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Recent questions and answers in Calculus
0
votes
1
answer
TIFRGS2021 Question
Find the following sum $\frac{1}{2^2 – 1} + \frac{1}{4^2 – 1} + \frac{1}{6^2 – 1} + … + \frac{1}{40^2 – 1}$ (A) $\frac{20}{41}$ (B) $\frac{10}{41}$ (C) $\frac{10}{21}$ (D) $\frac{20}{21}$ (E) $1$
answered
Mar 24
in
Calculus
by
ankitgupta.1729
(
357
points)

29
views
numberseries
sum
tifr2021
0
votes
1
answer
TIRFGS2021 Question
What is the area of a rectangle with the largest perimeter that can be inscribed in a unit circle (i.e., all the vertices of the rectangle are on the circle with radius 1)? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5
answered
Mar 24
in
Calculus
by
ankitgupta.1729
(
357
points)

40
views
tifr2021
area
0
votes
0
answers
TIFRGS2021 Question
Consider the sequence $y_n = \frac{1}{\int_{1}^{n}\frac{1}{(1 + x/n)^3}dx}$ for $n = 2, 3, 4, ...$. Which of the following is TRUE? (A) The sequence $\{y_n\}$ does not have a limit as $n\rightarrow \infty$. (B) $y_n\leq 1$ ... $0$. (E) The sequence $\{y_n\}$ first increases and then decreases as $n$ takes values $2, 3, 4, ...$
asked
Mar 24
in
Calculus
by
zxy123
(
3.6k
points)

3
views
tifr2021
limits
0
votes
0
answers
I have a doubt in engineering mathematics.
despite knowing different numerical methods like taylor’s series , R K Method , Eulers method , which one to choose based on the matrix pattern.
asked
Mar 2
in
Calculus
by
einstein
(
5
points)

11
views
calculus
+1
vote
0
answers
#madeeasy #limits
1/4 1/8 1/16 none of above ans given is c but according to me it would tends to infinity bcz in numerator n^4 will generate that is asymptotically larger than n3 in denominator. so answer should be d
asked
Jan 23
in
Calculus
by
404 found
(
37
points)

16
views
madeeasytest
0
votes
0
answers
PREVIOUS YEAR MATHS SELF DOUBT
https://gateoverflow.in/1925/gate2014147 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
(
29
points)

14
views
selfdoubt
0
votes
0
answers
Applied mathematics by budnick
Marriage Prospects Data released by the Census Bureau in 1986 indicated the likelihood that nevermarried 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)

18
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
(
14
points)

13
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)

17
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)

22
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
(
801
points)

58
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
(
801
points)

35
views
gatebook
engineeringmathematics
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
(
801
points)

35
views
gatebook
engineeringmathematics
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
(
801
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)

34
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
GATE2014147 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 $f(y)$ = $f(2y)$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)

12
views
gate20141
calculus
continuity
normal
videosolution
0
votes
0
answers
GATE2015226 Video Solution
Let $f(x)=x^{\left(\frac{1}{3}\right)}$ and $A$ denote the area of region bounded by $f(x)$ and the Xaxis, 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)

8
views
gate20152
continuity
functions
normal
videosolution
0
votes
0
answers
GATE201816 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)

10
views
gate2018
calculus
integration
normal
numericalanswers
videosolution
0
votes
0
answers
GATE20129 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)

11
views
gate2012
calculus
maximaminima
normal
nielit
videosolution
0
votes
0
answers
GATE201416 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)

7
views
gate20141
calculus
differentiation
normal
videosolution
0
votes
0
answers
GATE201539 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
gate20153
calculus
limits
normal
videosolution
0
votes
0
answers
GATE2016202 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)

29
views
gate20162
calculus
normal
numericalanswers
differentiation
videosolution
0
votes
0
answers
GATE201436 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)

10
views
gate20143
calculus
integration
limits
numericalanswers
easy
videosolution
0
votes
0
answers
GATE2015345 Video Solution
If for nonzero $x, \: af(x) + bf(\frac{1}{x}) = \frac{1}{x}  25$ 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
gate20153
calculus
integration
normal
videosolution
0
votes
0
answers
GATE2017210 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
gate20172
engineeringmathematics
calculus
differentiation
videosolution
0
votes
0
answers
GATE20081 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
videosolution
0
votes
0
answers
GATE201613 Video Solution
$\lim _{x\rightarrow 4}\frac{\sin(x4)}{x4}$=____.
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)

8
views
gate20161
calculus
limits
easy
numericalanswers
videosolution
0
votes
0
answers
GATE201131 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)

9
views
gate2011
calculus
integration
normal
videosolution
0
votes
0
answers
GATE2015144 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
gate20151
calculus
integration
normal
numericalanswers
videosolution
0
votes
0
answers
GATE201514 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
gate20151
calculus
limits
normal
videosolution
0
votes
0
answers
GATE2017128 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
gate20171
calculus
limits
normal
videosolution
0
votes
0
answers
GATE200825 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 $3x^416x^3+24x^2+37$ is $0$ $1$ $2$ $3$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)

8
views
gate2008
calculus
maximaminima
easy
videosolution
0
votes
0
answers
GATE2014347 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
gate20143
calculus
limits
integration
normal
videosolution
0
votes
0
answers
GATE201322 Video Solution
Which one of the following functions is continuous at $x = 3?$ $f(x) = \begin{cases} 2,&\text{if $x = 3$ } \\ x1& \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^327}&\text{if $x \neq 3$ } \end{cases}$
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)

8
views
gate2013
calculus
continuity
normal
videosolution
0
votes
0
answers
GATE20105 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)

6
views
gate2010
calculus
limits
normal
videosolution
0
votes
0
answers
GATE2008IT31 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)

12
views
gate2008it
calculus
maximaminima
normal
videosolution
0
votes
0
answers
GATE201913 Video Solution
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^481}{2x^25x3}$ $1$ $53/12$ $108/7$ Limit does not exist
asked
Apr 18, 2020
in
Calculus
by
admin
(
573
points)

8
views
gate2019
engineeringmathematics
calculus
limits
videosolution
0
votes
0
answers
GATE20002.3 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
videosolution
0
votes
0
answers
GATE20152GA3 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
gate20152
settheory&algebra
functions
normal
maximaminima
videosolution
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