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Most viewed questions in Calculus
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GATE2016-1-28
The value of the integral $\displaystyle{\int_{-\infty }^{\infty }\frac{\sin x}{x^2+2x+2}}dx$ evaluated using contour integration and the residue theorem is $\displaystyle{\frac{-\pi \sin(1)}{e}}\\$ $\displaystyle{\frac{-\pi \cos (1)}{e}} \\$ $\displaystyle{\frac{\sin (1)}{e}} \\$ $\displaystyle{\frac{\cos (1)}{e}}$
The value of the integral $$\displaystyle{\int_{-\infty }^{\infty }\frac{\sin x}{x^2+2x+2}}dx$$ evaluated using contour integration and the residue theorem is$\displaysty...
Arjun
28.5k
points
Arjun
asked
Feb 24, 2017
Calculus
gateme-2016-set1
calculus
definite-integrals
+
–
1
answers
0
votes
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 $v(x,y)$ ...
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 $v(x,y)$ must satisfy$\dfrac{\partial u}{ \partial x} ...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set2
calculus
partial-derivatives
complex-variables
analytic-functions
+
–
0
answers
0
votes
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 ... $\dfrac{\overrightarrow{r}}{\overrightarrow{r} \cdot \overrightarrow{r} } \\ $ $\dfrac{\overrightarrow{r}}{\mid \overrightarrow{r} \mid^3} $
For a position vector $\overrightarrow{r} = x \hat{i}+y \hat{j} + z\hat{k}$ the norm of the vector can be defined as $\mid \overrightarrow{r} \mid = \sqrt{x^2+y^2+z^2}$. ...
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Calculus
gateme-2018-set2
calculus
vector-identities
+
–
0
answers
1
votes
GATE ME 2012 | Question: 54
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below. ... critical path for the project is $a-b-e-g-h$ $a-c-g-h$ $a-d-f-h$ $a-b-c-f-h$
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below.$\begi...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
+
–
1
answers
0
votes
GATE2019 ME-1: 51
The value of the following definite integral is __________ (round off to three decimal places) $\int_1^e (x \: \ln \: x) dx$
The value of the following definite integral is __________ (round off to three decimal places)$$\int_1^e (x \: \ln \: x) dx$$
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set1
numerical-answers
calculus
definite-integrals
+
–
0
answers
0
votes
GATE ME 2012 | Question: 55
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below. ... the project remain the same critical path changes but the total duration to complete the project changes to $17$ days
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below.$\begi...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
+
–
0
answers
0
votes
#MADE EASY MOCK TEST GATE2021
The area common to both circles r=a$\sqrt{2}$ and r=2a cos$\theta$.
The area common to both circles r=a$\sqrt{2}$ and r=2a cos$\theta$.
Gokulan K
160
points
Gokulan K
asked
Sep 3, 2020
Calculus
#made-easy
mock-gate
2021
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 26
The value of $\int_{0}^{^{\pi }/_{2}}\int_{0}^{\cos\theta }r\sin\theta \:dr\:d\theta$ is $0$ $\frac{1}{6}$ $\frac{4}{3}$ $\pi$
The value of $\int_{0}^{^{\pi }/_{2}}\int_{0}^{\cos\theta }r\sin\theta \:dr\:d\theta$ is $0$$\frac{1}{6}$$\frac{4}{3}$$\pi$
go_editor
5.0k
points
go_editor
asked
Mar 1, 2021
Calculus
gateme-2021-set2
calculus
definite-integrals
double-interals
+
–
0
answers
0
votes
GATE2015-1-26
Consider a spatial curve in three-dimensional space given in parametric form by $x(t)= \cos t, \:y(t)=\sin t, z(t)=\dfrac{2}{\pi } t \: 0\leq t\leq \dfrac{\pi }{2}$ The length of the curve is _______
Consider a spatial curve in three-dimensional space given in parametric form by $$x(t)= \cos t, \:y(t)=\sin t, z(t)=\dfrac{2}{\pi } t \: 0\leq t\leq \dfrac{\pi }{2}$$ The...
Arjun
28.5k
points
Arjun
asked
Feb 24, 2017
Calculus
gateme-2015-set1
numerical-answers
calculus
curves
+
–
0
answers
0
votes
GATE2016-2-26
A scalar potential $\varphi$ has the following gradient: $\bigtriangledown \varphi =yz\hat{i}+xz\hat{j}+xy\hat{k}$ . Consider the integral $\int_{c}^{ }\bigtriangledown \varphi .d\overrightarrow{r}$ on the curve $\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}$. The curve $C$ ... . The value of the integral is ________
A scalar potential $\varphi$ has the following gradient: $\bigtriangledown \varphi =yz\hat{i}+xz\hat{j}+xy\hat{k}$ . Consider the integral $\int_{c}^{ }\bigtriangledown \...
