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Questions without a selected answer in Calculus
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GATE CH 2021 | Question: 2
The function $\cos(x)$ is approximated using Taylor series around $x=0$ as $\cos(x) \approx 1 + ax + bx^2 + cx^3 + dx^4$. The values ... $a=-0.5, \: b=0,\: c=0.042, \: d=0$
The function $\cos(x)$ is approximated using Taylor series around $x=0$ as $\cos(x) \approx 1 + ax + bx^2 + cx^3 + dx^4$. The values of $a,b,c$ and $d$ are$a=1, \: b=-0....
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Calculus
gatech-2021
calculus
taylor-series
+
–
0
answers
0
votes
GATE CH 2021 | Question: 5
A three-dimensional velocity field is given by $V=5x^2y \: i + Cy \: j-10xyz \: k$, where $i,j,k$ are the unit vectors in ... fluid flow, the value of $C$ is $-1$ $0$ $1$ $5$
A three-dimensional velocity field is given by $V=5x^2y \: i + Cy \: j-10xyz \: k$, where $i,j,k$ are the unit vectors in $x,y,z$ directions, respectively, describing a c...
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Calculus
gatech-2021
calculus
vector-calculus
vector-identities
+
–
0
answers
0
votes
GATE CH 2021 | Question: 16
For the function $f(x) = \begin{cases} -x, & x<0 \\ x^2, & x \geq 0 \end{cases}$ ... $x=0$ $f(x)$ is differentiable at $x=0$
For the function $f(x) = \begin{cases} -x, & x<0 \\ x^2, & x \geq 0 \end{cases}$ the $\text{CORRECT}$ statement(s) is/are$f(x)$ is continuous at $x=1$$f(x) $ is different...
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Calculus
gatech-2021
calculus
continuity-and-differentiability
multiple-selects
+
–
0
answers
0
votes
GATE CH 2021 | Question: 34
To solve an algebraic equation $f(x)=0$, an iterative scehme of the type $x_{n+1} = g(x_n)$ ... order of convergence for this iterative scheme near the solution is ________
To solve an algebraic equation $f(x)=0$, an iterative scehme of the type $x_{n+1} = g(x_n)$ is proposed, where $g(x)=x-\dfrac{f(x)}{f’(x)}$.At the solution $x=s,\: g’...
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Calculus
gatech-2021
numerical-answers
calculus
convergence
+
–
0
answers
0
votes
GATE Chemical 2020 | Question: 27
The maximum value of the function $f(x)=-\dfrac{5}{3} x^3 +10x^2-15x+16$ in the interval $(0.5,3.5)$ is$0$$8$$16$$48$
soujanyareddy13
1.8k
points
soujanyareddy13
asked
Nov 16, 2020
Calculus
gate2020
calculus
maxima-minima
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–
0
answers
0
votes
GATE Chemical 2020 | Question: 3
Consider the following continuously differentiable function $$\textbf{v}(x,y,z)=3x^2y \textbf{ i} + 8y^2z \textbf{ j} + 5xyz \textbf{ k}$$ where $\textbf{i, j,}$ and $\te...
soujanyareddy13
1.8k
points
soujanyareddy13
asked
Nov 16, 2020
Calculus
gate2020
calculus
vector-calculus
vector-identities
+
–
0
answers
0
votes
GATE Chemical 2019 | Question: 2
The value of the expression $\underset{x\rightarrow \frac{\pi }{2}}{\lim}\: \mid \frac{\tan\:x}{x} \mid $ is $\infty$$0$$1$$-1$
Arjun
4.7k
points
Arjun
asked
Feb 24, 2019
Calculus
gate2019
calculus
limits
+
–
0
answers
0
votes
GATE Chemical 2019 | Question: 34
If $x,y$ and $z$ are directions in a Cartesian coordinate system and $i$, $j$ and $k$ are the respective unit vectors, the directional derivative of the function $u\left ...
Arjun
4.7k
points
Arjun
asked
Feb 24, 2019
Calculus
gate2019
numerical-answers
calculus
vector-calculus
directional-derivatives
+
–
0
answers
0
votes
GATE Chemical 2017 | Question: 1
The value of $\underset{x\rightarrow 0}{\lim}\:\frac{\tan\left ( x \right )}{x}$ is ________________.
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2017
numerical-answers
calculus
limits
+
–
0
answers
0
votes
GATE Chemical 2017 | Question: 3
The number of positive roots of the function $f(x)$ shown below in the range $0<x<6$ is ___________________.
