Recent questions and answers in Calculus

+7 votes

3 answers

1

TIFR2015-A-11
Suppose that $f(x)$ is a continuous function such that $0.4 \leq f(x) \leq 0.6$ for $0 \leq x \leq 1$. Which of the following is always true? $f(0.5) = 0.5$. There exists $x$ between $0$ and $1$ such that $f(x) = 0.8x$. There exists $x$ between $0$ and $0.5$ such that $f(x) = x$. $f(0.5) > 0.5$. None of the above statements are always true.

answered 4 days ago in Calculus by Gyanu (31 points) | 316 views

+1 vote

2 answers

2

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 Aug 9 in Calculus by CJ147 (17 points) | 66 views

0 votes

1 answer

3

Calculus-Self Doubt
Is the function $f(x)=\frac{1}{x^{\frac{1}{3}}}$ continous in the interval [-1 0) ?

answered Aug 9 in Calculus by CJ147 (17 points) | 67 views

0 votes

1 answer

4

lt x→0(3cosx+2sin3x)^(1/x)

answered Aug 8 in Calculus by arvin Active (3.5k points) | 15 views

0 votes

1 answer

5

ugc net 2018 july -82
Which of the following statements is false about convex minimization problem? If a local minimum exists, then it is a global minimum the set of all global minimum is a convex set the set of all global minimum is concave set for each is strictly convex function, if the function has minimum, then the minimum is a unique

answered Aug 6 in Calculus by Shivang Agarwal (11 points) | 280 views

+11 votes

5 answers

6

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 Jul 31 in Calculus by ramji (169 points) | 1.2k views

0 votes

1 answer

7

Finding Maxima Minima
The greatest value of the function f(x) = 2 sin x + sin 2x on the interval [ 0,3pi/2 ] is ____

answered Jul 19 in Calculus by Prateek Raghuvanshi Loyal (5.3k points) | 82 views

0 votes

2 answers

8

SELF DOUBT
0/infinity is determinent form or inderminent form while solving limits

answered Jul 6 in Calculus by kavya kamish upadhya (165 points) | 60 views

+1 vote

2 answers

9

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 Jun 26 in Calculus by Prateek Raghuvanshi Loyal (5.3k points) | 136 views

+7 votes

1 answer

10

ISI2017 MMA
Let S ⊆ R. Consider the statement: "There exists a continuous function f:S -> S such that f(x) != x for all x belongs to S." This statement is false if S equals A) [2,3] B) (2,3] c) [-3,-2] union [2,3] D) (-infinity to +infinity)

answered Jun 18 in Calculus by Kushagra Chatterjee Loyal (8.2k points) | 309 views

0 votes

1 answer

11

ISI 2014 MMA- 7

answered Jun 12 in Calculus by Subarna Das Boss (11.2k points) | 63 views

0 votes

0 answers

12

ISI 2014 MMA - 5

asked Jun 12 in Calculus by Sammohan Ganguly (435 points) | 57 views

0 votes

1 answer

13

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 (92.1k points) | 97 views

0 votes

1 answer

14

Calculus

answered Jun 4 in Calculus by Prateek Raghuvanshi Loyal (5.3k points) | 60 views

+1 vote

1 answer

15

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 (17.5k points) | 94 views

+8 votes

3 answers

16

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 (2.2k points) | 1.5k views

+2 votes

2 answers

17

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 (22.6k points) | 114 views

+2 votes

1 answer

18

ISRO2016- EC Calculus
.

answered May 21 in Calculus by pankaj_vir Loyal (9.2k points) | 109 views

0 votes

1 answer

19

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) | 83 views

0 votes

0 answers

20

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 (92.1k points) | 169 views

+13 votes

3 answers

21

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 (92.1k points) | 1.3k views

+1 vote

1 answer

22

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) | 87 views

+30 votes

6 answers

23

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 (92.1k points) | 3.6k views

+10 votes

3 answers

24

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 (22.6k points) | 1.7k views

+1 vote

1 answer

25

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) | 55 views

+1 vote

1 answer

26

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) | 63 views

0 votes

1 answer

27

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 (16.2k points) | 45 views

0 votes

1 answer

28

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

answered Apr 30 in Calculus by pankaj_vir Loyal (9.2k points) | 58 views

0 votes

0 answers

29

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

asked Apr 28 in Calculus by kd..... (285 points) | 59 views

0 votes

0 answers

30

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..... (285 points) | 49 views

0 votes

3 answers

31

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

answered Apr 25 in Calculus by Subarna Das Boss (11.2k points) | 95 views

0 votes

0 answers

32

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 (16.2k points) | 85 views

0 votes

0 answers

33

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

asked Apr 24 in Calculus by kd..... (285 points) | 62 views

0 votes

2 answers

34

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 (16.2k points) | 103 views

0 votes

0 answers

35

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 (92.1k points) | 80 views

0 votes

2 answers

36

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) | 208 views

0 votes

2 answers

37

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) | 150 views

0 votes

2 answers

38

definite integration

answered Apr 16 in Calculus by pankaj_vir Loyal (9.2k points) | 85 views

0 votes

1 answer

39

Maths calculus

answered Apr 13 in Calculus by sonveer tomar 1 Active (3k points) | 49 views

0 votes

1 answer

40

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

answered Apr 11 in Calculus by pankaj_vir Loyal (9.2k points) | 57 views

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