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Recent questions and answers in Calculus
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PREVIOUS YEAR MATHS SELF DOUBT
https://gateoverflow.in/1925/gate2014-1-47 WHY THE B CANT BE ANSWER IF WE DO THE SAME WAY WE DID FOR A AND D? PLEASE SEE...
asked
Dec 29, 2020
in
Calculus
by
eyeamgj
(
25
points)
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12
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selfdoubt
0
votes
0
answers
Applied mathematics by budnick
Marriage Prospects Data released by the Census Bureau in 1986 indicated the likelihood that never-married women would eventually marry. The data indicated that the older the woman, the less the likelihood of marriage. Specifically, two statistics indicated that women who were 45 and ... on this function is 20<=x<= 50, determine f(20), f(30), f(40), and f(50).
asked
Dec 27, 2020
in
Calculus
by
emankamal
(
5
points)
|
16
views
calculus
0
votes
0
answers
Calculus testbook question
Consider a function f(y) = $y^3 - 7y^2 + 5$ given on interval [p,q]. If f(y) satisfies hypothesis of Rolle’s theorem and p=0 then what is the value of q? The answer given was 7
asked
Dec 10, 2020
in
Calculus
by
Dheera
(
-22
points)
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11
views
calculus
0
votes
0
answers
The function f(x)=2.5loge(2+exp(x2−4x+5)) attains a minimum at x=?
asked
Nov 26, 2020
in
Calculus
by
neel19
(
7
points)
|
14
views
selfdoubt
enggmaths
calculus
0
votes
0
answers
In the interval [0,π] the equation x=cosx has ...
asked
Nov 26, 2020
in
Calculus
by
neel19
(
7
points)
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17
views
enggmaths
gatesyllabus
selfdoubt
0
votes
1
answer
Calculus doubt
How to draw graph of f(x)= xsinx+cosx with any proper source to understand.
answered
Aug 16, 2020
in
Calculus
by
Arkaprava
(
723
points)
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54
views
0
votes
1
answer
Gatebook:Calculus
The area of triangle is calculated by the formula . If the angle A is measure with 1% error. Find the % error in area. (A) (B) (C) (D)
answered
Aug 15, 2020
in
Calculus
by
Arkaprava
(
723
points)
|
33
views
gatebook
engineering-mathematics
calculus
0
votes
1
answer
Gatebook: Calculus
The area enclosed between the parabola and straight line is (A) (B) (C) (D)
answered
Aug 15, 2020
in
Calculus
by
Arkaprava
(
723
points)
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33
views
gatebook
engineering-mathematics
calculus
0
votes
1
answer
Trigonometry
I’m not able to understand my mistake, Please point it out.
answered
Aug 12, 2020
in
Calculus
by
Arkaprava
(
723
points)
|
49
views
calculus
0
votes
1
answer
self doubt on limits when it tends to infinity
Here , we can’t use L’ Hospital rule since limit is inifinity and what to do with (sinx)^2 ? Please someone explain.
answered
Jul 27, 2020
in
Calculus
by
AVICS
(
145
points)
|
33
views
0
votes
0
answers
self doubt on double integration
What to do for y^2 ? Please explain.