Arjun
28.5k
points
Arjun
asked
Feb 24, 2017
Calculus
gateme-2016-set2
numerical-answers
calculus
integrals
vector-identities
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 2
The value of $\displaystyle{} \lim_{x \rightarrow 0} \left( \frac{1 – \cos x}{x^{2}}\right)$ is $\frac{1}{4}$ $\frac{1}{3}$ $\frac{1}{2}$ $1$
The value of $\displaystyle{} \lim_{x \rightarrow 0} \left( \frac{1 – \cos x}{x^{2}}\right)$ is$\frac{1}{4}$$\frac{1}{3}$$\frac{1}{2}$$1$
gatecse
1.6k
points
gatecse
asked
Feb 22, 2021
Calculus
gateme-2021-set1
calculus
limits
+
–
0
answers
0
votes
GATE2019 ME-2: 28
The derivative of $f(x)= \cos x$ can be estimated using the approximation $f'(x)=\dfrac{f(x+h)-f(x-h)}{2h}$. The percentage error is calculated as $\bigg( \dfrac{\text{Exact value - Approximate value}}{\text{Exact value}} \bigg) \times 100$. The percentage error in the derivative of $f(x)$ ... $> 0.1 \% \text{ and } <1 \%$ $> 1 \% \text{ and } <5 \%$ $>5 \%$
The derivative of $f(x)= \cos x$ can be estimated using the approximation $f’(x)=\dfrac{f(x+h)-f(x-h)}{2h}$. The percentage error is calculated as $\bigg( \dfrac{\text{...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set2
calculus
derivatives
+
–
0
answers
0
votes
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 $\sqrt{2}$ $2$ $2 \sqrt{2}$ $4 \sqrt{2}$
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}$$4...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set2
calculus
directional-derivatives
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 11
For a two-dimensional, incompressible flow having velocity components $u$ and $v$ in the $x$ and $y$ directions, respectively, the expression $\frac{\partial \left ( u^{2} \right )}{\partial x}+\frac{\partial \left ( uv \right )}{\partial y}$ can ... $u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}$
For a two-dimensional, incompressible flow having velocity components $u$ and $v$ in the $x$ and $y$ directions, respectively, the expression$$\frac{\partial \left ( u^{2...
go_editor
5.0k
points
go_editor
asked
Mar 1, 2021
Calculus
gateme-2021-set2
calculus
partial-derivatives
+
–
0
answers
0
votes
GATE2019 ME-1: 2
A parabola $x=y^2$ with $0 \leq x \leq 1$ is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by $360^{\circ}$ around x-axis is $\dfrac{\pi}{4} \\$ $\dfrac{\pi}{2} \\$ ${\pi} \\$ $2 \pi$
A parabola $x=y^2$ with $0 \leq x \leq 1$ is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by $360^{\circ}$ around x-axis ...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set1
calculus
area-under-curve
+
–
0
answers
0
votes
GATE2015-3-16
The value of $\displaystyle{\lim_{x\rightarrow 0}\left(\frac{-\sin x}{2\sin x+x\cos x}\right)}$ is ________
The value of $\displaystyle{\lim_{x\rightarrow 0}\left(\frac{-\sin x}{2\sin x+x\cos x}\right)}$ is ________
Arjun
28.5k
points
Arjun
asked
Feb 24, 2017
Calculus
gateme-2015-set3
numerical-answers
calculus
limits
+
–
0
answers
0
votes
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 = $ $f(\xi)(b-a)$ $f(b)(\xi-a)$ $f(a)(b-\xi)$ $0$
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 = $...
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Calculus
gateme-2018-set1
calculus
mean-value-theorems
definite-integrals
+
–
0
answers
0
votes
GATE2020-ME-2: 3
Let $I=\displaystyle \int_{x=0}^1 \int_{y=0}^{x^2} xy^2 dy \: dx$. Then, $I$ may also be expressed as $\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} xy^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=\sqrt{y}}^1 yx^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=\sqrt{y}}^1 xy^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} yx^2 dx \: dy$
Let $I=\displaystyle \int_{x=0}^1 \int_{y=0}^{x^2} xy^2 dy \: dx$. Then, $I$ may also be expressed as$\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} xy^2 dx \: dy$$\dis...
