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Hot questions in Calculus
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21
GATE Electrical 2017 Set 2 | Question: 19
Let $x$ and $y$ be integers satisfying the following equations $2x^{2}+y^{2}=34$ $x+2y=11$ The value of $(x+y)$ is _______.
Let $x$ and $y$ be integers satisfying the following equations$2x^{2}+y^{2}=34$$x+2y=11$The value of $(x+y)$ is _______.
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-2
numerical-answers
calculus
curves
+
–
0
votes
0
answers
22
GATE Electrical 2017 Set 1 | Question: 26
A function $f(x)$ is defined as $f(x)= \begin{cases} e^{x}, & x < 1 \\ \text{In } x+ax^{2}+bx, & x\geq 1 \end{cases}$, where $x \in \mathbb{R}$ Which one of the following statement is TRUE? $f(x)$ is NOT differentiable at $x=1$ ... for all values of $a$ and $b$ such that $a+b=e$. $f(x)$ is differentiable at $x=1$ for all values of $a$ and $b$.
A function $f(x)$ is defined as$f(x)= \begin{cases} e^{x}, & x < 1 \\ \text{In } x+ax^{2}+bx, & x\geq 1 \end{cases}$, where $x \in \mathbb{R}$Which one of the followin...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-1
calculus
continuity-and-differentiability
+
–
0
votes
0
answers
23
GATE Electrical 2017 Set 1 | Question: 17
Let $I= c\int \int _{R} xy^{2} dxdy$, where $R$ is the region shown in the figure and $c= 6 \times 10^{-4}$. The value of $I$ equals _________. (Give the answer up to two decimal places.)
Let $I= c\int \int _{R} xy^{2} dxdy$, where $R$ is the region shown in the figure and $c= 6 \times 10^{-4}$. The value of $I$ equals _________. (Give the answer up to two...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-1
numerical-answers
calculus
double-integral
+
–
0
votes
0
answers
24
GATE Electrical 2017 Set 2 | Question: 18
Consider a function $f(x, y, z)$ given by $f(x, y, z)=(x^{2}+y^{2}-2z^{2})(y^{2}+z^{2})$ The partial derivative of this function with respect to $x$ at the point, $x=2, y=1$ and $z=3$ is _______.
Consider a function $f(x, y, z)$ given by$f(x, y, z)=(x^{2}+y^{2}-2z^{2})(y^{2}+z^{2})$The partial derivative of this function with respect to $x$ at the point, $x=2, y=1...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-2
numerical-answers
calculus
derivatives
partial-derivatives
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–
0
votes
0
answers
25
GATE Electrical 2017 Set 2 | Question: 20
Let $y^{2}-2y+1=x$ and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals _________. (Give the answer up to three decimal places).
Let $y^{2}-2y+1=x$ and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals _________. (Give the answer up to three decimal places).
