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Recent questions and answers in Calculus

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1 answer

1

Mathematics for Natural Science
Determine the domain of the function $f(x) = |x – 2|$

Amartya007 answered in Calculus Mar 13

106 views

0 votes

1 answer

2

Maths for natural science
Determine the domain of the function $f(x)=\left | x \right |+1$

Amartya007 answered in Calculus Mar 13

133 views

2 votes

1 answer

3

#Made Easy
Find the value of $\lim_{x \rightarrow 0 } \dfrac{x \tan2x - 2x\tan x}{(1-\cos 2x)^2} \rule{1 in}{.5 pt}.$

Amartya007 answered in Calculus Mar 12

151 views

1 vote

1 answer

4

ISI2015-MMA-81
If $f$ is continuous in $[0,1]$ then $\displaystyle \lim_ {n \to \infty} \sum_{j=0}^{[n/2]} \frac{1}{n} f \left(\frac{j}{n} \right)$ (where $[y]$ is the largest integer less than or equal to $y$) does not exist exists and is equal to $\frac{1}{2} \int_0^1 f(x) dx$ exists and is equal to $ \int_0^1 f(x) dx$ exists and is equal to $\int_0^{1/2} f(x) dx$

KAUNIL answered in Calculus Mar 10

by KAUNIL

244 views

0 votes

1 answer

5

ISI2015-MMA-73
$f(x)$ is a differentiable function on the real line such that $\underset{x \to \infty=}{\lim} f(x) =1$ and $\underset{x \to \infty=}{\lim} f’(x) =\alpha$. Then $\alpha$ must be $0$ $\alpha$ need not be $0$, but $\mid \alpha \mid <1$ $\alpha >1$ $\alpha < -1$

KAUNIL answered in Calculus Mar 9

by KAUNIL

285 views

0 votes

2 answers

6

limits
the value of $lim_{x-> 0}(1-sinx.cosx)^{cosec2x}$ is: A $e^{2}$ B $e^{-2}$ C$e^{1/2}$ D $e^{-1/2}$

wizard_2004 answered in Calculus Mar 4

130 views

1 vote

2 answers

7

GATE CSE 2023 | Question: 21
The value of the definite integral \[ \int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1}\left(4 x^{2} y-z^{3}\right) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x \] is _________. (Rounded off to the nearest integer)

ankitgupta.1729 answered in Calculus Feb 16

by ankitgupta.1729

797 views

2 votes

2 answers

8

GATE CSE 2023 | Question: 18
Let $\qquad f(x)=x^{3}+15 x^{2}-33 x-36$ be a real-valued function. Which of the following statements is/are $\text{TRUE}?$ $f(x)$ does not have a local maximum. $f(x)$ has a local maximum. $f(x)$ does not have a local minimum. $f(x)$ has a local minimum.

Hira Thakur answered in Calculus Feb 16

819 views

0 votes

2 answers

9

GATE CSE 2023 | Memory Based Question: 11
Let $f(x)=x^3+15 x^2-33 x-36$ be a real valued function. Which statement is/are TRUE? $f(x)$ has a local maximum. $f(x)$ does NOT have a local maximum. $f(x)$ has a local minimum. $f(x)$ does NOT have a local minimum. closed

ankitgupta.1729 answered in Calculus Feb 8

by ankitgupta.1729

433 views

1 vote

0 answers

10

DRDO CSE 2022 Paper 1 | Question: 4
Let the function $f(x)$ be defined as follows. \[f(x)=\left\{\begin{array}{ll} x^{2} & x \leq 1 \\ 2 a x^{2}+bx + c & 1 < x \leq 2 \\ x + 2d & x>1 \end{array}\right.\] Find the values of $a, b, c$ and $d$ such that $f$ is continuous and differentiable everywhere.

admin asked in Calculus Dec 15, 2022

by admin

42 views

3 votes

2 answers

11

TIFR-2011-Maths-A-25
The function $f(x) = \begin{cases} 0 & \text{if x is rational} \\ x& \text{if x is irrational} \end{cases}$ is not continuous anywhere on the real line.

