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Recent questions and answers in Calculus

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1

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

Hailemariam asked in Calculus Aug 5

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2

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

Hailemariam asked in Calculus Aug 3

41 views

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3

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

kidussss asked in Calculus Jul 29

72 views

0 votes

2 answers

4

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

ASNR1010 answered in Calculus Jul 9

251 views

0 votes

2 answers

5

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

Kabir5454 answered in Calculus Jul 9

74 views

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1 answer

6

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

Kabir5454 answered in Calculus Jul 9

48 views

0 votes

2 answers

7

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

ASNR1010 answered in Calculus Jul 8

69 views

2 votes

3 answers

8

Integration
Solve the following $\int_{0}^{\infty}e^{-x^2}x^4dx$

Kabir5454 answered in Calculus May 18

452 views

2 votes

2 answers

9

Gate 2014 CE Set 2
The expression $\lim_{a \to 0}\frac{x^{a}-1}{a}$ is equal to (A)$\log x$ (B)0 (c)$x\log x$ (D)$\infty$

Kabir5454 answered in Calculus May 18

1.6k views

23 votes

6 answers

10

GATE CSE 2010 | Question: 5
What is the value of $ \displaystyle\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ? $0$ $e^{-2}$ $e^{-1/2}$ $1$

Kabir5454 answered in Calculus May 17

5.9k views

19 votes

5 answers

11

GATE IT 2008 | Question: 31
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ? $f(x) = \begin{cases} \frac{25}{8x} &\text{ when } x \leq \frac{3}{2} \\ x+ \frac{1}{x} &\text { otherwise}\end{cases}$ $2$ $2 \frac{1}{12}$ $2\frac{1}{6}$ $2\frac{1}{2}$

Kabir5454 answered in Calculus May 17

5.2k views

0 votes

0 answers

12

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

77 views

1 vote

2 answers

13

ISI2015-DCG-45
The value of $\underset{x \to 0}{\lim} \dfrac{\tan ^2 x – x \tan x }{\sin x}$ is $\frac{\sqrt{3}}{2}$ $\frac{1}{2}$ $0$ None of these

Kabir5454 answered in Calculus May 12

175 views

0 votes

2 answers

14

NIELIT 2016 MAR Scientist B - Section B: 13
$\underset{x\to 0}{\lim} \dfrac{(1-\cos x)}{2}$ is equal to $0$ $1$ $1/3$ $1/2$

Kabir5454 answered in Calculus May 11

369 views

0 votes

1 answer

15

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

Kabir5454 answered in Calculus May 11

209 views

2 votes

1 answer

16

ISI2016-MMA-20
Let $f : (0, \infty) \rightarrow (0, \infty)$ be a strictly decreasing function. Consider $h(x) = \dfrac{f(\frac{x}{1+x})}{1+f(\frac{x}{1+x})}$. Which one of the following is always true? $h$ is strictly decreasing $h$ is strictly increasing $h$ is strictly decreasing at first and then strictly increasing $h$ is strictly increasing at first and then strictly decreasing

Kabir5454 answered in Calculus May 11

179 views

0 votes

1 answer

17

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

Kabir5454 answered in Calculus May 11

208 views

0 votes

1 answer

18

ISI2018-DCG-28
Let $f(x)=e^{-\big( \frac{1}{x^2-3x+2} \big) };x\in \mathbb{R} \: \: \& x \notin \{1,2\}$. Let $a=\underset{n \to 1^+}{\lim}f(x)$ and $b=\underset{x \to 1^-}{\lim} f(x)$. Then $a=\infty, \: b=0$ $a=0, \: b=\infty$ $a=0, \: b=0$ $a=\infty, \: b=\infty$

Kabir5454 answered in Calculus May 11

160 views

0 votes

1 answer

19

ISI2016-DCG-56
$\underset{x\rightarrow \infty}{\lim} \left(1+\dfrac{1}{x^{2}}\right)^{x}$ equals $-1$ $0$ $1$ Does not exist

Kabir5454 answered in Calculus May 11

128 views

1 vote

3 answers

20

ISI2015-MMA-20
The limit $\underset{n \to \infty}{\lim} \left( 1- \frac{1}{n^2} \right) ^n$ equals $e^{-1}$ $e^{-1/2}$ $e^{-2}$ $1$