go_editor
5.0k
points
go_editor
asked
Sep 18, 2020
Calculus
gateme-2020-set2
calculus
definite-integrals
double-interals
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 13
A two dimensional flow has velocities in $x$ and $y$ directions given by $u = 2xyt$ and $v = -y^{2}t$, where $\text{t}$ denotes time. The equation for streamline passing through $x=1,\:y=1$ is $x^{2}y=1$ $xy^{2}=1$ $x^{2}y^{2}=1$ $x/y^{2}=1$
A two dimensional flow has velocities in $x$ and $y$ directions given by $u = 2xyt$ and $v = -y^{2}t$, where $\text{t}$ denotes time. The equation for streamline passing ...
go_editor
5.0k
points
go_editor
asked
Mar 1, 2021
Calculus
gateme-2021-set2
calculus
derivatives
+
–
0
answers
0
votes
GATE2016-3-28
$\displaystyle{}\lim_{x\rightarrow \infty }\sqrt{x^2+x-1}-x$ is $0$ $\infty$ $1/2$ $-\infty$
$\displaystyle{}\lim_{x\rightarrow \infty }\sqrt{x^2+x-1}-x$ is$0$$\infty$$1/2$$-\infty$
Arjun
28.5k
points
Arjun
asked
Feb 24, 2017
Calculus
gateme-2016-set3
calculus
limits
+
–
0
answers
0
votes
GATE2019 ME-2: 26
Given a vector $\overrightarrow{u} = \dfrac{1}{3} \big(-y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k} \big)$ and $\hat{n}$ as the unit normal vector to the surface of the hemipshere $(x^2+y^2+z^2=1; \: z \geq 0)$ ... $S$ is $- \dfrac{\pi}{2} \\$ $\dfrac{\pi}{3} \\$ $\dfrac{\pi}{2} \\$ $\pi$
Given a vector $\overrightarrow{u} = \dfrac{1}{3} \big(-y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k} \big)$ and $\hat{n}$ as the unit normal vector to the surface of the hemi...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set2
calculus
vector-identities
+
–
0
answers
0
votes
GATE2017 ME-1: 28
A parametric curve defined by $x= \cos \left ( \dfrac{\Pi u}{2} \right ), y= \sin \left ( \dfrac{\Pi u}{2} \right )$ in the range $0 \leq u \leq 1$ is rotated about the $X$-axis by $360$ degrees. Area of the surface generated is $\dfrac{\Pi }{2} \\$ $\pi \\$ $2 \pi \\$ $4 \pi$
A parametric curve defined by $x= \cos \left ( \dfrac{\Pi u}{2} \right ), y= \sin \left ( \dfrac{\Pi u}{2} \right )$ in the range $0 \leq u \leq 1$ is rotated about the $...
Arjun
28.5k
points
Arjun
asked
Feb 26, 2017
Calculus
gateme-2017-set1
calculus
area-under-curve
+
–
0
answers
0
votes
GATE2020-ME-1: 27
A vector field is defined as ... shell formed by two concentric spheres with origin as the center, and internal and external radii of $1$ and $2$, respectively, is $0$ $2\pi$ $4\pi$ $8\pi$
A vector field is defined as $$\overrightarrow{f}\left ( x,y,z \right )=\dfrac{x}{\left [ x^{2}+y^{2}+z^{2} \right ]^{\frac{3}{2}}}\widehat{i}\:+\:\dfrac{y}{\left [ x^{2}...
go_editor
5.0k
points
go_editor
asked
Feb 19, 2020
Calculus
gateme-2020-set1
calculus
vector-identities
+
–
1
answers
0
votes
GATE2017 ME-2: 29
If $f(z)=(x^{2}+ay^{2})+i bxy$ is a complex analytic function of $z=x+iy$, where $i=\sqrt{-1}$, then $a=-1, b=-1$ $a=-1, b=2$ $a=1, b= 2$ $a=2, b=2$
If $f(z)=(x^{2}+ay^{2})+i bxy$ is a complex analytic function of $z=x+iy$, where $i=\sqrt{-1}$, then$a=-1, b=-1$$a=-1, b=2$$a=1, b= 2$$a=2, b=2$
Arjun
28.5k
points
Arjun
asked
Feb 26, 2017
Calculus
gateme-2017-set2
calculus
complex-variables
+
–
0
answers
0
votes
GATE2020-ME-1: 2
The value of $\displaystyle{}\lim_{x \to \infty}\left ( \dfrac{1 -e^{-c\left ( 1-x \right )}}{1-x\:e^{-c\left ( 1-x \right )}} \right )$ is $\text{c} \\$ $\text{c + 1} \\$ $\dfrac{c}{c+1} \\$ $\dfrac{c+1}{c}$
The value of $\displaystyle{}\lim_{x \to \infty}\left ( \dfrac{1 -e^{-c\left ( 1-x \right )}}{1-x\:e^{-c\left ( 1-x \right )}} \right )$ is$\text{c} \\$$\text{c + 1} \\$$...
