Recent questions and answers in Calculus

0 votes

1 answer

1

ISI 2014 MMA- 7

answered Jun 12 in Calculus by Subarna Das Boss (10.5k points) | 52 views

0 votes

0 answers

2

ISI 2014 MMA - 5

asked Jun 12 in Calculus by Sammohan Ganguly (417 points) | 50 views

0 votes

1 answer

3

Definite Integral
S = $\int_{0}^{2\Pi } \sqrt{4cos^{2}t +sin^{2}t} \, \, dt$ Please explain how to solve it.

answered Jun 11 in Calculus by srestha Veteran (86.8k points) | 66 views

0 votes

1 answer

4

Calculus

answered Jun 4 in Calculus by Prateek Raghuvanshi Active (3.9k points) | 52 views

+1 vote

1 answer

5

Limit
Puzzle $\lim_{y\rightarrow \alpha }\left (y-\left ( y^{2}+y \right )^{\frac{1}{2}}\right )$

answered May 30 in Calculus by Deepakk Poonia (Dee) Boss (13.2k points) | 75 views

+8 votes

3 answers

6

GATE2015-1-4
$\lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is $\infty $ 0 1 Not defined

answered May 29 in Calculus by sutanay3 Active (1.2k points) | 1.4k views

+2 votes

2 answers

7

Limit
Is answer will be 1 or 5? $\lim_{x\rightarrow \alpha }\left ( \frac{x+6}{x+1} \right )^{x+4}$

answered May 26 in Calculus by abhishekmehta4u Boss (14.3k points) | 93 views

+2 votes

1 answer

8

ISRO2016- EC Calculus
.

answered May 21 in Calculus by pankaj_vir Loyal (8.5k points) | 107 views

0 votes

1 answer

9

Regarding Preparation
I know this question has been asked many times, but yeah. I am weak in calculus and linear algebra and have never studied probability properly. Now according to internet suggestions, I should read Kreyzig or BS Grewal, but I will most probably want ... time for GATE 2019 should i watch lectures of Gilbert Strang, Stats 110 and calculus textbook, or should i stick to kreyzig?

answered May 19 in Calculus by jay rathod (227 points) | 76 views

0 votes

0 answers

10

Integration
$f\left ( x \right )=$$\int_{-2}^{2}x^{-\frac{2}{7}}dx$ Is this function f(x) is continuous, bounded and differentiable? (In exam hall is it possible to draw the graph for this function f(x), or some other procedure to follow to ans this)

asked May 18 in Calculus by srestha Veteran (86.8k points) | 158 views

+13 votes

3 answers

11

GATE2014-3-47
The value of the integral given below is $$\int \limits_0^{\pi} \: x^2 \: \cos x\:dx$$ $-2\pi$ $\pi$ $-\pi$ $2\pi$

answered May 17 in Calculus by srestha Veteran (86.8k points) | 1.2k views

+1 vote

1 answer

12

Doubt
A polynomial of degree 4 with real coefficients A) Can possibly have no extrema and no zero crossings B) May have up to four extrema and up to 3 zero crossings C) Cannot have more than three extrema and more than four zero crossings D) Will have an equal number of extrema and zero crossings

answered May 14 in Calculus by Karan Dodwani (53 points) | 77 views

+30 votes

6 answers

13

GATE2014-1-47
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 the interval ... of the function in the interval $(0,2)$ is $1$ There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $-f(2-y)$

answered May 13 in Calculus by srestha Veteran (86.8k points) | 3.5k views

+11 votes

4 answers

14

GATE2011-31
Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$ ? $0$ $2$ $-i$ $i$

answered May 11 in Calculus by srestha Veteran (86.8k points) | 1.2k views

+10 votes

3 answers

15

GATE2017-2-10
If $f(x) = R \: \sin ( \frac{\pi x}{2}) + S. f’(\frac{1}{2}) = \sqrt{2}$ 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 $\frac{16}{\pi}$

answered May 9 in Calculus by abhishekmehta4u Boss (14.3k points) | 1.7k views

+1 vote

1 answer

16

IIT M MS Question
Since given increasing,so $N'(t)>0$ but what will be $N''(t)$ for the slow rate part?

answered May 7 in Calculus by Kushagra Chatterjee Loyal (8.2k points) | 50 views

+1 vote

1 answer

17

How Ans. A is correct
At x = 0, the function f(x)=|x| has (A) a minimum (B) a maximum (C) a point of inflection (D) neither a maximum nor minimum

answered May 7 in Calculus by Prateek Raghuvanshi Active (3.9k points) | 58 views

+1 vote

1 answer

18

ISI MMA QROR
For n ≥ 1, let Gn be the geometric mean of { sin (π/2 . k/n) : 1 ≤ k ≤ n } Then lim n→∞ Gn is

answered May 1 in Calculus by tathatj (67 points) | 57 views

0 votes

1 answer

19

ISI 2016 MMA 24
let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a strictly increasing function. Then which one of the following is always true? A) The limits $\lim_{x\rightarrow a+} f(X)$ and $\lim_{x\rightarrow a-} f(X)$ exist for all real number a B) if $f$ is differentiable at a ... that $f(x) < B$ for all real $x$ D) There cannot not be a real number $L$ such that $f(x) > L$ for all real $x$

answered Apr 30 in Calculus by Tesla! Boss (16.1k points) | 42 views

0 votes

1 answer

20

Mean Value Theorem ( Lagrange's), How to take Domain in this type of questions?)