asked
Jul 26, 2020
in
Calculus
by
Jhaiyam
(
7
points)
|
12
views
0
votes
0
answers
GATE2014-1-47 Video Solution
A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true? There exists a $y$ in the interval $(0,1)$ such that $f(y) = f(y+1)$ For every $y$ in ... of the function in the interval $(0,2)$ is $1$ There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $-f(2-y)$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
10
views
gate2014-1
calculus
continuity
normal
video-solution
0
votes
0
answers
GATE2015-2-26 Video Solution
Let $f(x)=x^{-\left(\frac{1}{3}\right)}$ and $A$ denote the area of region bounded by $f(x)$ and the X-axis, when $x$ varies from $-1$ to $1$. Which of the following statements is/are TRUE? $f$ is continuous in $[-1, 1]$ $f$ is not bounded in $[-1, 1]$ $A$ is nonzero and finite II only III only II and III only I, II and III
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
7
views
gate2015-2
continuity
functions
normal
video-solution
0
votes
0
answers
GATE2018-16 Video Solution
The value of $\int^{\pi/4} _0 x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$) is ____
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
7
views
gate2018
calculus
integration
normal
numerical-answers
video-solution
0
votes
0
answers
GATE2012-9 Video Solution
Consider the function $f(x) = \sin(x)$ in the interval $x =\left[\frac{\pi}{4},\frac{7\pi}{4}\right]$. The number and location(s) of the local minima of this function are One, at $\dfrac{\pi}{2}$ One, at $\dfrac{3\pi}{2}$ Two, at $\dfrac{\pi}{2}$ and $\dfrac{3\pi}{2}$ Two, at $\dfrac{\pi}{4}$ and $\dfrac{3\pi}{2}$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
8
views
gate2012
calculus
maxima-minima
normal
nielit
video-solution
0
votes
0
answers
GATE2014-1-6 Video Solution
Let the function ... exists $\theta \in (\frac{\pi}{6},\frac{\pi}{3})$ such that $f'(\theta)\neq 0$ I only II only Both I and II Neither I Nor II
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
5
views
gate2014-1
calculus
differentiation
normal
video-solution
0
votes
0
answers
GATE2015-3-9 Video Solution
The value of $\lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is $0$ $\frac{1}{2}$ $1$ $\infty$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
7
views
gate2015-3
calculus
limits
normal
video-solution
0
votes
0
answers
GATE2016-2-02 Video Solution
Let $f(x)$ be a polynomial and $g(x)=f'(x)$ be its derivative. If the degree of $(f(x)+f(-x))$ is $10$, then the degree of $(g(x) - g(-x))$ is __________.
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
25
views
gate2016-2
calculus
normal
numerical-answers
differentiation
video-solution
0
votes
0
answers
GATE2014-3-6 Video Solution
If $\int \limits_0^{2 \pi} |x \: \sin x| dx=k\pi$, then the value of $k$ is equal to ______.
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
7
views
gate2014-3
calculus
integration
limits
numerical-answers
easy
video-solution
0
votes
0
answers
GATE2015-3-45 Video Solution
If for non-zero $x, \: af(x) + bf(\frac{1}{x}) = \frac{1}{x} - 25$ where a $a \neq b \text{ then } \int_1^2 f(x)dx$ is $\frac{1}{a^2 - b^2} \begin{bmatrix} a(\ln 2 - 25) + \frac{47b}{2} \end{bmatrix}$ ... $\frac{1}{a^2 - b^2} \begin{bmatrix} a(\ln 2 - 25) - \frac{47b}{2} \end{bmatrix}$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
7
views
gate2015-3
calculus
integration
normal
video-solution
0
votes
0
answers
GATE2017-2-10 Video Solution
If $f(x) = R \: \sin ( \frac{\pi x}{2}) + S, f’\left(\frac{1}{2}\right) = \sqrt{2}$ and $\int_0^1 f(x) dx = \frac{2R}{\pi}$, then the constants $R$ and $S$ are $\frac{2}{\pi}$ and $\frac{16}{\pi}$ $\frac{2}{\pi}$ and 0 $\frac{4}{\pi}$ and 0 $\frac{4}{\pi}$ and $\frac{16}{\pi}$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
7
views
gate2017-2
engineering-mathematics
calculus
differentiation
video-solution
0
votes
0
answers
GATE2008-1 Video Solution
$\lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
10
views
gate2008
calculus
limits
easy
video-solution
0
votes
0
answers
GATE2016-1-3 Video Solution
$\lim _{x\rightarrow 4}\frac{\sin(x-4)}{x-4}$=____.
