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Recent questions and answers in Calculus
+1
vote
1
answer
1
ISIMMA 2019 Sample Questions23
For $n \geq1$, Let $a_{n} = \frac{1}{2^{2}} + \frac{2}{3^{2}} +.....+ \frac{n}{(n+1)^{2}}$ and $b_{n} = c_{0} + c_{1}r + c_{2}r^{2}+.....+c_{n}r^{n},$ where$c_{k} \leq M$ for all integers $k$ ... not a Cauchy sequence (C) $\{a_n\}$ is not a Cauchy sequence but $\{b_n\}$ is a Cauchy sequence (D) neither $\{a_n\}$ nor $\{b_n\}$ is a Cauchy sequence.
answered
Mar 18
in
Calculus
by
Kushagra Chatterjee
Loyal
(
9k
points)

53
views
sequenceseries
calculus
0
votes
1
answer
2
UPPCL AE 2018:81
answered
Mar 11
in
Calculus
by
Ram Swaroop
Active
(
2.6k
points)

45
views
uppcl2018
+1
vote
1
answer
3
Continuity and Differentiability
If the function f(x) =[(x2)3 /a] sin(x2) + acos(x2), [.] denotes greatest integer function, is continuous & differentiable in (4,6) then find ‘a’ range: (A) a ϵ (∞,∞) (B) a ϵ [64, ∞) (C) a ϵ [128, ∞) (D) Not defined
answered
Mar 10
in
Calculus
by
jinal99
(
21
points)

260
views
0
votes
2
answers
4
ISRO2012ECE Engineering Mathematics
a) 1x b) (1x)/x c)1/x d)x/(1x)
answered
Mar 10
in
Calculus
by
abhishekmehta4u
Boss
(
33.4k
points)

62
views
engineeringmathematics
isro2012ece
isroece
calculus
0
votes
1
answer
5
ISI MMA2015
Let, $a_{n} \;=\; \left ( 1\frac{1}{\sqrt{2}} \right ) ... \left ( 1 \frac{1}{\sqrt{n+1}} \right )$ , $n \geq 1$. Then $\lim_{n\rightarrow \infty } a_{n}$ (A) equals $1$ (B) does not exist (C) equals $\frac{1}{\sqrt{\pi }}$ (D) equals $0$
answered
Feb 21
in
Calculus
by
venkatesh pagadala
(
471
points)

99
views
engineeringmathematics
calculus
userisi2015
usermod
sequenceseries
limits
+1
vote
1
answer
6
ISI MMA2015
If two real polynomials $f(x)$ and $g(x)$ of degrees $m\;(\geq2)$ and $n\;(\geq1)$ respectively, satisfy $f(x^{2}+1) = f(x)g(x)$ $,$ for every $x\in \mathbb{R}$ , then (A) $f$ has exactly one real root $x_{0}$ such that $f'(x_{0}) \neq 0$ (B) $f$ has exactly one real root $x_{0}$ such that $f'(x_{0}) = 0$ (C) $f$ has $m$ distinct real roots (D) $f$ has no real root.
answered
Feb 21
in
Calculus
by
Kushagra Chatterjee
Loyal
(
9k
points)

67
views
engineeringmathematics
calculus
userisi2015
usermod
+1
vote
5
answers
7
GATE201913
Compute $\lim_{x \rightarrow 3} \frac{x^481}{2x^25x3}$ $1$ $53/12$ $108/7$ Limit does not exist
answered
Feb 12
in
Calculus
by
Satbir
Loyal
(
5.9k
points)

1.5k
views
gate2019
engineeringmathematics
calculus
limits
+2
votes
3
answers
8
VALUE OF LIMIT
What is value of $\lim_{x\rightarrow 0, Y\rightarrow 0}\frac{xY}{x^2+Y^2}$ 1 1 0 Does not exist
answered
Jan 28
in
Calculus
by
Sai Shravan
(
149
points)

280
views
limits
+5
votes
3
answers
9
TIFR2011A11
$\int_{0}^{1} \ln x\, \mathrm{d}x=$ $1$ $1$ $\infty $ $\infty $ None of the above.
answered
Jan 26
in
Calculus
by
Lakshman Patel RJIT
Boss
(
34.5k
points)

450
views
tifr2011
calculus
integration
0
votes
0
answers
10
How to solve such question.
$\frac{d}{dx}\int_{1}^{x^4} sect\space dt$
asked
Jan 20
in
Calculus
by
`JEET
Active
(
3.4k
points)