answered Apr 30 in Calculus by pankaj_vir Loyal (8.5k points) | 43 views

0 votes

0 answers

21

Integration
Evaluate $\Large\int_3^7 \sqrt[4]{(x-3)(7-x)} dx$

asked Apr 28 in Calculus by kd..... (239 points) | 49 views

0 votes

0 answers

22

Multiple integration
Evaluate $\Large\int_1^4\Large\int_\sqrt{y}^2(x^{2}+y^{2})dA $ by changing the order of integration

asked Apr 28 in Calculus by kd..... (239 points) | 44 views

0 votes

3 answers

23

Integration
$\int \left ( \sin\theta \right )^{\frac{1}{2}}d\theta$

answered Apr 25 in Calculus by Subarna Das Boss (10.5k points) | 89 views

0 votes

0 answers

24

ISI 2017 MMA 25
For a,b $\in \mathbb{R}$ and b > a , the maximum possible value of the integral $\int_{a}^{b}(7x-x^{2}-10)dx$ is A) $\frac{7}{2}$ B) $\frac{9}{2}$ C) $\frac{11}{2}$ D) none of these

asked Apr 24 in Calculus by Tesla! Boss (16.1k points) | 73 views

+1 vote

1 answer

25

Integration- CE 2013
Find the value of the integral $$\int_{0}^{\pi/6}cos^43\theta\ sin^36\theta\ d\theta$$ Please show the steps.(upload a pic of your solution) a) 0 b) 1/15 c) 8/3 d) 1

answered Apr 24 in Calculus by kd..... (239 points) | 85 views

0 votes

0 answers

26

Calculus Integration
$\int_{3}^{7}((x-3)(7-x))^{\frac{1}{4}}$

asked Apr 24 in Calculus by kd..... (239 points) | 45 views

0 votes

2 answers

27

ISI 2017 MMA 1
The area lying in the first quadrant and bounded by the circle $x^{2}+y^{2}=4$ and the lines $x= 0$ and $x=1$ is given by $\frac{\pi}{3}+\frac{\sqrt{3}}{2}$ $\frac{\pi}{6}+\frac{\sqrt{3}}{4}$ $\frac{\pi}{3}-\frac{\sqrt{3}}{2}$ $\frac{\pi}{6}+\frac{\sqrt{3}}{2}$

answered Apr 23 in Calculus by Tesla! Boss (16.1k points) | 88 views

0 votes

0 answers

28

General Math
What is value of $\log _{2}10$? In general calculator $\ln _{2}10$ is giving 2.3.... But it should be 3. something right?

asked Apr 20 in Calculus by srestha Veteran (86.8k points) | 76 views

0 votes

2 answers

29

ISRO 2013- Integration [EE]
The integrating factor of equation sec 2 y dy/dx + x tan y = x3 is a) [e]x^2/2 b) [e] -x^2/2 c) [e]x/2 d) [e]-x/2

answered Apr 20 in Calculus by sampurnanand mishra (123 points) | 199 views

0 votes

2 answers

30

ISRO 2013- Functions [EE]
The minimum point of the function (x3 /3)- x is at a) x= 1 b) x = -1 c) x = 0 d) x = 1/ √ 3

answered Apr 20 in Calculus by sampurnanand mishra (123 points) | 148 views

0 votes

2 answers

31

definite integration

answered Apr 16 in Calculus by pankaj_vir Loyal (8.5k points) | 80 views

0 votes

1 answer

32

Maths calculus

answered Apr 13 in Calculus by sonveer tomar 1 Active (3k points) | 48 views

0 votes

1 answer

33

Maths calculus
a)π/√2 B) √π/2 C) π/2 D)√(π/2

answered Apr 11 in Calculus by pankaj_vir Loyal (8.5k points) | 53 views

0 votes

0 answers

34

Maths calculus

asked Apr 11 in Calculus by Prince Sindhiya Junior (699 points) | 51 views

0 votes

0 answers

35

Problems in Calculus Of One Variable by I.A. Maron

asked Apr 10 in Calculus by pmshukla96 (49 points) | 35 views

+6 votes

3 answers

36

GATE2013-22
Which one of the following functions is continuous at $x = 3?$ $f(x) = \begin{cases} 2,&\text{if $x = 3$ } \\ x-1& \text{if $x > 3$}\\ \frac{x+3}{3}&\text{if $x < 3$ } \end{cases}$ $f(x) = \begin{cases} 4,&\text{if $x = 3$ } \\ 8-x& \ ... \\ x-4& \text{if $x > 3$} \end{cases}$ $f(x) = \begin{cases} \frac{1}{x^3-27}&\text{if $x \neq 3$ } \end{cases}$

answered Apr 10 in Calculus by himanshukumarpatel (89 points) | 1.2k views

+5 votes

2 answers

37

GATE2007-1
Consider the following two statements about the function $f(x)=\left\vert x\right\vert$: P. $f(x)$ is continuous for all real values of $x$. Q. $f(x)$ is differentiable for all real values of $x$ . Which of the following is TRUE? $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are true. Both $P$ and $Q$ are false.

answered Apr 10 in Calculus by himanshukumarpatel (89 points) | 1k views

+4 votes

4 answers

38

GATE1998-1.4
Consider the function $y=|x|$ in the interval $[-1, 1]$. In this interval, the function is continuous and differentiable continuous but not differentiable differentiable but not continuous neither continuous nor differentiable

answered Apr 10 in Calculus by himanshukumarpatel (89 points) | 589 views

0 votes

0 answers

39

ISI-SAMPLE-2014-19

asked Apr 7 in Calculus by jjayantamahata Active (1.5k points) | 67 views

+2 votes

1 answer

40

Calculus- +2math book
If an = 1000*n /n!, for n = 1, 2, 3, ...., then the sequence {an } (a) doesn't have a maximum (b) attains maximum at exactly one value of n (c) attains maximum at exactly two values of n (d) attains maximum for infinitely many values of n

answered Apr 1 in Calculus by pankaj_vir Loyal (8.5k points) | 48 views

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