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Recent questions tagged differentiation

2 votes

1 answer

31

ISI2018-DCG-9
Let $f(x)=1+x+\dfrac{x^2}{2}+\dfrac{x^3}{3}...+\dfrac{x^{2018}}{2018}.$ Then $f’(1)$ is equal to $0$ $2017$ $2018$ $2019$

gatecse asked in Calculus Sep 18, 2019

416 views

1 vote

1 answer

32

ISI2018-DCG-10
Let $f’(x)=4x^3-3x^2+2x+k,$ $f(0)=1$ and $f(1)=4.$ Then $f(x)$ is equal to $4x^4-3x^3+2x^2+x+1$ $x^4-x^3+x^2+2x+1$ $x^4-x^3+x^2+2(x+1)$ none of these

gatecse asked in Calculus Sep 18, 2019

251 views

0 votes

1 answer

33

ISI2018-DCG-24
Let $[x]$ denote the largest integer less than or equal to $x.$ The number of points in the open interval $(1,3)$ in which the function $f(x)=a^{[x^2]},a\gt1$ is not differentiable, is $0$ $3$ $5$ $7$

gatecse asked in Calculus Sep 18, 2019

246 views

0 votes

0 answers

34

ISI2018-DCG-29
Let $f(x)=(x-1)(x-2)(x-3)g(x); \: x\in \mathbb{R}$ where $g$ is twice differentiable function. Then there exists $y\in(1,3)$ such that $f’’(y)=0.$ there exists $y\in(1,2)$ such that $f’’(y)=0.$ there exists $y\in(2,3)$ such that $f’’(y)=0.$ none of the above is true.

gatecse asked in Calculus Sep 18, 2019

238 views

0 votes

1 answer

35

Gate 2002 - ME
Which of the following functions is not differentiable in the domain $[-1,1]$ ? (a) $f(x) = x^2$ (b) $f(x) = x-1$ (c) $f(x) = 2$ (d) $f(x) = Maximum (x,-x)$

balchandar reddy san asked in Calculus May 4, 2019

by balchandar reddy san

1.9k views

1 vote

1 answer

36

Applied Course | Mock GATE | Test 1 | Question: 11
The value of derivative of $f(x) = \mid x -1 \mid + \mid x -3 \mid \text{ at } x = 2$ is $-2$ $0$ $2$ Not defined

Applied Course asked in Calculus Jan 16, 2019

by Applied Course

493 views

0 votes

0 answers

37

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?

shreyansh jain asked in Mathematical Logic Dec 18, 2018

by shreyansh jain

219 views

1 vote

0 answers

38

NIELIT 2018-19
If $u=f(y-z, \: \: z-x, \: \: x-y)$, then $\frac{ \partial u}{ \partial x} + \frac{ \partial u}{ \partial y} + \frac{ \partial u}{ \partial z} $ is equal to: $x+y+z$ $1+x+y+z$ $1$ $0$

Arjun asked in Others Dec 7, 2018

by Arjun

478 views

1 vote

0 answers

39

NIELIT 2018-23
If $w=f(z)=u(x,y)+i \: v(x,y)$ is an analytic function, then $\frac{dw}{dz}$ is: $\frac{ \partial u } {\partial x}- i \frac{ \partial u}{\partial y}$ $\frac{ \partial u } {\partial x}+ i \frac{ \partial v}{\partial y}$ $\frac{ \partial u } {\partial x}- i \frac{ \partial v}{\partial x}$ $\frac{ \partial u } {\partial x}+ i \frac{ \partial u}{\partial y}$

Arjun asked in Others Dec 7, 2018

by Arjun

1.0k views

0 votes

0 answers

40

ISI2017-PCB-A-4
Let $\lceil x \rfloor$ denote the integer nearest to $x$. For example, $\lceil 1.1 \rfloor =1, \lceil 1.5 \rfloor =1$ and $\lceil 1.6 \rfloor$ =2. Draw the graph of the function $y= \mid x - \lceil x \rfloor \mid$ for $0 \leq x \leq 4$. Find all the points $x, \: 0 \leq x \leq 4$, where the function is not differentiable. Justify your answer.