Kabir5454 answered in Calculus May 11

385 views

1 vote

1 answer

21

ISI2014-DCG-21
Suppose that the function $h(x)$ is defined as $h(x)=g(f(x))$ where $g(x)$ is monotone increasing, $f(x)$ is concave, and $g’’(x)$ and $f’’(x)$ exist for all $x$. Then $h(x)$ is always concave always convex not necessarily concave None of these

Kabir5454 answered in Calculus May 10

275 views

0 votes

1 answer

22

Calculus by Spivak 4th edition Chapter 10 problem 9

ankitgupta.1729 answered in Calculus May 3

by ankitgupta.1729

77 views

5 votes

3 answers

23

ISI2004-MIII: 13
Let $X =\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\ldots+\frac{1}{3001}$. Then $X< 1$ $X>\frac{3}{2}$ $1< X< \frac{3}{2}$ none of the above

ankitgupta.1729 answered in Calculus May 3

by ankitgupta.1729

1.8k views

9 votes

2 answers

24

ISI2004-MIII: 12
The maximum possible value of $xy^2z^3$ subjected to condition $x,y,z \geq 0$ and $x+y+z=3$ is $1$ $\frac{9}{8}$ $\frac{9}{4}$ $\frac{27}{16}$

niks77 answered in Calculus Apr 30

by niks77

827 views

1 vote

1 answer

25

ISI2015-MMA-77
Let $R$ be the triangle in the $xy$ – plane bounded by the $x$-axis, the line $y=x$, and the line $x=1$. The value of the double integral $ \int \int_R \frac{\sin x}{x}\: dxdy$ is $1-\cos 1$ $\cos 1$ $\frac{\pi}{2}$ $\pi$

niks77 answered in Calculus Apr 29

by niks77

277 views

0 votes

2 answers

26

NIELIT 2017 DEC Scientific Assistant A - Section B: 10
The function $f\left ( x \right )=\dfrac{x^{2}-1}{x-1}$ at $x=1$ is : Continuous and differentiable Continuous but not differentiable Differentiable but not continuous Neither continuous nor differentiable

s_dr_13 answered in Calculus Mar 22

565 views

0 votes

2 answers

27

NIELIT 2016 MAR Scientist B - Section B: 11
What is the derivative w.r.t $x$ of the function given by $\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$, $2x^2$ $\sqrt x$ $0$ $1$

s_dr_13 answered in Calculus Mar 22

323 views

0 votes

2 answers

28

NIELIT 2016 MAR Scientist C - Section B: 13
$\displaystyle \lim_{x \rightarrow 0}\frac{1}{x^{6}} \displaystyle \int_{0}^{x^{2}}\frac{t^{2}dt}{t^{6}+1}=$? $1/4$ $1/3$ $1/2$ $1$

Anuj2000 answered in Calculus Mar 16

240 views

1 vote

1 answer

29

ISI2015-DCG-56
$\underset{x \to \infty}{\lim} \left( 1 + \dfrac{1}{x^2} \right) ^x$ equals $-1$ $0$ $1$ Does not exist

preeti0448 answered in Calculus Feb 27

203 views

1 vote

0 answers

30

#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

by Jeetu Bhaiya

91 views

3 votes

4 answers

31

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

ankitgupta.1729 answered in Calculus Feb 23

by ankitgupta.1729

906 views

0 votes

0 answers

32

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

97 views

0 votes

1 answer

33

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

Kabir5454 answered in Calculus Jan 24

149 views

1 vote

1 answer

34

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...

LRU answered in Calculus Jan 18

by LRU

153 views

1 vote

1 answer

35

me book mathematics
Which of following function is strictly bounded?

zeikion answered in Calculus Dec 1, 2021

1.7k views

0 votes

2 answers

36

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

wer 123 answered in Calculus Nov 25, 2021

181 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

161 views

4 votes

4 answers

38

TIFR2010-Maths-A-8
Let $f(x)= |x|^{3/2}, x \in \mathbb{R}$. Then $f$ is uniformly continuous. $f$ is continuous, but not differentiable at $x=0$. $f$ is differentiable and $f ' $ is continuous. $f$ is differentiable, but $f ' $ is discontinuous at $x=0$.

huny answered in Calculus Oct 9, 2021

by huny

805 views

0 votes

0 answers

39

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

amit166 asked in Calculus Sep 25, 2021

160 views

0 votes

1 answer

40

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

Nibchee answered in Calculus Sep 15, 2021

110 views

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Recent questions and answers in Calculus