Recent questions and answers in Calculus

0 votes

1 answer

1

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 2 days ago in Calculus by venkatesh pagadala (415 points) | 37 views

+1 vote

1 answer

2

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 2 days ago in Calculus by Kushagra Chatterjee Loyal (8.8k points) | 32 views

+1 vote

5 answers

3

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 Active (5.1k points) | 1.4k views

+2 votes

3 answers

4

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) | 269 views

+5 votes

3 answers

5

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 (29k points) | 439 views

0 votes

0 answers

6

How to solve such question.
$\frac{d}{dx}\int_{1}^{x^4} sect\space dt$

asked Jan 20 in Calculus by `JEET Active (3.3k points) | 70 views

0 votes

0 answers

7

Made easy workbok

asked Jan 19 in Calculus by chanchala3993 (7 points) | 17 views

0 votes

0 answers

8

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) | 27 views

0 votes

0 answers

9

ACE TEST SERIES
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 (215 points) | 51 views

0 votes

1 answer

10

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 (11 points) | 55 views

0 votes

1 answer

11

Integration
How to solve it?

answered Jan 11 in Calculus by adeemajain (281 points) | 50 views

0 votes

1 answer

12

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) | 70 views

0 votes

1 answer

13

ME TEST SERIES

answered Jan 10 in Calculus by Kunal Kadian Active (2.6k points) | 49 views

+1 vote

1 answer

14

UPPCL AE 2018:85

answered Jan 5 in Calculus by Lakshman Patel RJIT Boss (29k points) | 80 views

0 votes

0 answers

15

UPPCL AE 2018:81

asked Jan 5 in Calculus by Lakshman Patel RJIT Boss (29k points) | 36 views

0 votes

1 answer

16

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) | 40 views

0 votes

1 answer

17

calculus question
Question Number 4?

answered Jan 5 in Calculus by GATE2021 (11 points) | 40 views

0 votes

1 answer

18

GATE 2013 MA Calculus

answered Jan 3 in Calculus by pradeepchaudhary Active (1.1k points) | 22 views

0 votes

0 answers

19

#integration
I=$\int_{1}^{\infty }a^{-ceil (log _{b} x ) } dx$

asked Jan 3 in Calculus by amit166 Junior (693 points) | 43 views

0 votes

0 answers

20

#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 (693 points) | 61 views

0 votes

0 answers

21

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 (108k points) | 49 views

0 votes

0 answers

22

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 (6.5k points) | 22 views

0 votes

1 answer

23

Integration
If n is a positive integer, then $\int_{0}^{\pi} \frac{sin(2nx)}{sinx} dx$

answered Dec 27, 2018 in Calculus by vg653 (111 points) | 61 views

0 votes

0 answers

24

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 (1.5k points) | 64 views

0 votes

0 answers

25

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 (29k points) | 84 views

+1 vote

2 answers

26

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 (2.5k points) | 74 views

0 votes

0 answers

27

GATE EE 2018
[closed]

asked Dec 18, 2018 in Calculus by aditi19 Active (2.3k points) | 52 views

0 votes

0 answers

28

#maths #limit

asked Dec 18, 2018 in Calculus by Manan Shah (129 points) | 43 views

+3 votes

2 answers

29

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) | 565 views

0 votes

0 answers

30

aai 2018

asked Dec 13, 2018 in Calculus by pream sagar Active (1.7k points) | 43 views

0 votes

0 answers

31

GATE 2016 MA Limits

asked Dec 12, 2018 in Calculus by Balaji Jegan Active (4.8k points) | 23 views

0 votes

0 answers

32

GATE 2016 MA Calculus

asked Dec 12, 2018 in Calculus by Balaji Jegan Active (4.8k points) | 24 views

0 votes

0 answers

33

GATE 2013 MA Calculus

asked Dec 12, 2018 in Calculus by Balaji Jegan Active (4.8k points) | 21 views

0 votes

0 answers

34

GATE 2013 MA Calculus

asked Dec 12, 2018 in Calculus by Balaji Jegan Active (4.8k points) | 24 views

0 votes

0 answers

35

Self Doubt
Plese explain me this series

asked Dec 11, 2018 in Calculus by HeadShot Active (4.6k points) | 42 views

+1 vote

0 answers

36

GATE 2007 MA Calculus

asked Dec 11, 2018 in Calculus by Balaji Jegan Active (4.8k points) | 26 views

+3 votes

1 answer

37

TIFR GS 2019
How to solve it$?$ $\int_{0}^{1}\frac{x^{300}}{(x^{3}+x^{2}+1)}dx$ a.0.00 b.0.33 c.0.02 d.0.03 d.0.04 two decimal digit

answered Dec 10, 2018 in Calculus by rahulvats1996 (175 points) | 491 views

0 votes

0 answers

38

diffrentiability test
which of the following are differentiable at x=0 $X^{3}$ 2. | $X^{3}$ |

asked Dec 9, 2018 in Calculus by hitendra singh Active (1.7k points) | 40 views

+12 votes

5 answers

39

GATE2017-1-28
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

answered Dec 6, 2018 in Calculus by Rackson Active (1.9k points) | 2.1k views

+5 votes

2 answers

40

TIFR2011-A-4
Consider the problem of maximizing $x^{2}-2x+5$ such that $0< x< 2$. The value of $x$ at which the maximum is achieved is: $0.5$ $1$ $1.5$ $1.75$ None of the above.

answered Dec 4, 2018 in Calculus by HeadShot Active (4.6k points) | 372 views

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