80
views
calculus
integration
0
votes
0
answers
11
MadeEasy Workbook: Calculus  Maxima Minima
asked
Jan 19
in
Calculus
by
chanchala3993
(
7
points)

35
views
engineeringmathematics
calculus
maximaminima
madeeasybooklet
0
votes
0
answers
12
Calculating average mean
The aggregate monthly expenditure of a family was $ 6240 during first 3 months, $ 6780 during next 4 months, and $7236 during last 5 months of a year. If total saving during the year is $ 7080. Find average monthly income of family?
asked
Jan 13
in
Calculus
by
Alina
(
27
points)

31
views
0
votes
0
answers
13
Ace Test Series: Calculus  Integration
Can anyone help me with solving this type of problem? I want some resource from where I can learn to solve this type on integration, as according to solution it is a function of α, so I did not understand the solution.
asked
Jan 12
in
Calculus
by
jhaanuj2108
(
227
points)

60
views
acetestseries
calculus
integration
0
votes
1
answer
14
How to solve such question with different variable in the limit.
$\int_{a}^{x} \frac{sint}{t} dt$ (x > 0), then f(x) has _________________. (A) a maximum at x = $n\pi$ where n is even (B) a minimum at x = $n\pi$ where n is odd (C) a maximum at x = $n\pi$ where n is odd (D) a minimum at x = $\frac{n\pi}{2}$ where n is odd.
answered
Jan 12
in
Calculus
by
Pranavapp
(
21
points)

59
views
0
votes
1
answer
15
Integration
How to solve it?
answered
Jan 11
in
Calculus
by
adeemajain
(
201
points)

53
views
0
votes
1
answer
16
GATEBOOK2019 Grand Test Mathematics8
The value of $\large\int\limits_{1}^{4} \mid y2 \mid dy$ is $3$ $\left (\dfrac{3}{2} \right )$ $\left (\dfrac{5}{2} \right )$ $\left (\dfrac{7}{2} \right )$
answered
Jan 10
in
Calculus
by
pranay562
Active
(
1.2k
points)

77
views
gb2019gtmaths
0
votes
1
answer
17
ME TEST SERIES
answered
Jan 10
in
Calculus
by
Kunal Kadian
Active
(
2.6k
points)

50
views
+1
vote
1
answer
18
UPPCL AE 2018:85
answered
Jan 5
in
Calculus
by
Lakshman Patel RJIT
Boss
(
34.5k
points)

89
views
uppcl2018
0
votes
1
answer
19
self doubt
$\lim_{x\rightarrow \frac{\pi }{2}}cosx^{cosx}$ can we straight away say $0^{0}=0$ ?
answered
Jan 5
in
Calculus
by
Nandkishor3939
Active
(
1.2k
points)

44
views
calculus
0
votes
1
answer
20
calculus question
Question Number 4?
answered
Jan 5
in
Calculus
by
GATE2021
(
11
points)

45
views
calculus
0
votes
1
answer
21
GATE 2013 MA Calculus
answered
Jan 3
in
Calculus
by
pradeepchaudhary
Active
(
1.2k
points)

27
views
0
votes
0
answers
22
#integration
I=$\int_{1}^{\infty }a^{ceil (log _{b} x ) } dx$
asked
Jan 3
in
Calculus
by
amit166
Junior
(
761
points)

44
views
integration
0
votes
0
answers
23
#integration
$I=\int sin(2x) cos(3x) dx$ 1.(5cosxcos5x)/10 2.(5sinxsin5x)/10 3.both 4.none
asked
Jan 3
in
Calculus
by
amit166
Junior
(
761
points)

64
views
integration
0
votes
0
answers
24
Math doubt
Is it true $\frac{1}{1+x^{2}}=1x^{2}$ Is it applied every function? (like limit func, generating func)?
asked
Jan 3
in
Calculus
by
srestha
Veteran
(
111k
points)

51
views
discretemathematics
0
votes
0
answers
25
Clarification on Topic
In the syllabus it was said “differentiability” does this mean we have partial differentiation.??
asked
Jan 2
in
Calculus
by
Hemanth_13
Loyal
(
6.6k
points)

23
views
generalquery
0
votes
1
answer
26
Integration
If n is a positive integer, then $\int_{0}^{\pi} \frac{sin(2nx)}{sinx} dx$
answered
Dec 27, 2018
in
Calculus
by
vg653
(
125
points)