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2017
numerical-answers
calculus
maxima-minima
+
–
0
answers
0
votes
GATE Chemical 2017 | Question: 4
Let $i$ and $j$ be the unit vectors in the $x$ and $y$ directions, respectively. For the function $F\left ( x,y \right )=x^{3}+y^{2}$ the gradient of the function. i.e.. ...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2017
calculus
vector-calculus
unit-vectors
gradient
+
–
0
answers
0
votes
GATE Chemical 2016 | Question: 29
The Lagrange mean-value theorem is satisfied for $f\left ( x \right )=x^{3}+5$, in the interval $\left ( 1,4 \right )$ at a value (rounded off to the second decimal place...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2016
numerical-answers
calculus
mean-value-theorems
+
–
0
answers
0
votes
GATE Chemical 2015 | Question: 11
The following set of the three vectors$$\begin{pmatrix} 1\\2\\1 \end{pmatrix}, \begin{pmatrix} x\\6\\x \end{pmatrix}\:and \:\begin{pmatrix} 3\\4 \\2 \end{pmatrix},$$is li...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015
calculus
vector-calculus
vector-identities
+
–
0
answers
0
votes
GATE Chemical 2015 | Question: 15
A scalar function in the $xy$-plane is given by $\phi \left ( x,y \right )=x^{2}+y^{2}$. If $\hat{i}$ and $\hat{j}$ are unit vectors in the $x$ and $y$ directions, the d...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015
calculus
vector-calculus
unit-vectors
+
–
0
answers
0
votes
GATE Chemical 2015 | Question: 37
A vector $u=-2y\hat{i}+2x\hat{j}$, where $\hat{i}$ and $\hat{j}$ are unit vectors in $x$ and $y$ directions, respectively. Evaluate the line integral$$I=\oint _{C}u.dr$$w...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015
numerical-answers
calculus
line-integral
vector-identities
+
–
0
answers
0
votes
GATE Chemical 2014 | Question: 9
Integral of the time-weighted absolute error $(ITAE)$ is expressed as$\int _{0}^{\infty }\frac{\left | \varepsilon \left ( t \right ) \right |}{t^{2}}dt$$\int _{0}^{\inft...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014
calculus
definite-integrals
+
–
0
answers
0
votes
GATE Chemical 2014 | Question: 3
If $f*(x)$ is the complex conjugate of $f(x)=\cos(x) + i\: \sin(x)$, then for real $a$ and $b$, $\int _{a}^{b}f*\left ( x \right )f\left ( x \right )$ is $ALWAYS$positive...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014
calculus
definite-integrals
+
–
0
answers
0
votes
GATE Chemical 2014 | Question: 1
Gradient of a scalar variable is alwaysa vectora scalara dot productzero
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014
calculus
vector-calculus
gradient
+
–
0
answers
0
votes
GATE Chemical 2013 | Question: 7
An equation of state is explicit in pressure $p$ and cubic in the specific volume $v$. At the critical point $‘c’$ , the isotherm passing through $‘c’$ satisfies$...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2013
calculus
partial-derivatives
+
–
0
answers
0
votes
GATE Chemical 2013 | Question: 4
Evaluate ${\displaystyle \int \frac{dx}{e^x – 1}}$(Note: C is a constant of integration)$\frac{e^x}{e^x -1}$ + C$\frac {In(e^x -1)}{e^x}$ + CIn$(\frac {e^x}{e^x -1})$ ...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2013
calculus
integrals
+
–
0
answers
0
votes
GATE Chemical 2012 | Question: 27
If $a$ is a constant, then the value of the integral $a^{2}\int^\infty_0 xe^{-ax}dx$ is$1/a$$a$$1$$0$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012
calculus
definite-integrals
+
–
0
answers
0
votes
GATE Chemical 2012 | Question: 3
For the function $f(t) = e^{-t}/\tau$,the Taylor series approximation for $t\ll$$\tau$ is$1+\frac{t}{\tau}$$1-\frac{t}{\tau}$$1-\frac{t^2}{2\tau^2}$$1+t$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012
calculus
taylor-series
+
–
0
answers
0
votes
GATE Chemical 2018 | Question: 46
If $y=e^{-x^{2}}$ then the value of $\underset{x\rightarrow \infty }{\lim}\frac{1}{x}\frac{dy}{dx}$ is __________
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Calculus
gate2018
numerical-answers
calculus
limits
+
–
0
answers
0
votes
GATE Chemical 2018 | Question: 4
The figure which represents for $y=\frac{sin \:x}{x}$ for $x>0$ ($x$ in radians) is
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Calculus
gate2018
calculus
functions
graphs
+
–
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