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Recent questions and answers in Calculus
0
votes
0
answers
1
GATE2017 CE219
The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________
asked
Aug 7
in
Calculus
by
gatecse
(
3.9k
points)
gate2017ce2
vectorcalculus
divergence
0
votes
0
answers
2
GATE2017 CE227
Consider the following definite integral: $I= \int_0^1 \frac{(\sin ^{1}x)^2}{\sqrt{1x^2}} dx$. The value of the integral is $\frac{\pi ^3}{24}$ $\frac{\pi ^3}{12}$ $\frac{\pi ^3}{48}$ $\frac{\pi ^3}{64}$
asked
Aug 7
in
Calculus
by
gatecse
(
3.9k
points)
gate2017ce2
definite
integral
+1
vote
0
answers
3
GATE2019 CE1: 1
Which one of the following is correct? $\lim_{x\rightarrow 0} ( \frac{sin4x}{sin2x})=2 $ and $\lim_{x\rightarrow 0} ( \frac{tanx}{x})=1$ $\lim_{x\rightarrow 0} ( \frac{sin4x}{sin2x})=1$ and $\lim_{x\rightarrow 0} ( \frac{tanx}{x})=1$ ... $\lim_{x\rightarrow 0} ( \frac{sin4x}{sin2x})=2$ and $\lim_{x\rightarrow 0} ( \frac{tanx}{x})= \infty$
asked
Feb 14
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce1
calculus
limit
+1
vote
0
answers
4
GATE2019 CE1: 4
For a small value of $h$, the Taylor series expansion for $f(x+h)$ is $f(x)+h{f}’ (x) + \frac{h^2}{2!}{f}’’(x) + \frac{h^3}{3!}{f}’'’(x)+...\infty $ $f(x)h{f}’ (x) + \frac{h^2}{2!}{f}’’(x)  \frac{h^3}{3!}{f}’'’(x)+...\infty $ $f(x)+h{f}’ (x) + \frac{h^2}{2}{f}’’(x) + \frac{h^3}{3}{f}’'’(x)+...\infty $ $f(x)h{f}’ (x) + \frac{h^2}{2}{f}’’(x)  \frac{h^3}{3}{f}’'’(x)+...\infty $
asked
Feb 14
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce1
taylorseries
0
votes
0
answers
5
GATE2019 CE1: 26
Which one of the following is NOT a correct statement? The function $\sqrt[x]{x}, \: (x>0)$, has the global maxima at $x=e$ The function $\sqrt[x]{x}, \: (x>0)$, has the global minima at $x=e$ The function $x^3$ has neither global minima nor global maxima The function $\mid x \mid$ has the global minima at $x=0$
asked
Feb 14
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce1
maximaminima
0
votes
0
answers
6
GATE2019 CE2: 3
The following inequality is true for all $x$ close to $0$. $2\dfrac{x^2}{3} < \dfrac{x \sin x}{1 \cos x} <2$ What is the value of $\underset{x \to 0}{\lim} \dfrac{x \sin x}{1 – \cos x}$? $0$ $1/2$ $1$ $2$
asked
Feb 12
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce2
limit
0
votes
0
answers
7
GATE201625
What is the value of $\underset{x \rightarrow 0 \\ y \rightarrow 0}{\lim} \frac{xy}{x^2+y^2}$? $1$ $1$ $0$ Limit does not exist
asked
Mar 28, 2018
in
Calculus
by
Milicevic3306
(
11.8k
points)
gate2016ce2
limit
0
votes
0
answers
8
GATE2016228
The angle of intersection of the curves $x^{2}=4y$ and $y^{2} = 4x$ at point $(0,0)$ is $0^{\circ}$ $30^{\circ}$ $45^{\circ}$ $90^{\circ}$
asked
Mar 28, 2018
in
Calculus
by
Milicevic3306
(
11.8k
points)
gate2016ce2
0
votes
0
answers
9
GATE2016229
The area between the parabola $x^2=8y$ and the straight line $y=8$ is _______.
asked
Mar 28, 2018
in
Calculus
by
Milicevic3306
(
11.8k
points)
gate2016ce2
definiteintegral
area
0
votes
0
answers
10
GATE201524
$\underset{x \to \infty}{\lim} \bigg( 1+ \frac{1}{x} \bigg)^{2x} $ is equal to $e^{2}$ $e$ $1$ $e^2$
asked
Mar 26, 2018
in
Calculus
by
Milicevic3306
(
11.8k
points)
gate2015ce2
0
votes
0
answers
11
GATE2018 CE1: 26
The value of the integral $\int_0^{\pi} x \cos^2 x \: dx$ is $\pi^2/8$ $\pi^2/4$ $\pi^2/2$ $\pi^2$
asked
Feb 17, 2018
in
Calculus
by
gatecse
(
3.9k
points)
gate2018ce1
integration
0
votes
0
answers
12
GATE2018 CE1: 3
At the point $x= 0$, the function $f(x) = x^3$ has local maximum local minimum both local maximum and minimum neither local maximum nor local minimum
asked
Feb 17, 2018
in
Calculus
by
gatecse
(
3.9k
points)
gate2018ce1
maximaminima
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