63
views
0
votes
0
answers
27
Shortcut Method to find Maxima and Minima in Calculus
https://www.youtube.com/watch?v=tyiQLindzCE This is a great video but covers formula for cubic root what about for any given equation x^n,what would be the solution?
asked
Dec 26, 2018
in
Calculus
by
sripo
Active
(
2.6k
points)

76
views
calculus
maximaminima
engineeringmathematics
+2
votes
3
answers
28
TIFR2019A15
Consider the matrix $\begin{bmatrix} \frac{1}{2} &\frac{1}{2} & 0\\ 0& \frac{3}{4} & \frac{1}{4}\\ 0& \frac{1}{4} & \frac{3}{4} \end{bmatrix}$ What is $lim_{n→\infty}$A^n$ ? $\begin{bmatrix} \ 0 & 0 & 0\\ 0& 0 & 0\ ... The limit exists, but it none of the above
answered
Dec 25, 2018
in
Calculus
by
AsiaPacific
(
103
points)

253
views
tifr2019
engineeringmathematics
calculus
limits
0
votes
0
answers
29
self doubt
How to solve these questions $(1)$ $I=\int_{0}^{1}(xlogx)^{4}dx$ $(2)$ $I=\frac{1}{\sqrt{2\pi}}\int_{0}^{\infty}e^{\frac{x^{2}}{8}}dx$ $(3)$ $I=\int_{0}^{\infty}x^{\frac{1}{4}}.e^{\sqrt{x}}dx$
asked
Dec 23, 2018
in
Calculus
by
Lakshman Patel RJIT
Boss
(
34.5k
points)

88
views
engineeringmathematics
calculus
+1
vote
2
answers
30
Maths: Limit question
$\lim_{n\rightarrow \infty} \left[\frac{n.2^n}{e^n}\right]$ The detailed solution, please?
answered
Dec 20, 2018
in
Calculus
by
Peeyush Pandey
Active
(
2.6k
points)

86
views
limits
calculus
engineeringmathematics
0
votes
0
answers
31
GATE EE 2018
[closed]
asked
Dec 18, 2018
in
Calculus
by
aditi19
Active
(
2.9k
points)

65
views
gate2018analysis
engineeringmathematics
calculus
continuity
differentiability
0
votes
0
answers
32
TIFR2019A13
Consider the integral $\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3}$dx$ What is the value of this integral correct up to two decimal places ? $0.00$ $0.02$ $0.10$ $0.33$ $1.00$
asked
Dec 18, 2018
in
Calculus
by
Arjun
Veteran
(
396k
points)

170
views
tifr2019
engineeringmathematics
calculus
integration
0
votes
0
answers
33
#maths #limit
asked
Dec 18, 2018
in
Calculus
by
Manan Shah
(
129
points)

44
views
+3
votes
2
answers
34
Lagrange 's Mean Value Theorem 2
If f ' (x) =$\frac{8}{x^{}2+3x+4}$ and f(0) =1 then the lower and upper bounds of f(1) estimated by Langrange 's Mean Value Theorem are ___
answered
Dec 15, 2018
in
Calculus
by
Mounodeep
(
21
points)

588
views
meanvaluetheorem
calculus
0
votes
0
answers
35
aai 2018
asked
Dec 13, 2018
in
Calculus
by
pream sagar
Active
(
2.7k
points)

44
views
0
votes
0
answers
36
GATE 2016 MA Limits
asked
Dec 12, 2018
in
Calculus
by
Balaji Jegan
Loyal
(
5.4k
points)

26
views
0
votes
0
answers
37
GATE 2016 MA Calculus
asked
Dec 12, 2018
in
Calculus
by
Balaji Jegan
Loyal
(
5.4k
points)

29
views
0
votes
0
answers
38
GATE 2013 MA Calculus
asked
Dec 12, 2018
in
Calculus
by
Balaji Jegan
Loyal
(
5.4k
points)

25
views
0
votes
0
answers
39
GATE 2013 MA Calculus
asked
Dec 12, 2018
in
Calculus
by
Balaji Jegan
Loyal
(
5.4k
points)

27
views
0
votes
0
answers
40
Self Doubt
Plese explain me this series
asked
Dec 11, 2018
in
Calculus
by
HeadShot
Active
(
4.9k
points)

43
views
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