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-2
numerical-answers
calculus
curves
+
–
0
votes
0
answers
26
GATE Electrical 2017 Set 2 | Question: 27
The value of the contour integral in the complex plane $\oint \frac{z^{3}-2z+3}{z-2} dz$ along the contour $\mid z \mid =3$, taken counter- clockwise is $-18 \pi i$ $0$ $14 \pi i$ $48 \pi i$
The value of the contour integral in the complex plane $\oint \frac{z^{3}-2z+3}{z-2} dz$ along the contour $\mid z \mid =3$, taken counter- clockwise is$-18 \pi i$$0$$14...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-2
calculus
contour-integral
+
–
0
votes
0
answers
27
GATE Electrical 2017 Set 1 | Question: 28
Consider the line integral $I=\int_{c} (x^{2}+iy^{2})dz$, where $z=x+iy$. The line $c$ is shown in the figure below. The value of $I$ is $\frac{1}{2}i \\ $ $\frac{2}{3}i \\ $ $\frac{3}{4}i \\ $ $\frac{4}{5}i$
Consider the line integral $I=\int_{c} (x^{2}+iy^{2})dz$, where $z=x+iy$. The line $c$ is shown in the figure below.The value of $I$ is$\frac{1}{2}i \\ $$\frac{2}{3}i \\ ...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-1
calculus
line-integral
+
–
0
votes
0
answers
28
GATE Electrical 2017 Set 2 | Question: 3
The figures show diagramatic representations of vector fields $\vec{X}, \vec{Y}, \text{and} \vec{Z}$ ... $\bigtriangledown . \vec{X}=0,\bigtriangledown \times \vec{Y} = 0, \bigtriangledown \times \vec{Z}=0$
The figures show diagramatic representations of vector fields $\vec{X}, \vec{Y}, \text{and} \vec{Z}$ respectively. Which one of the following choices is true?$\bigtriangl...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-2
calculus
field-vectors
+
–
0
votes
0
answers
29
GATE Electrical 2017 Set 1 | Question: 2
For a complex number $z,\displaystyle{} \lim_{z \rightarrow i} \frac{z^{2}+1}{z^{3}+2z-i (z^{2}+2)}$ is $-2i$ $-i$ $i$ $2i$
For a complex number $z,\displaystyle{} \lim_{z \rightarrow i} \frac{z^{2}+1}{z^{3}+2z-i (z^{2}+2)}$ is$-2i$$-i$$i$$2i$
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-1
calculus
limits
complex-number
+
–
0
votes
0
answers
30
GATE Electrical 2014 Set 1 | Question: 17
In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of only one root at the origin Imaginary roots only positive real roots only negative real roots
In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence ofonl...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2014-ee-1
calculus
polynomial
routh-hurwitz-array
+
–
0
votes
0
answers
31
GATE Electrical 2014 Set 1 | Question: 28
The line integral of function $F = yzi$, in the counterclockwise direction, along the circle $x^2+y^2 = 1$ at $z = 1$ is $-2\pi$ $-\pi$ $\pi$ $2\pi$
The line integral of function $F = yzi$, in the counterclockwise direction, along the circle $x^2+y^2 = 1$ at $z = 1$ is$-2\pi$$-\pi$$\pi$$2\pi$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2014-ee-1
calculus
line-integral
circle-equation
+
–
0
votes
0
answers
32
GATE Electrical 2015 Set 2 | Question: 26
The volume enclosed by the surface $f(x, y) = e^{x}$ over the triangle bounded by the lines $x = y; x = 0; y = 1$ in the $xy$ plane is ________.
The volume enclosed by the surface $f(x, y) = e^{x}$ over the triangle bounded by the lines $x = y; x = 0; y = 1$ in the $xy$ plane is ________.
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2015-ee-2
calculus
volume-integral
numerical-answers
+
–
0
votes
0
answers
33
GATE Electrical 2014 Set 2 | Question: 28
The minimum value of the function $f(x)=x^3-3x^2-24x+100$ in the interval $[-3,3]$ is $20$ $28$ $16$ $32$
The minimum value of the function $f(x)=x^3-3x^2-24x+100$ in the interval $[-3,3]$ is$20$$28$$16$$32$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2014-ee-2
calculus
maxima-minima
+
–
0
votes
0
answers
34
GATE Electrical 2013 | Question: 24
Given a vector field $\textbf{F}=y^2x \textbf{a}_x-yz \textbf{a}_y-x^2 \textbf{a}_z$ the line integral $\int \textbf{F} \cdot d \textbf{l}$ evaluated along a segment on the $x$-axis from $x=1$ to $x=2$ is $-2.33$ $0$ $2.33$ $7$
Given a vector field $\textbf{F}=y^2x \textbf{a}_x-yz \textbf{a}_y-x^2 \textbf{a}_z$ the line integral $\int \textbf{F} \cdot d \textbf{l}$ evaluated along a segment on t...
