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Recent questions tagged calculus
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1
GATE2020-CE-1-2
The value of $\lim_{x\to\infty}\dfrac{x^2-5x+4}{4x^2+2x}$ is $0 \\$ $\dfrac{1}{4} \\$ $\dfrac{1}{2} \\$ $1$
asked
Feb 28, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020-ce-1
engineering-mathematics
limit
calculus
0
votes
0
answers
2
GATE2020-CE-1-27
A continuous function $f(x)$ is defined. If the third derivative at $x_i$ is to be computed by using the fourth order central finite-divided-difference scheme (with step length $=h$ ...
asked
Feb 28, 2020
in
Calculus
by
jothee
(
2.7k
points)
gate2020-ce-1
calculus
functions
engineering-mathematics
0
votes
0
answers
3
GATE2020-CE-1-39
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, 2020
in
Calculus
by
jothee
(
2.7k
points)
gate2020-ce-1
calculus
engineering-mathematics
integrals
numerical-answers
0
votes
0
answers
4
GATE2020 CE-2-3
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 ... NON-zero error. Only the rectangular rule of estimation will give zero error. Only Simpson's rule of estimation will give zero error.
asked
Feb 13, 2020
in
Calculus
by
jothee
(
2.7k
points)
gate2020-ce-2
calculus
engineering-mathematics
integrals
0
votes
0
answers
5
GATE2020 CE-2-24
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, 2020
in
Calculus
by
jothee
(
2.7k
points)
gate2020-ce-2
numerical-answers
calculus
engineering-mathematics
gradient
0
votes
0
answers
6
GATE2017 CE-2-19
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)
gate2017-ce-2
vector-calculus
divergence
numerical-answers
calculus
engineering-mathematics
0
votes
0
answers
7
GATE2017 CE-2-27
Consider the following definite integral: $I= \int_0^1 \dfrac{(\sin ^{-1}x)^2}{\sqrt{1-x^2}} dx$. 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)
gate2017-ce-2
definite
integral
calculus
engineering-mathematics
+2
votes
1
answer
8
GATE2019 CE-1: 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 $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})= \infty$
asked
Feb 14, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019-ce-1
calculus
limit
engineering-mathematics
+1
vote
0
answers
9
GATE2019 CE-1: 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)
gate2019-ce-1
taylor-series
calculus
engineering-mathematics
0
votes
0
answers
10
GATE2019 CE-1: 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)
gate2019-ce-1
maxima-minima
calculus
engineering-mathematics
0
votes
0
answers
11
GATE2019 CE-1: 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)
gate2019-ce-1
calculus
engineering-mathematics
functions
0
votes
0
answers
12
GATE2019 CE-2: 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)
gate2019-ce-2
limit
calculus
engineering-mathematics
0
votes
0
answers
13
GATE2019 CE-2: 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)
gate2019-ce-2
curl
vector-identities
calculus
engineering-mathematics
0
votes
0
answers
14
GATE2016-2-2
The optimum value of the function $f(x)=x^2-4x+2$ is $2$ (maximum) $2$ (minimum) $ – 2$ (maximum) $ – 2$ (minimum)
asked
Mar 28, 2018
in
Calculus
by
Milicevic3306
(
11.9k
points)
gate2016-ce-2
calculus
engineering-mathematics
functions
0
votes
0
answers
15
GATE2016-2-5
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)
gate2016-ce-2
limit
calculus
engineering-mathematics
0
votes
0
answers
16
GATE2016-2-29
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)
gate2016-ce-2
definite-integral
area
numerical-answers
engineering-mathematics
calculus
0
votes
0
answers
17
GATE2016-1-29
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 x-axis) 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)
gate2016-ce-1
calculus
engineering-mathematics
vectors
0
votes
0
answers
18
GATE2017 CE-1: 2
The number of parameters in the univariate exponential and Gaussian distributions, repsectively, are $2$ and $2$ $1$ and $2$ $2$ and $1$ $1$ and $1$
asked
Mar 26, 2018
in
Engineering Mathematics
by
Milicevic3306
(
11.9k
points)
gate2017-ce-1
engineering-mathematics
gaussian-distributions
calculus
0
votes
0
answers
19
GATE2017 CE-1: 3
Let $x$ be a continuous variable defined over the interval $(- \infty, \infty)$, and $f(x) = e^{-x-e^{-x}}$. 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)
gate2017-ce-1
calculus
engineering-mathematics
integrals
0
votes
0
answers
20
GATE2015-2-1
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)
gate2015-ce-2
calculus
engineering-mathematics
functions
0
votes
0
answers
21
GATE2015-2-3
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)
gate2015-ce-2
calculus
engineering-mathematics
integrals
0
votes
0
answers
22
GATE2015-2-29
For step-size, $\Delta x =0.4$, 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)
gate2015-ce-2
numerical-answers
calculus
engineering-mathematics
integrals
0
votes
0
answers
23
GATE2015-1-2
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)
gate2015-ce-1
calculus
integrals
engineering-mathematics
0
votes
0
answers
24
GATE2015-1-29
Consider the following complex function: $f(z) = \frac{9}{(z-1)(z+2)^2}$ 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)
gate2015-ce-1
calculus
engineering-mathematics
complex-function
0
votes
0
answers
25
GATE2015-1-30
The directional derivative of the field $u(x,y,z) = x^2-3yz$ 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)
gate2015-ce-1
numerical-answers
calculus
engineering-mathematics
vector-identities
0
votes
0
answers
26
GATE2013-51
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)
gate2013-ce
numerical-answers
calculus
engineering-mathematics
gradient
0
votes
0
answers
27
GATE2013-50
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)
gate2013-ce
numerical-answers
calculus
engineering-mathematics
gradient
0
votes
0
answers
28
GATE2018 CE-2: 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)
gate2018-ce-2
function
calculus
engineering-mathematics
0
votes
0
answers
29
GATE2018 CE-1: 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)
gate2018-ce-1
integration
integrals
calculus
engineering-mathematics
0
votes
0
answers
30
GATE2018 CE-1: 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)
gate2018-ce-1
maxima-minima
calculus
engineering-mathematics
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