go_editor asked in Calculus Sep 19, 2018

146 views

0 votes

0 answers

41

ISI2017-MMA-13
An even function $f(x)$ has left derivative $5$ at $x=0$. Then the right derivative of $f(x)$ at $x=0$ need not exist the right derivative of $f(x)$ at $x=0$ exists and is equal to $5$ the right derivative of $f(x)$ at $x=0$ exists and equal to $-5$ none of the above is necessarily true

go_editor asked in Quantitative Aptitude Sep 15, 2018

295 views

2 votes

2 answers

42

ISI2016-MMA-8
Let $g: \mathbb{R} \rightarrow \mathbb{R}$ be differentiable with $g'(x^2)=x^3$ for all $x>0$ and $g(1) =1$. Then $g(4)$ equals $64/5$ $32/5$ $37/5$ $67/5$

go_editor asked in Calculus Sep 13, 2018

494 views

0 votes

0 answers

43

ISI2016-MMA-24
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a strictly increasing function. Then which one the following is always true? The limits $\lim_{x \rightarrow a+} f(x) $ and $\lim_{x \rightarrow a-} f(x)$ exist for all real numbers $a$ If $f$ is differentiable at $a$ then ... such that $f(x)<B$ for all real $x$ There cannot be any real number $L$ such that $f(x)>L$ for all real $x$

go_editor asked in Calculus Sep 13, 2018

266 views

1 vote

0 answers

44

ISI2016-MMA-26
Let $x$ and $y$ be real numbers satisfying $9x^2+16y^2=1$. Then $(x+y)$ is maximum when $y=9x/16$ $y=-9x/16$ $y=4x/3$ $y=-4x/3$

go_editor asked in Others Sep 13, 2018

161 views

2 votes

2 answers

45

ISI2016-MMA-27
Consider the function $f(x) = \dfrac{e^{- \mid x \mid}}{\text{max}\{e^x, e^{-x}\}}, \: \: x \in \mathbb{R}$. Then $f$ is not continuous at some points $f$ is continuous everywhere, but not differentiable anywhere $f$ is continuous everywhere, but not differentiable at exactly one point $f$ is differentiable everywhere

go_editor asked in Calculus Sep 13, 2018

288 views

0 votes

0 answers

46

Differentiable
Why is a function not differentiable at x=k when f'(x) limits to infinity? Limit can be infinite too?

bts asked in Mathematical Logic Jun 25, 2018

by bts

265 views

3 votes

3 answers

47

ISI2017-MMA-13
An even function $f(x)$ has left derivative $5$ at $x=0$. Then the right derivative of $f(x)$ at $x=0$ need not exist the right derivative of $f(x)$ at $x=0$ exists and is equal to $5$ the right derivative of $f(x)$ at $x=0$ exists and is equal to $-5$ none of the above is necessarily true

jjayantamahata asked in Calculus Mar 27, 2018

by jjayantamahata

1.6k views

3 votes

1 answer

48

Mathematics GATE 2018 EE: 11
Let $f$ be a real-valued function of a real variable defined as $f(x) = x^{2}$ for $x\geq0$ and $f(x) = -x^{2}$ for $x < 0$.Which one of the following statements is true? $f(x) \text{is discontinuous at x = 0}$ ... $f(x) \text{is differentiable but its first derivative is not differentiable at x = 0} $

Lakshman Patel RJIT asked in Calculus Feb 21, 2018

by Lakshman Patel RJIT

2.6k views

1 vote

1 answer

49

MadeEasy Test Series: Calculus - Differentiability
At the point x = 1, the function

Kuldeep Pal asked in Calculus Jan 6, 2018

268 views

3 votes

1 answer

50

TIFR CSE 2018 | Part A | Question: 5
Which of the following is the derivative of $f(x)=x^{x}$ when $x>0$ ? $x^{x}$ $x^{x} \ln \;x$ $x^{x}+x^{x}\ln\;x$ $(x^{x}) (x^{x}\ln\;x)$ $\text{None of the above; function is not differentiable for }x>0$

Arjun asked in Calculus Dec 10, 2017

by Arjun

1.0k views

0 votes

0 answers

51

Calculus
#Calculus Let f(x)= |x|^3/2, x€R then A.f is uniformly continuous B.f is Continous but not differentiable ar x=0 C. f is differentiable and f' is continuous D. f is differentiable but f' is discontinuous at x=0 What is the answer and how to solve this kind of questions? My Answer is option D , I want to confirm if my reasoning to this question is correct as im learning calculus now.