piyag476
1.6k
points
piyag476
asked
Feb 11, 2017
Calculus
gate2013-ee
calculus
field-vector
integral
+
–
0
votes
0
answers
35
GATE Electrical 2014 Set 2 | Question: 3
Minimum of the real valued function $f(x)=(x-1)^{2/3}$ occurs at $x$ equal to $-\infty$ $0$ $1$ $\infty$
Minimum of the real valued function $f(x)=(x-1)^{2/3}$ occurs at $x$ equal to$-\infty$$0$$1$$\infty$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2014-ee-2
calculus
maxima-minima
+
–
0
votes
0
answers
36
GATE Electrical 2014 Set 2 | Question: 26
To evaluate the double integral $\displaystyle \int_{0}^{8} \bigg (\int_{(y/2)}^{y/2+1} \bigg (\dfrac{2x-y}{2} \bigg)dx \bigg)dy$ , we make the substitution $u=\bigg (\dfrac{2x-y}{2} \bigg)$ and $v=\dfrac{y}{2}$ ... $\displaystyle \int_{0}^{4} \bigg (\int_{0}^{2}u \: du \bigg ) dv$
To evaluate the double integral $\displaystyle \int_{0}^{8} \bigg (\int_{(y/2)}^{y/2+1} \bigg (\dfrac{2x-y}{2} \bigg)dx \bigg)dy$ , we make the substitution $u=\bigg (\df...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2014-ee-2
calculus
definite-integral
double-integral
+
–
0
votes
0
answers
37
GATE Electrical 2013 | Question: 46
A function $y=5x^2+10x$ is defined over an open interval $x$ = $(1, 2)$ . At least at one point in this interval, $\dfrac{\mathrm{dy} }{\mathrm{d} x}$ is exactly $20$ $25$ $30$ $35$
A function $y=5x^2+10x$ is defined over an open interval $x$ = $(1, 2)$ . At least at one point in this interval, $\dfrac{\mathrm{dy} }{\mathrm{d} x}$ is exactly$20$$25$$...
piyag476
1.6k
points
piyag476
asked
Feb 11, 2017
Calculus
gate2013-ee
calculus
derivatives
+
–
0
votes
0
answers
38
GATE Electrical 2014 Set 1 | Question: 2
Let $f(x)=xe^{-x}$ . The maximum value of the function in the interval $(0,\infty)$ is $e^{-1}$ $e$ $1-e^{-1}$ $1+e^{-1}$
Let $f(x)=xe^{-x}$ . The maximum value of the function in the interval $(0,\infty)$ is$e^{-1}$$e$$1-e^{-1}$$1+e^{-1}$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2014-ee-1
calculus
maxima-minima
+
–
0
votes
0
answers
39
GATE Electrical 2015 Set 2 | Question: 3
Match the following. ... $P-4; Q-1; R-3; S-2$ $P-4; Q-3; R-1; S-2$ $P-3; Q-4; R-2; S-1$
Match the following.$\begin{array}{|l|l|l|l|} \hline P. & \text{Stokes’s Theorem} & 1. & ∯ D.ds = Q \\ \hline Q. & \text{Gauss’s Theorem} & 2. & \oint f(z) dz =0 \\...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2015-ee-2
calculus
divergence
+
–
0
votes
0
answers
40
GATE Electrical 2014 Set 3 | Question: 3
Let $\nabla .(fv)=x^2y+y^2z+z^2x$ , where $f$ and $v$ are scalar and vector fields respectively. If $v=yi+zj+xk$ then $v.\Delta f$ is $x^2y+y^2z+z^2x$ $2xy+2yz+2zx$ $x+y+z$ $0$
Let $\nabla .(fv)=x^2y+y^2z+z^2x$ , where $f$ and $v$ are scalar and vector fields respectively. If $v=yi+zj+xk$ then $v.\Delta f$ is$x^2y+y^2z+z^2x$$2xy+2yz+2zx$$x+y+z$...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Calculus
gate2014-ee-3
calculus
field-vectors
+
–
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