Keval ahir answered in Calculus Oct 22, 2022

428 views

0 votes

0 answers

12

[email protected] 2022 Test Series
Answer -3.7

SKMAKM asked in Calculus Oct 22, 2022

by SKMAKM

171 views

1 vote

2 answers

13

TIFR-2011-Maths-A-2
$\lim_{x \rightarrow 0} \sin \left(1/x^{2}\right)$ equals. $1$ $0$ $\infty$ Oscillates

Keval ahir answered in Calculus Oct 20, 2022

370 views

0 votes

0 answers

14

Internet
For f(x)=√x x€[0,b] the number c satisfying mean value therom is c=1

Katyayani0306 asked in Calculus Sep 21, 2022

by Katyayani0306

123 views

1 vote

3 answers

15

ISRO2006-ECE calculus

shuham kumar answered in Calculus Sep 20, 2022

by shuham kumar

436 views

0 votes

2 answers

16

ISRO 2009-ECE Engineering Mathematics
There is a function f(x), such that f(0) = 1 and f ' (0)= -1 and f(x) is positive for all values of x. Then, a) f"(x) < 0 for all x b) -1 < f'' (x) < 0 for all x c) -2 < f '' (x) < -1 for all x d) None of the above

shuham kumar answered in Calculus Sep 20, 2022

by shuham kumar

284 views

3 votes

1 answer

17

Calculus
It should be 1 and 3 ?? please correct me if I'm wrong.

shuham kumar answered in Calculus Sep 20, 2022

by shuham kumar

701 views

2 votes

1 answer

18

Continuity and Differentiability of root mod function
1) Consider f(x) = $|x|^{3/2}$ Check for Differentiability and Continuity. I am getting Cont and Differentiable both. 2) Consider f(x) = $|x-1|^{3/2}$ Check for Differentiability and Continuity. I am getting Cont and Differentiable both. 3) Find the value of $f(x) = \int_{-2}^{2}|1-x^4|dx$. I am getting 8/5, but answer is 12.

shuham kumar answered in Calculus Sep 20, 2022

by shuham kumar

738 views

1 vote

2 answers

19

NIELIT 2016 MAR Scientist B - Section B: 5
The greatest and the least value of $f(x)=x^4-8x^3+22x^2-24x+1$ in $[0,2]$ are $0,8$ $0,-8$ $1,8$ $1,-8$

neel19 answered in Calculus Sep 16, 2022

by neel19

420 views

1 vote

2 answers

20

GATE Overflow | Mock GATE | Test 1 | Question: 19
Evaluate the limit: $ \lim_{x \to -3} \frac{\sqrt{2x+22}-4}{x+3}$ $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{8}$ $\frac{1}{16}$

MANSI_SOMANI answered in Calculus Sep 13, 2022

by MANSI_SOMANI

766 views

0 votes

0 answers

21

TIFR CSE 2022 | Part A | Question: 6
Let $f$ be a polynomial of degree $n \geq 3$ all of whose roots are non-positive real numbers. Suppose that $f(1)=1$. What is the maximum possible value of $f^{\prime}(1)?$ $1$ $n$ $n+1$ $\frac{n(n+1)}{2}$ $f^{\prime}(1)$ can be arbitrarily large given only the constraints in the question

Lakshman Patel RJIT asked in Calculus Sep 1, 2022

by Lakshman Patel RJIT

139 views

0 votes

0 answers

22

TIFR CSE 2022 | Part A | Question: 14
Suppose $w(t)=4 e^{i t}, x(t)=3 e^{i(t+\pi / 3)}, y(t)=3 e^{i(t-\pi / 3)}$ and $z(t)=3 e^{i(t+\pi)}$ are points that move in the complex plane as the time $t$ varies in $(-\infty, \infty)$. Let $c(t)$ ... $\frac{1}{2 \pi}$ $2 \pi$ $\sqrt{3} \pi$ $\frac{1}{\sqrt{3} \pi}$ $1$