MancunianDevil asked in Calculus Apr 19, 2017

by MancunianDevil

587 views

3 votes

0 answers

52

differentiable
The function is defined as follows. Which of the following is true? (A) f is discontinuous at all (B) f is continuous only at x = 0 and differentiable only at x = 0. (C) f is continuous only at x=0 and non differentiable at all (D) f is continuous at all and non differentiable at all

firki lama asked in Calculus Mar 1, 2017

567 views

1 vote

2 answers

53

ISRO2012-ECE Engineering Mathematics
$1-x$ $(1-x)/x$ $1/x$ $x/(1-x)$

sh!va asked in Calculus Feb 28, 2017

by sh!va

329 views

23 votes

2 answers

54

GATE CSE 2017 Set 2 | Question: 10
If $f(x) = R \: \sin ( \frac{\pi x}{2}) + S, f’\left(\frac{1}{2}\right) = \sqrt{2}$ 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 $\frac{16}{\pi}$

Madhav asked in Calculus Feb 14, 2017

by Madhav

6.5k views

14 votes

2 answers

55

TIFR CSE 2017 | Part A | Question: 9
Consider the $majority$ function on three bits, $\textbf{maj}: \{0, 1\}^3 \rightarrow \{0, 1\}$ where $\textbf{maj}(x_1, x_2, x_3)=1$ if and only if $x_1+x_2+x_3 \geq 2$. Let $p(\alpha)$ be the probability that the output is $1$ when each input is set to ... $3 \alpha$ $\alpha^2$ $6\alpha(1-\alpha)$ $3\alpha^2 (1-\alpha)$ $6\alpha(1-\alpha)+\alpha^2$

go_editor asked in Probability Dec 21, 2016

1.0k views

0 votes

1 answer

56

Diffrentiability+Limits
how to solve diffrentiability with standard procedure of f(a+h).

Rahul Jain25 asked in Calculus Dec 9, 2016

by Rahul Jain25

488 views

5 votes

1 answer

57

ISRO2011-59
$n$-th derivative of $x^n$ is $nx^{n-1}$ $n^n.n!$ $nx^n!$ $n!$

go_editor asked in Calculus Jun 23, 2016

1.7k views

30 votes

5 answers

58

GATE CSE 2016 Set 2 | Question: 02
Let $f(x)$ be a polynomial and $g(x)=f'(x)$ be its derivative. If the degree of $(f(x)+f(-x))$ is $10$, then the degree of $(g(x) - g(-x))$ is __________.

Akash Kanase asked in Calculus Feb 12, 2016

by Akash Kanase

8.1k views

2 votes

1 answer

59

MadeEasy Test Series: Calculus - Differentiability
Q.64 A function f (x) is differentiated twice such that its differential equation λ2f (x) – 2λf ′(x) + f ′′(x) = 0 provides two equal value of λ for all x. It f (0) = 1, f′(0) = 2, then f(x) at x = 1 will be _________. Given ans -> 7.39 (7.00 - 7.80)

Akash Kanase asked in Calculus Dec 19, 2015

by Akash Kanase

360 views

3 votes

1 answer

60

TIFR-2015-Maths-A-5
Let $f : \mathbb{R} \rightarrow \mathbb{R}$ denote the function defined by $f(x)= (1-x^{2})^{\frac{3}{2}}$ if $|x| < 1$, and $f(x)=0$ if $|x| \geq 1$. Which of the following statements is correct ? $f$ is not continuous $f$ is continuous but not differentiable $f$ is differentiable but $f'$ is not continuous. $f$ is differentiable and $f'$ is continuous.

makhdoom ghaya asked in Calculus Dec 19, 2015

by makhdoom ghaya

435 views

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Recent questions tagged differentiation