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Recent questions and answers in Calculus
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1
GATE2020CE127
A continuous function $f(x)$ is defined. If the third derivative at $x_i$ is to be computed by using the fourth order central finitedivideddifference scheme (with step length $=h$ ...
asked
Feb 28
in
Calculus
by
jothee
(
2.7k
points)
gate2020ce1
calculus
functions
engineeringmathematics
0
votes
0
answers
2
GATE2020CE139
If $C$ represents a line segment between $(0,0,0)$ and $(1,1,1)$ in Cartesian coordinate system, the value (expressed as integer) of the line integral $\int_C [(y+z)dx+(x+z)dy+(x+y)dz] $ is ______
asked
Feb 28
in
Calculus
by
jothee
(
2.7k
points)
gate2020ce1
calculus
engineeringmathematics
integrals
numericalanswers
0
votes
0
answers
3
GATE2020 CE23
The integral $\int\limits_{0}^{1} (5x^3 + 4x^2 + 3x + 2) dx$ is estimated numerically using three alternative methods namely the rectangular,trapezoidal and Simpson's rules with a common step size. In this context, which one of the following ... NONzero error. Only the rectangular rule of estimation will give zero error. Only Simpson's rule of estimation will give zero error.
asked
Feb 13
in
Calculus
by
jothee
(
2.7k
points)
gate2020ce2
calculus
engineeringmathematics
integrals
0
votes
0
answers
4
GATE2020 CE224
Velocity distribution in a boundary layer is given by $\dfrac{u}{U_\infty} = \sin\large \left( \dfrac{\pi}{2}\dfrac{y}{\delta} \right)$, where $u$ is the velocity at vertical coordinate $y,\: U_\infty$ is the free stream velocity and $\delta$ is the boundary layer ... $\ s^{1}$, round off to two decimal places) at $y = 0$, is ________.
asked
Feb 13
in
Calculus
by
jothee
(
2.7k
points)
gate2020ce2
numericalanswers
calculus
engineeringmathematics
gradient
+2
votes
1
answer
5
GATE2019 CE1: 1
Which one of the following is correct? $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=2 $ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})=1 \\$ $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=1$ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})=1 \\$ ... $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=2$ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})= \infty$
answered
Jan 17
in
Calculus
by
KUSHAGRA गुप्ता
(
140
points)
gate2019ce1
calculus
limit
engineeringmathematics
0
votes
0
answers
6
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, 2019
in
Calculus
by
gatecse
(
3.9k
points)
gate2017ce2
vectorcalculus
divergence
numericalanswers
calculus
engineeringmathematics
0
votes
0
answers
7
GATE2017 CE227
Consider the following definite integral: $I= \int_0^1 \dfrac{(\sin ^{1}x)^2}{\sqrt{1x^2}} dx$. The value of the integral is $\dfrac{\pi ^3}{24} \\$ $\dfrac{\pi ^3}{12} \\$ $\dfrac{\pi ^3}{48} \\$ $\dfrac{\pi ^3}{64}$
asked
Aug 7, 2019
in
Calculus
by
gatecse
(
3.9k
points)
gate2017ce2
definite
integral
calculus
engineeringmathematics
+1
vote
0
answers
8
GATE2019 CE1: 4
For a small value of $h$, the Taylor series expansion for $f(x+h)$ is $f(x)+h{f}' (x) + \dfrac{h^2}{2!}{f}''(x) + \dfrac{h^3}{3!}{f}'''(x)+\dots \infty \\$ $f(x)h{f}' (x) + \dfrac{h^2}{2!}{f}''(x)  \dfrac{h^3}{3!}{f}'''(x)+ \dots \infty \\$ ... $f(x)h{f}' (x) + \dfrac{h^2}{2}{f}''(x)  \dfrac{h^3}{3}{f}'''(x)+ \dots \infty $
asked
Feb 14, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce1
taylorseries
calculus
engineeringmathematics
0
votes
0
answers
9
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, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce1
maximaminima
calculus
engineeringmathematics
0
votes
0
answers
10
GATE2019 CE1: 30
Consider two functions: $x=\psi \text{ ln } \phi$ and $y= \phi \text{ ln } \psi$. Which one of the following is the correct expression for $\frac{\partial \psi}{\partial x}$? $\dfrac{x \: \text{ln } \psi}{\text{ln } \phi \text{ ln } \psi 1} \\$ ... $\dfrac{\: \text{ln } \psi}{\text{ln } \phi \text{ ln } \psi 1}$
asked
Feb 14, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce1
calculus
engineeringmathematics
functions
0
votes
0
answers
11
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, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce2
limit
calculus
engineeringmathematics
0
votes
0
answers
12
GATE2019 CE2: 4
What is curl of the vector field $2x^2y \textbf{i} + 5z^2 \textbf{j} – 4yz \textbf{k}$? $6z \textbf{i} + 4x \textbf{j} – 2x^2 \textbf{k}$ $6z \textbf{i}  8xy \textbf{j} + 2x^2 y\textbf{k}$ $ 14 z \textbf{i} + 6y \textbf{j} + 2x^2 \textbf{k}$ $14z \textbf{i} – 2x^2 \textbf{k}$
asked
Feb 12, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce2
curl
vectoridentities
calculus
engineeringmathematics
0
votes
0
answers
13
GATE201622
The optimum value of the function $f(x)=x^24x+2$ is $2$ (maximum) $2$ (minimum) $ – 2$ (maximum) $ – 2$ (minimum)
asked
Mar 28, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2016ce2
calculus
engineeringmathematics
functions
0
votes
0
answers
14
GATE201625
What is the value of $\underset{x \rightarrow 0 \\ y \rightarrow 0}{\lim} \dfrac{xy}{x^2+y^2}$? $1$ $1$ $0$ Limit does not exist
asked
Mar 28, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2016ce2
limit
calculus
engineeringmathematics
0
votes
0
answers
15
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
(
11.9k
points)
gate2016ce2
engineeringmathematics
0
votes
0
answers
16
GATE2016229
The area between the parabola $x^2=8y$ and the straight line $y=8$ is _______.
