Recent questions and answers in Calculus

+1 vote

1 answer

1

ISI-MMA 2019 Sample Questions-23
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

0 votes

1 answer

2

UPPCL AE 2018:81

answered Mar 11 in Calculus by Ram Swaroop Active (2.6k points) | 45 views

+1 vote

1 answer

3

Continuity and Differentiability
If the function f(x) =[(x-2)3 /a] sin(x-2) + acos(x-2), [.] 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

ISRO2012-ECE Engineering Mathematics
a) 1-x b) (1-x)/x c)1/x d)x/(1-x)

answered Mar 10 in Calculus by abhishekmehta4u Boss (33.4k points) | 62 views

0 votes

1 answer

5

ISI MMA-2015
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

+1 vote

1 answer

6

ISI MMA-2015
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

+1 vote

5 answers

7

GATE2019-13
Compute $\lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$ $1$ $53/12$ $108/7$ Limit does not exist

answered Feb 12 in Calculus by Satbir Loyal (5.9k points) | 1.5k views

+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

+5 votes

3 answers

9

TIFR2011-A-11
$\int_{0}^{1} \ln x\, \mathrm{d}x=$ $1$ $-1$ $\infty $ $-\infty $ None of the above.

answered Jan 26 in Calculus by Lakshman Patel RJIT Boss (34.5k points) | 450 views

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

0 votes

0 answers

11

MadeEasy Workbook: Calculus - Maxima Minima

asked Jan 19 in Calculus by chanchala3993 (7 points) | 35 views

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

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

GATEBOOK-2019 Grand Test Mathematics-8
The value of $\large\int\limits_{1}^{4} \mid y-2 \mid dy$ 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

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

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

0 votes

1 answer

20

calculus question
Question Number 4?

answered Jan 5 in Calculus by GATE2021 (11 points) | 45 views

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

0 votes

0 answers

23

#integration
$I=\int sin(2x) cos(3x) dx$ 1.(5cosx-cos5x)/10 2.(5sinx-sin5x)/10 3.both 4.none

asked Jan 3 in Calculus by amit166 Junior (761 points) | 64 views

0 votes

0 answers

24

Math doubt
Is it true $\frac{1}{1+x^{2}}=1-x^{2}$ Is it applied every function? (like limit func, generating func)?

asked Jan 3 in Calculus by srestha Veteran (111k points) | 51 views

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

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

+2 votes

3 answers

28

TIFR2019-A-15
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

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

+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

0 votes

0 answers

31

GATE EE 2018
[closed]

asked Dec 18, 2018 in Calculus by aditi19 Active (2.9k points) | 65 views

0 votes

0 answers

32

TIFR2019-A-13
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

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

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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