Lakshman Patel RJIT asked in Calculus Sep 1, 2022

by Lakshman Patel RJIT

119 views

1 vote

0 answers

23

Engineering Mathematics
Please verify the solution(the differentiation part ),

Overflow04 asked in Calculus Aug 21, 2022

201 views

0 votes

0 answers

24

Mathematics for Natural Science
Sketch the graph of $f(x) = \frac{x^{3}-1}{x^{2}-1}$

kidussss asked in Calculus Jul 29, 2022

158 views

1 vote

2 answers

25

Applied Mathematics Calculus and Limit Question
Evaluate the question of the following limits. $\lim_{x\rightarrow 1} \frac{x}{(x-1)^{2}}$

kidussss asked in Calculus Jul 9, 2022

406 views

0 votes

1 answer

26

Applied Mathematics Derivative
Please find derivation of the following equation. Let $f(x)=e^{x^{2}}\ln x,$ then find, ${f}'(x)$.

kidussss asked in Calculus Jul 8, 2022

149 views

0 votes

2 answers

27

Applied Mathematics Calculus and Limit Question
Evaluate the question of the following limits. $\lim_{x\rightarrow \infty} \frac{2x^{3}+3x-5}{5x^{3}+1}$

kidussss asked in Calculus Jul 8, 2022

175 views

0 votes

2 answers

28

Applied Mathematics Question
Let $f(x) = e^{x^2},$ then find $f''(x).$

kidussss asked in Calculus Jul 8, 2022

172 views

0 votes

0 answers

29

iit kanpur Calculas practice question
Does there exist a differentiable function f : [0, 2] → R satisfying f(0) = −1, f(2) = 4 and f’(x) ≤ 2 for all x ∈ [0, 2]?

Kabir5454 asked in Calculus May 16, 2022

137 views

0 votes

1 answer

30

Calculus by Spivak 4th edition Chapter 10 problem 9

AngshukN asked in Calculus May 3, 2022

126 views

1 vote

0 answers

31

#ISI2021
Let f(x-y) = $\frac{f(x)}{f(y)}$ for all x,y $\epsilon$ R and f’(0) = p, f’(5) = q. Then the value of f’(-5) is q -q $\frac{p}{q}$ $\frac{p^2}{q}$

Jeetu Bhaiya asked in Calculus Feb 24, 2022

by Jeetu Bhaiya

144 views

7 votes

4 answers

32

GATE CSE 2022 | Question: 24
The value of the following limit is ________________. $\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$

Arjun asked in Calculus Feb 15, 2022

by Arjun

2.6k views

0 votes

0 answers

33

Global and Local Minimum
Suppose that we have an objective function X ⊆ R^n → R and Y ⊂ X. Which of the following are correct: Every global minimizer of f in X is global minimizer in Y Every local minimizer of f in Y is local minimizer in X My answer is that 1) and 2) are correct. I want to check if my answers are correct or we can prove something other with some example.

AlgoHuman asked in Calculus Feb 14, 2022

160 views

0 votes

1 answer

34

Made Easy Full length Test
Options Given were: (pi)/2 pi -(pi) none

Sagar475 asked in Calculus Jan 24, 2022

209 views

1 vote

1 answer

35

Made Easy Test Series Engineering Maths
Dear Friends can any body tell me limit exists at 1 or not? as According to me the limit exists at 1 as both gives -1 at 1 but in madeeasy it’s given that the limit doesn’t exists...

Sagar475 asked in Calculus Jan 18, 2022

202 views

0 votes

2 answers

36

Calculus self doubt
Calculus looks difficult for me. Any resources to learn calculus for GATE

kabilan45 asked in Calculus Nov 25, 2021

282 views

0 votes

0 answers

37

Applied Test Series
What is the correct procedure to solve this limit ?

LRU asked in Calculus Nov 5, 2021

by LRU

203 views

0 votes

0 answers

38

math book
$\int_{0}^{1}\tan^{-1} (1-\frac{1}{x})$ d(x) find

amit166 asked in Calculus Sep 25, 2021

197 views

0 votes

1 answer

39

#mathematics
What is the difference between Integration and Summation? Which one produces a greater value in the same range?

Crackca asked in Calculus Sep 14, 2021

146 views

2 votes

0 answers

40

#calculus #limits
$\lim_{x\rightarrow a} f(x)^{g(x)} = e^{\lim_{x\rightarrow a}g(x)[f(x)-1]}$ Solve the below limit without using the above formula, $\lim_{x \rightarrow 0} ({\frac{sin x}{x}})^{\frac{sin x}{x - sin x}}$

dutta007sourish asked in Calculus Sep 7, 2021

by dutta007sourish

195 views

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Recent questions and answers in Calculus