Recent questions tagged calculus

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1

GATE2020-CE-1-2
The value of $\lim_{x\to\infty}\frac{x^2-5x+4}{4x^2+2x}$ is $0 \\$ $\large\frac{1}{4} \\$ $\large\frac{1}{2} \\$ $\:1$

asked Feb 28 in Others by jothee (2.7k points)

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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 in Others by jothee (2.7k points)

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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 in Others by jothee (2.7k points)

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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 in Others by jothee (2.7k points)

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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 in Others by jothee (2.7k points)

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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)

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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)

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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)

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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)

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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)

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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 Others by Arjun (2.8k points)

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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)

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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 Others by Arjun (2.8k points)

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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 Others by Milicevic3306 (11.9k points)

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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)

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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)

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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 Others by Milicevic3306 (11.9k points)

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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 $1$