go_editor
5.0k
points
go_editor
asked
Feb 19, 2020
Calculus
gateme-2020-set1
calculus
limits
+
–
0
answers
0
votes
GATE2015-1-4
The value of $\displaystyle{} \lim_{x\rightarrow 0}\dfrac{1- \cos(x^2)}{2x^4}$ is $0 \\$ $\dfrac{1}{2} \\$ $\dfrac{1}{4} \\$ undefined
The value of $\displaystyle{} \lim_{x\rightarrow 0}\dfrac{1- \cos(x^2)}{2x^4}$ is$0 \\$$\dfrac{1}{2} \\$$\dfrac{1}{4} \\$undefined
Arjun
28.5k
points
Arjun
asked
Feb 24, 2017
Calculus
gateme-2015-set1
calculus
limits
+
–
0
answers
0
votes
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 $-0.5$ $0.0$ $0.5$ $1.0$
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 $...
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Calculus
gateme-2018-set2
calculus
fourier-series
+
–
0
answers
0
votes
GATE ME 2012 | Question: 12
$\underset{x \rightarrow 0}{\lim} \bigg( \dfrac{1- \cos x}{x^2} \bigg)$ is $1/4$ $1/2$ $1$ $2$
$\underset{x \rightarrow 0}{\lim} \bigg( \dfrac{1- \cos x}{x^2} \bigg)$ is$1/4$$1/2$$1$$2$
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
limits
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 19
Value of $\left ( 1+i \right )^{8}$, where $i=\sqrt{-1}$, is equal to $4$ $16$ $4i$ $16i$
Value of $\left ( 1+i \right )^{8}$, where $i=\sqrt{-1}$, is equal to$4$$16$$4i$$16i$
go_editor
5.0k
points
go_editor
asked
Mar 1, 2021
Calculus
gateme-2021-set2
calculus
complex-variables
+
–
0
answers
0
votes
GATE ME 2013 | Question: 26
The following surface integral is to be evaluated over a sphere for the given steady velocity vector field $F$ = $xi$ + $yj$+ $zk$ defined with respect to a Cartesian coordinate system having $i$, $j$ and $k$ ... is the outward unit normal vector to the sphere. The value of the surface integral is $\pi$ $2\pi$ $3\pi/4$ $4\pi$
The following surface integral is to be evaluated over a sphere for the given steady velocity vector field $F$ = $xi$ + $yj$+ $zk$ defined with respect to a Cartesian coo...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Calculus
gateme-2013
calculus
integrals
area-under-curve
+
–
0
answers
0
votes
GATE2017 ME-1: 2
The value of $\displaystyle{}\lim_{x \rightarrow 0}\dfrac{x^{3}-\sin(x)}{x}$ is $0$ $3$ $1$ $-1$
The value of $\displaystyle{}\lim_{x \rightarrow 0}\dfrac{x^{3}-\sin(x)}{x}$ is$0$$3$$1$$-1$
Arjun
28.5k
points
Arjun
asked
Feb 26, 2017
Calculus
gateme-2017-set1
calculus
limits
+
–
0
answers
0
votes
GATE2018-2-26
Let $z$ be a complex variable. For a counter-clockwise integration around a unit circle $C$, centered at origin, $\oint_C \frac{1}{5z-4} dz=A \pi i$, the value of $A$ is $2/5$ $1/2$ $2$ $4/5$
Let $z$ be a complex variable. For a counter-clockwise integration around a unit circle $C$, centered at origin, $$\oint_C \frac{1}{5z-4} dz=A \pi i$$, the value of $A$ i...