asked
Mar 28, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2016ce2
definiteintegral
area
numericalanswers
engineeringmathematics
calculus
0
votes
0
answers
17
GATE2016129
The magnitudes of vectors $\textbf{P, Q}$ and $\textbf{R}$ are $100$ kN, $250$ kN and $150$ kN, respectively as shown in the figure. The respective values of the magnitude (in kN) and the direction (with respect to the xaxis) of the resultant vector are $290.9$ and $96.0^{\circ}$ $368.1$ and $94.7^{\circ}$ $330.4$ and $118.9^{\circ}$ $400.1$ and $113.5^{\circ}$
asked
Mar 28, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2016ce1
calculus
engineeringmathematics
vectors
0
votes
0
answers
18
GATE2017 CE1: 3
Let $x$ be a continuous variable defined over the interval $( \infty, \infty)$, and $f(x) = e^{xe^{x}}$. The integral $g(x)= \int f(x) \: dx$ is equal to $e^{e^{x}}$ $e^{e^{x}}$ $e^{e^{x}}$ $e^{x}$
asked
Mar 26, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2017ce1
calculus
engineeringmathematics
integrals
0
votes
0
answers
19
GATE201521
While minimizing the function $f(x)$, necessary and sufficient conditions for a point, $x_0$ to be a minima are: $f’(x_0) > 0$ and $f’’(x_0)=0$ $f’(x_0) < 0$ and $f’’(x_0)=0$ $f’(x_0) = 0$ and $f’’(x_0)<0$ $f’(x_0) = 0$ and $f’’(x_0)>0$
asked
Mar 26, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2015ce2
calculus
engineeringmathematics
functions
0
votes
0
answers
20
GATE201523
Given, $i=\sqrt{1}$, the value of the definite integral, $I= \int_0^{\pi/2} \dfrac{\cos x+ i \sin x}{\cos x – i \sin x} dx$ is: $1$ $1$ $i$ $i$
asked
Mar 26, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2015ce2
calculus
engineeringmathematics
integrals
0
votes
0
answers
21
GATE201524
$\underset{x \to \infty}{\lim} \bigg( 1+ \dfrac{1}{x} \bigg)^{2x} $ is equal to $e^{2}$ $e$ $1$ $e^2$
asked
Mar 26, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2015ce2
engineeringmathematics
0
votes
0
answers
22
GATE2015229
For stepsize, $\Delta x =0.4$, the value of following integral using Simpson’s $1/3$ rule is _______. $\int_0^{0.8} (0.2 + 25 x – 200 x^2 + 675 x^3 – 900 x^4 +400 x^5) dx$
asked
Mar 26, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2015ce2
numericalanswers
calculus
engineeringmathematics
integrals
0
votes
0
answers
23
GATE201512
The integral $\int_{x_{1}}^{x_{2}}x^{2}\:dx$ with $x_{2}>x_{1}>0$ is evaluated analytically as well as numerically using a single application of the trapezoidal rule. If $I$ is the exact value of the integral obtained analytically and ... , which of the following statement is correct about their relationship? $J>I$ $J<I$ $J=I$ Insufficient data to determine the relationship
asked
Mar 26, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2015ce1
calculus
integrals
engineeringmathematics
0
votes
0
answers
24
GATE2015129
Consider the following complex function: $f(z) = \frac{9}{(z1)(z+2)^2}$ Which of the following is one of the residues of the above function? $1$ $9/16$ $2$ $9$
asked
Mar 26, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2015ce1
calculus
engineeringmathematics
complexfunction
0
votes
0
answers
25
GATE2015130
The directional derivative of the field $u(x,y,z) = x^23yz$ in the direction of the vector $(\hat{i}+\hat{j}2 \hat{k})$ at point $(2, 1, 4)$ is _________.
asked
Mar 26, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2015ce1
numericalanswers
calculus
engineeringmathematics
vectoridentities
0
votes
0
answers
26
GATE201351
For a portion of national highway where a descending gradient of $1$ in $25$ meets with an ascending gradient of $1$ in $20$, a valley curve needs to be designed for a vehicle travelling at $90$ kmph based on the following conditions. headlight sight distance equal to ... m; and beam angle $1^{\circ}$. What is the length of valley curve (in m) based on the comfort condition? __________
asked
Mar 26, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2013ce
numericalanswers
calculus
engineeringmathematics
gradient
0
votes
0
answers
27
GATE201350
For a portion of national highway where a descending gradient of $1$ in $25$ meets with an ascending gradient of $1$ in $20$, a valley curve needs to be designed for a vehicle travelling at $90$ kmph based on the following conditions. headlight sight distance ... angle $1^{\circ}$. What is the length of valley curve (in m) based on the head light sight distance condition? ___________
asked
Mar 26, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2013ce
numericalanswers
calculus
engineeringmathematics
gradient
0
votes
0
answers
28
GATE2018 CE2: 2
The graph of a function $f(x)$ is shown in the figure. $1/3$ $2/3$ $1$ $3$
asked
Feb 17, 2018
in
Calculus
by
gatecse
(
3.9k
points)
gate2018ce2
function
calculus
engineeringmathematics
0
votes
0
answers
29
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
integrals
calculus
engineeringmathematics
0
votes
0
answers
30
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
calculus
engineeringmathematics
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