME2: 5
The Laplace transform of $te^{t}$ is $\frac{s}{(s+1)^{2}}$ $\frac{1}{(s1)^{2}}$ $\frac{1}{(s+1)^{2}}$ $\frac{s}{(s1)}$
asked
Feb 27, 2017
in
Calculus
by
Arjun
(
21.2k
points)
gate2017me2
0
votes
0
answers
GATE2017 ME1: 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)
gate2017me1
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