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Calculus
gateme-2018-set2
calculus
complex-variables
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 4 | Question: 44
Consider a velocity field $\overrightarrow{V}=k(y\hat{i}+x\hat{k})$ , where $K$ is a constant. The vorticity, $Ω_Z$ , is $-K$ $K$ $-K/2$ $K/2$
Consider a velocity field $\overrightarrow{V}=k(y\hat{i}+x\hat{k})$ , where $K$ is a constant. The vorticity, $Ω_Z$ , is$-K$$K$$-K/2$$K/2$
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Calculus
gateme-2014-set4
calculus
vector-identities
velocity
+
–
0
answers
0
votes
GATE ME 2012 | Question: 24
At $x=0$, the function $f(x)=x^3+1$ has a maximum value a minimum value a singularity a point of inflection
At $x=0$, the function $f(x)=x^3+1$ hasa maximum valuea minimum valuea singularitya point of inflection
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
functions-of-single-variable
maxima-minima
+
–
0
answers
0
votes
GATE2018-1-27
The value of the integral over the closed surface $S$ bounding a volume $V$, where $\overrightarrow{r} = x \hat{i} + y \hat{j}+z \hat{k}$ is the position vector and $\overrightarrow{n}$ is the normal to the surface $S$, is $V$ $2V$ $3V$ $4V$
The value of the integralover the closed surface $S$ bounding a volume $V$, where $\overrightarrow{r} = x \hat{i} + y \hat{j}+z \hat{k}$ is the position vector and $\over...
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Calculus
gateme-2018-set1
calculus
surface-integral
vector-identities
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 2 | Question: 2
$ \displaystyle{}\lim_{x\rightarrow 0} \left( \dfrac{e^{2x}-1}{\sin(4x)} \right )$ is equal to $0$ $0.5$ $1$ $2$
$ \displaystyle{}\lim_{x\rightarrow 0} \left( \dfrac{e^{2x}-1}{\sin(4x)} \right )$ is equal to$0$$0.5$$1$$2$
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Calculus
gateme-2014-set2
calculus
limits
+
–
0
answers
0
votes
GATE2020-ME-2: 27
The function $f(z)$ of complex variable $z=x+iy$, where $i=\sqrt{-1}$, is given as $f(z)=(x^3-3xy^2)+i \: v(x,y)$. For this function to be analytic, $v(x,y)$ should be $(3xy^2-y^3) +$ constant $(3x^2y^2-y^3) +$ constant $(x^3-3x^2 y) +$ constant $(3x^2y-y^3) +$ constant
The function $f(z)$ of complex variable $z=x+iy$, where $i=\sqrt{-1}$, is given as $f(z)=(x^3-3xy^2)+i \: v(x,y)$. For this function to be analytic, $v(x,y)$ should be$(3...
go_editor
5.0k
points
go_editor
asked
Sep 18, 2020
Calculus
gateme-2020-set2
calculus
complex-variables
analytic-functions
+
–
0
answers
0
votes
GATE2015-1-27
Consider an ant crawling along the curve $(x-2)^2+y^2=4$ , where $x$ and $y$ are in meters. The ant starts at the point $(4, 0)$ and moves counter-clockwise with a speed of $1.57$ meters per second. The time taken by the ant to reach the point $(2, 2)$ is (in seconds) ____________
Consider an ant crawling along the curve $(x-2)^2+y^2=4$ , where $x$ and $y$ are in meters. The ant starts at the point $(4, 0)$ and moves counter-clockwise with a speed ...
Arjun
28.5k
points
Arjun
asked
Feb 24, 2017
Calculus
gateme-2015-set1
numerical-answers
calculus
curves
+
–
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GATE ME 2012 | Question: 25
For the spherical surface $x^2+y^2+z^2=1$, the unit outward normal vector at th point $\left( \dfrac{1}{\sqrt{2}}, \dfrac{1}{\sqrt{2}}, 0\right)$ is given by $\dfrac{1}{\sqrt{2}} \hat{i} +\dfrac{1}{\sqrt{2}} \hat{j} \\$ ... $\hat{k} \\$ $\dfrac{1}{\sqrt{3}} \hat{i} +\dfrac{1}{\sqrt{3}} \hat{j} +\dfrac{1}{\sqrt{3}} \hat{k}$
For the spherical surface $x^2+y^2+z^2=1$, the unit outward normal vector at th point $\left( \dfrac{1}{\sqrt{2}}, \dfrac{1}{\sqrt{2}}, 0\right)$ is given by$\dfrac{1}{\s...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
vector-identities
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–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 26
The integral $\oint_{c}^{ } (ydx-xdy)$ is evaluated along the circle $x^2+y^2=\frac{1}{4}$ traversed in counter clockwise direction. The integral is equal to $0$ $\frac{-\pi }{4}$ $\frac{-\pi }{2}$ $\frac{\pi }{4}$
The integral $\oint_{c}^{ } (ydx-xdy)$ is evaluated along the circle $x^2+y^2=\frac{1}{4}$ traversed in counter clockwise direction. The integral is equal to$0$$\frac{-\p...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Calculus
gateme-2014-set1
calculus
definite-integrals
area-under-curve
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