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
7
views
gate2016-1
calculus
limits
easy
numerical-answers
video-solution
0
votes
0
answers
GATE2011-31 Video Solution
Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$ ? $0$ $2$ $-i$ $i$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
5
views
gate2011
calculus
integration
normal
video-solution
0
votes
0
answers
GATE2015-1-44 Video Solution
Compute the value of: $\large \int_{\frac{1}{\pi}}^{\frac{2}{\pi}}\frac{\cos(1/x)}{x^{2}}dx$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
12
views
gate2015-1
calculus
integration
normal
numerical-answers
video-solution
0
votes
0
answers
GATE2015-1-4 Video Solution
$\lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is $\infty $ 0 1 Not defined
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
7
views
gate2015-1
calculus
limits
normal
video-solution
0
votes
0
answers
GATE2017-1-28 Video Solution
The value of $\lim_{x\rightarrow 1} \frac{x^{7}-2x^{5}+1}{x^{3}-3x^{2}+2}$ is $0$ is $-1$ is $1$ does not exist
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
5
views
gate2017-1
calculus
limits
normal
video-solution
0
votes
0
answers
GATE2008-25 Video Solution
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is $0$ $1$ $2$ $3$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
7
views
gate2008
calculus
maxima-minima
easy
video-solution
0
votes
0
answers
GATE2014-3-47 Video Solution
The value of the integral given below is $\int \limits_0^{\pi} \: x^2 \: \cos x\:dx$ $-2\pi$ $\pi$ $-\pi$ $2\pi$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
7
views
gate2014-3
calculus
limits
integration
normal
video-solution
0
votes
0
answers
GATE2013-22 Video Solution
Which one of the following functions is continuous at $x = 3?$ $f(x) = \begin{cases} 2,&\text{if $x = 3$ } \\ x-1& \text{if $x > 3$}\\ \frac{x+3}{3}&\text{if $x < 3$ } \end{cases}$ $f(x) = \begin{cases} 4,&\text{if $ ... $} \end{cases}$ $f(x) = \begin{cases} \frac{1}{x^3-27}&\text{if $x \neq 3$ } \end{cases}$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
7
views
gate2013
calculus
continuity
normal
video-solution
0
votes
0
answers
GATE2010-5 Video Solution
What is the value of $\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ? 0 $e^{-2}$ $e^{-1/2}$ 1
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
5
views
gate2010
calculus
limits
normal
video-solution
0
votes
0
answers
GATE2008-IT-31 Video Solution
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ? $f(x) = \begin{cases} \frac{25}{8x} \text{ when } x \leq \frac{3}{2} \\ x+ \frac{1}{x} \text { otherwise}\end{cases}$ $2$ $2 \frac{1}{12}$ $2\frac{1}{6}$ $2\frac{1}{2}$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
10
views
gate2008-it
calculus
maxima-minima
normal
video-solution
0
votes
0
answers
GATE2019-13 Video Solution
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$ $1$ $53/12$ $108/7$ Limit does not exist
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
7
views
gate2019
engineering-mathematics
calculus
limits
video-solution
0
votes
0
answers
GATE2000-2.3 Video Solution
Let $S = \sum_{i=3}^{100} i \log_{2} i$, and $T = \int_{2}^{100} x \log_{2}x dx$. Which of the following statements is true? $S > T$ $S = T$ $S < T$ and $2S > T$ $2S ≤ T$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
8
views
gate2000
calculus
integration
normal
video-solution
0
votes
0
answers
GATE2015-2-GA-3 Video Solution
Consider a function $f(x) = 1- |x| \text{ on } -1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the maximum value of the function are: $0, -1$ $-1, 0$ $0, 1$ $-1, 2$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
9
views
gate2015-2
set-theory&algebra
functions
normal
maxima-minima
video-solution
0
votes
0
answers
GATE1997-4.1 Video Solution
What is the maximum value of the function $f(x) = 2x^2 - 2x + 6$ in the interval $\left[0,2 \right]$? 6 10 12 5.5
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
5
views
gate1997
calculus
maxima-minima
normal
video-solution
0
votes
0
answers
GATE1996-1.6 Video Solution
The formula used to compute an approximation for the second derivative of a function $f$ at a point $X_0$ is $\dfrac{f(x_0 +h) + f(x_0 – h)}{2}$ $\dfrac{f(x_0 +h) - f(x_0 – h)}{2h}$ $\dfrac{f(x_0 +h) + 2f(x_0) + f(x_0 – h)}{h^2}$ $\dfrac{f(x_0 +h) - 2f(x_0) + f(x_0 – h)}{h^2}$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
10
views
gate1996
calculus
differentiation
normal
video-solution
0
votes
0
answers
GATE2005-IT-35 Video Solution
What is the value of $\int_{0}^{2\pi}(x-\pi)^2 (\sin x) dx$ $-1$ $0$ $1$ $\pi$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
14
views
gate2005-it
calculus
integration
normal
video-solution
0
votes
0
answers
GATE2007-1 Video Solution
Consider the following two statements about the function $f(x)=\left\vert x\right\vert$: P. $f(x)$ is continuous for all real values of $x$. Q. $f(x)$ is differentiable for all real values of $x$ . Which of the following is TRUE? $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are true. Both $P$ and $Q$ are false.
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
7
views
gate2007
calculus
continuity
differentiation
easy
video-solution
0
votes
0
answers
GATE2009-25 Video Solution
$\int^{\pi/4}_0 (1-\tan x)/(1+\tan x)\,dx $ $0$ $1$ $ln 2$ $1/2 ln 2$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)
|
6
views
gate2009
calculus
integration
normal
video-solution
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