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Recent questions tagged calculus
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GATE2019 EC: 16
The value of the contour integral $\frac{1}{2\pi j} \oint\left(z+\frac{1}{z}\right)^{2}dz$ evaluated over the unit circle $\mid z \mid=1$ is_______.
asked
Feb 12, 2019
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Arjun
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gate2019ec
numericalanswers
calculus
integrals
engineeringmathematics
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2
GATE2019 EC: 19
The value of the integral $\int_{0}^{\pi} \int_{y}^{\pi}\dfrac{\sin x}{x}dx\: dy ,$ is equal to __________.
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Feb 12, 2019
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Arjun
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gate2019ec
numericalanswers
integrals
calculus
engineeringmathematics
differentialequation
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3
GATE2019 EC: 27
Consider the line integral $\int_{c} (xdyydx)$ the integral being taken in a counterclockwise direction over the closed curve $C$ that forms the boundary of the region $R$ shown in the figure below. The region $R$ is the area enclosed by the union of a $2 \times 3$ rectangle and ... circle of radius $1$. The line integral evaluates to $6+ \dfrac{\pi}{2}$ $8+\pi$ $12+\pi$ $16+2\pi$
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Feb 12, 2019
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Arjun
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1.4k
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gate2019ec
integrals
calculus
engineeringmathematics
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4
GATE201634
The integral $\int\limits_{0}^{1}\large\frac{dx}{\sqrt{(1x)}}$ is equal to _______
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Mar 28, 2018
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by
Milicevic3306
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15.7k
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gate2016ec3
numericalanswers
integrals
calculus
engineeringmathematics
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5
GATE2016329
The values of the integral $\large\frac{1}{2\pi j}\oint_c\frac{e^z}{(z2)} \small dz$ along a closed contour $c$ in anticlockwise direction for the point $z_0=2$ inside the contour $c$, and the point $z_0=2$ outside the contour $c$, respectively,are $(i)2.72, \: (ii) 0$ $(i)7.39, \: (ii) 0$ $(i)0, \: (ii) 2.72$ $(i)0, \: (ii) 7.39$
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Mar 28, 2018
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by
Milicevic3306
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15.7k
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gate2016ec3
integrals
calculus
engineeringmathematics
0
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6
GATE2016126
The integral $\frac{1}{2\pi} \iint_D(x+y+10) \,dx\,dy$, where $D$ denotes the disc: $x^2+y^2\leq 4$,evaluates to _________
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Mar 28, 2018
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Milicevic3306
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15.7k
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gate2016ec1
numericalanswers
calculus
engineeringmathematics
integrals
0
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0
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7
GATE2016128
In the following integral, the contour $C$ encloses the points $2 \pi j$ and $ 2\pi j$ $\frac{1}{2\pi}\oint_C\frac{\sin z}{(z2\pi j)^3} \,dz$ The value of the integral is _________
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Mar 28, 2018
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Milicevic3306
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15.7k
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gate2016ec1
numericalanswers
calculus
engineeringmathematics
integrals
0
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8
GATE2015227
The value of the integral $\int_{\infty}^{\infty} 12\cos(2\pi t) \dfrac{\sin(4\pi t)}{4 \pi t}dt$ is _________.
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Mar 28, 2018
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Milicevic3306
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gate2015ec2
numericalanswers
calculus
engineeringmathematics
integrals
0
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0
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9
GATE2015228
If $C$ denotes the counterclockwise unit circle, the value of the contour integral $\dfrac{1}{2\pi j}\oint_{C} Re\{z\}dz$ is __________.
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Mar 28, 2018
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Milicevic3306
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gate2015ec2
numericalanswers
calculus
engineeringmathematics
integrals
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10
GATE201512
A function $f(x)=1x^2+x^3$ is defined in the closed interval $[1,1]$. The value of $x$, in the open interval $(1,1)$ for which the mean value theorem is satisfied, is $1/2$ $1/3$ $1/3$ $1/2$
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Mar 28, 2018
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Milicevic3306
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gate2015ec1
calculus
engineeringmathematics
meanvaluetheorem
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11
GATE201445
The directional derivative of $f(x,y)= \frac{xy}{\sqrt{2}} (x+y)$ at $(1,1)$ in the direction of the unit vector at an angle of $\frac{\pi}{4}$ with $y$axis, is given by _________.
asked
Mar 26, 2018
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Milicevic3306
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gate2014ec4
numericalanswers
calculus
engineeringmathematics
derivatives
0
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0
answers
12
GATE2014245
The value of the integral $\int_{\infty }^{\infty } \text{sinc}^{2}(5t) \: dt$ is _______.
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Mar 26, 2018
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Milicevic3306
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gate2014ec2
numericalanswers
calculus
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integrals
0
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13
GATE2014126
The Taylor series expansion of $3\sin x + 2 \cos x$ is $2 + 3xx^{2} – \frac{x^{3}}{2} + \dots$ $2 – 3x + x^{2} – \frac{x^{3}}{2} + \dots$ $2 + 3x + x^{2} + \frac{x^{3}}{2} + \dots$ $2 – 3x – x^{2} + \frac{x^{3}}{2} + \dots$
asked
Mar 26, 2018
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Milicevic3306
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15.7k
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gate2014ec1
calculus
taylorseries
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0
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14
GATE201824
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{\left ( \frac{t^{2}}{2} \right )}dt$ around $\text{x=0}$ has the form $f\left ( x \right )={a}_{0}+a_{1}x+a_{2}x^{2}+...$ The coefficient $a_{2}$ (correct to two decimal places) is equal to ________.
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Feb 19, 2018
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gatecse
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gate2018ec
numericalanswers
calculus
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taylorseries
0
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15
GATE20186
Consider $p(s)=s^{3}+ a_{2}s^{2}+a_{1}s+a_{0}$ with all real coefficients. It is known that its derivatives ${p}'(s)$ has no real roots. The number of real roots of $p(s)$ is $0$ $1$ $2$ $3$
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Feb 19, 2018
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gatecse
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gate2018ec
calculus
derivatives
engineeringmathematics
0
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0
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16
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
asked
Nov 23, 2017
in
Calculus
by
admin
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2.8k
points)
gate2017ec2
integrals
calculus
engineeringmathematics
0
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0
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17
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} $
asked
Nov 17, 2017
in
Calculus
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admin
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2.8k
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gate2017ec1
taylorseries
calculus
engineeringmathematics
0
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0
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18
GATE2017 EC1: 9
A bar of Gallium Arsenide (GaAs) is doped with silicon such that the silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statements is true? Silicon atoms act as $p$type dopants in Arsenic sites and $n$type ... in Arsenic sites as well as Gallium sites Silicon atoms act as $n$type dopants in Arsenic sites as well as Gallium sites
asked
Nov 17, 2017
in
Calculus
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admin
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2.8k
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gate2017ec1
volumeintegrals
calculus
engineeringmathematics
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