Recent questions tagged 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.

asked Mar 17 in Calculus by ankitgupta.1729 Boss (10.7k points) | 48 views

0 votes

1 answer

2

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 $0$

asked Feb 21 in Calculus by ankitgupta.1729 Boss (10.7k points) | 98 views

+1 vote

1 answer

3

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.

asked Feb 20 in Calculus by ankitgupta.1729 Boss (10.7k points) | 63 views

+1 vote

5 answers

4

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

asked Feb 7 in Calculus by Arjun Veteran (395k points) | 1.5k views

0 votes

0 answers

5

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) | 79 views

0 votes

0 answers

6

MadeEasy Workbook: Calculus - Maxima Minima

asked Jan 19 in Calculus by chanchala3993 (7 points) | 33 views

0 votes

0 answers

7

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) | 59 views

0 votes

1 answer

8

self doubt
$\lim_{x\rightarrow \frac{\pi }{2}}cosx^{cosx}$ can we straight away say $0^{0}=0$ ?

asked Jan 5 in Calculus by manisha11 Active (2k points) | 44 views

0 votes

1 answer

9

calculus question
Question Number 4?

asked Jan 4 in Calculus by pradeepchaudhary Active (1.2k points) | 45 views

0 votes

0 answers

10

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) | 75 views

0 votes

0 answers

11

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 (34.3k points) | 88 views

0 votes

0 answers

12

GATE EE 2018

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

0 votes

0 answers

13

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 (395k points) | 170 views

+2 votes

3 answers

14

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

asked Dec 18, 2018 in Calculus by Arjun Veteran (395k points) | 253 views

0 votes

0 answers

15

Testbook Test Series: Calculus - Differentiability
If $y = f(x)$ is a solution of $ d^2y/dx^2 = 0$ , with boundary conditions $y=8$ at $x=0$ and $dy/dx =4$ at $x=16$, Find the value of $f(-2)$ When they say, $y = f(x)$ is a solution of $ d^2y/dx^2 = 0$ What does that mean?

asked Dec 18, 2018 in Mathematical Logic by shreyansh jain Active (2.2k points) | 57 views

0 votes

1 answer

16

GradeUp quiz-Maxima minima

asked Nov 28, 2018 in Calculus by aditi19 Active (2.9k points) | 118 views

0 votes

0 answers

17

Gilbert Strang
$\int_{1}^{∞}\frac{dx}{x^6+1}$

asked Nov 22, 2018 in Calculus by aditi19 Active (2.9k points) | 66 views

+2 votes

1 answer

18

Calculus-Integration
$\int x^7.e^{x^4}dx$ How to do this?

asked Nov 22, 2018 in Calculus by Ayush Upadhyaya Boss (25.3k points) | 109 views

0 votes

1 answer

19

Integration
$\int_{0}^{1}\frac{x^{\alpha }-1}{logx}dx$ where $\alpha>0$

asked Nov 16, 2018 in Calculus by srestha Veteran (110k points) | 83 views

0 votes

0 answers

20

Gilbert Strang
$\int_{}^{}\frac{x dx}{\sqrt{x^4-1}}$

asked Nov 14, 2018 in Calculus by aditi19 Active (2.9k points) | 45 views

+2 votes

1 answer

21

Got from friend
Find the limit of the given expression $\lim_{x\to\frac{\pi}{2}}\left ( \sec x-\frac{1}{1-\sin x} \right )$

asked Nov 13, 2018 in Calculus by JeetRabari (89 points) | 168 views

0 votes

1 answer

22

Gilbert Strang
Differentiate y=$x^{-1/lnx}$

asked Oct 28, 2018 in Calculus by aditi19 Active (2.9k points) | 41 views

0 votes

0 answers

23

Gilbert Strang
$\int_{0}^{1}(x^2+1)^4dx$

asked Oct 25, 2018 in Calculus by aditi19 Active (2.9k points) | 65 views

0 votes

1 answer

24

Gilbert Strang
$\int \frac{x^3}{\sqrt{1+x^2}}.dx$

asked Oct 24, 2018 in Calculus by aditi19 Active (2.9k points) | 101 views

0 votes

0 answers

25

Virtual Gate Test Series: Calculus
i have solved it by putting the values

asked Oct 15, 2018 in Calculus by Prince Sindhiya Loyal (6.3k points) | 41 views

0 votes

1 answer

26

limits
Find the limit $\operatorname { lit } _ { x \rightarrow 1 } \left\{ \left( \frac { 1 + x } { 2 + x } \right) ^ { \left( \frac { 1 - \sqrt { x } } { 1 - x } \right) } \right\}$

asked Oct 14, 2018 in Calculus by MIRIYALA JEEVAN KUMA Active (2.5k points) | 108 views

+1 vote

1 answer

27

Calculus-Definite Integral
What is the value of $\int_0^\pi log(1+cosx)dx$

asked Oct 13, 2018 in Calculus by Ayush Upadhyaya Boss (25.3k points) | 74 views

0 votes

1 answer

28

Gilbert Strang Doubt
Locate the inflection points and region where f(x) is concave up or down f(x)=$-x^3+x^2+x$

asked Oct 12, 2018 in Calculus by aditi19 Active (2.9k points) | 45 views

0 votes

1 answer

29

Maxima and Minima
Find the stationary points, maxima and minima f(x)=|x+1|+|x-1| , -3<=x<=2

asked Oct 10, 2018 in Calculus by aditi19 Active (2.9k points) | 93 views

0 votes

1 answer

30

Integration
Solve $\int_{0}^{\pi }sin^{5}\frac{x}{2}dx$

asked Oct 6, 2018 in Calculus by srestha Veteran (110k points) | 96 views

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