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Recent questions tagged continuity

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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

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Best Open Video Playlist for Continuity Topic | Calculus
Please list out the best free available video playlist for Continuity Topic from Calculus as an answer here (only one playlist per answer). We'll then select the best playlist and add to GO classroom video lists. You can add any ... but standard ones are more likely to be selected as best. For the full list of selected videos please see here

makhdoom ghaya asked in Study Resources Aug 15, 2022

by makhdoom ghaya

46 views

13 votes

2 answers

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GATE CSE 2021 Set 2 | Question: 25
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that for every $x$ in the interval, $f’(x) \leq 2$. If $f(-3)=7$, then $f(3)$ is at most __________

Arjun asked in Calculus Feb 18, 2021

by Arjun

3.6k views

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4

TIFR-2018-Maths-A: 5
True/False Question : The function $f\left ( x \right )=cos\left ( e^{x} \right )$ is not uniformly continuous on $\mathbb{R}$.

soujanyareddy13 asked in Calculus Aug 30, 2020

by soujanyareddy13

99 views

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2 answers

5

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

Lakshman Patel RJIT asked in Calculus Mar 31, 2020

by Lakshman Patel RJIT

642 views

0 votes

1 answer

6

ISI2014-DCG-29
If $f(x) = \sin \bigg( \dfrac{1}{x^2+1} \bigg),$ then $f(x)$ is continuous at $x=0$, but not differentiable at $x=0$ $f(x)$ is differentiable at $x=0$, and $f’(0) \neq 0$ $f(x)$ is differentiable at $x=0$, and $f’(0) = 0$ None of the above

Arjun asked in Calculus Sep 23, 2019

by Arjun

463 views

2 votes

2 answers

7

ISI2014-DCG-37
Let $f: \bigg( – \dfrac{\pi}{2}, \dfrac{\pi}{2} \bigg) \to \mathbb{R}$ be a continuous function, $f(x) \to +\infty$ as $x \to \dfrac{\pi^-}{2}$ and $f(x) \to – \infty$ as $x \to -\dfrac{\pi^+}{2}$. Which one of the following functions satisfies the above properties of $f(x)$? $\cos x$ $\tan x$ $\tan^{-1} x$ $\sin x$

Arjun asked in Calculus Sep 23, 2019

by Arjun

363 views

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1 answer

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ISI2015-MMA-69
Consider the function $f(x) = \begin{cases} \int_0^x \{5+ \mid 1-y \mid \} dy & \text{ if } x>2 \\ 5x+2 & \text{ if } x \leq 2 \end{cases}$ Then $f$ is not continuous at $x=2$ $f$ is continuous and differentiable everywhere $f$ is continuous everywhere but not differentiable at $x=1$ $f$ is continuous everywhere but not differentiable at $x=2$

Arjun asked in Calculus Sep 23, 2019

by Arjun

534 views

1 vote

1 answer

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ISI2015-MMA-71
Let $f(x,y) = \begin{cases} 1, & \text{ if } xy=0, \\ xy, & \text{ if } xy \neq 0. \end{cases}$ Then $f$ is continuous at $(0,0)$ and $\frac{\partial f}{\partial x}(0,0)$ exists $f$ is not continuous at $(0,0)$ ... $f$ is not continuous at $(0,0)$ and $\frac{\partial f}{\partial x}(0,0)$ does not exist

Arjun asked in Others Sep 23, 2019

by Arjun

290 views

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1 answer

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ISI2015-DCG-57
Let $y=\lfloor x \rfloor$, where $\lfloor x \rfloor$ is greatest integer less than or equal to $x$. Then $y$ is continuous and many-one $y$ is not differentiable and many-one $y$ is not differentiable $y$ is differentiable and many-one

gatecse asked in Calculus Sep 18, 2019

244 views

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ISI2016-DCG-58
Let $y=\left \lfloor x \right \rfloor$ where $\left \lfloor x \right \rfloor$ is greatest integer less than or equal to $x$. Then $y$ is continuous and many-one. $y$ is not differentiable and many-one. $y$ is not differentiable. $y$ is differentiable and many-one.

gatecse asked in Calculus Sep 18, 2019

185 views

1 vote

2 answers

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ISI2018-MMA-28
Consider the following functions $f(x)=\begin{cases} 1, & \text{if } \mid x \mid \leq 1 \\ 0, & \text{if } \mid x \mid >1 \end{cases}.$ ... at $\pm1$ $h_2$ is continuous everywhere and $h_1$ has discontinuity at $\pm2$ $h_1$ has discontinuity at $\pm 2$ and $h_2$ has discontinuity at $\pm1$.

akash.dinkar12 asked in Calculus May 11, 2019

by akash.dinkar12

908 views

0 votes

1 answer

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ISI2016-PCB-A-2
Let $n$ be a fixed positive integer. For any real number $x,$ if for some integer $q,$ $x=qn+r, \: \: \: 0 \leq r < n,$ then we define $x \text{ mod } n=r$. Specify the points of discontinuity of the function $f(x)=x \text{ mod } 3$ with proper reasoning.

go_editor asked in Calculus Sep 18, 2018

294 views

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2 answers

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ISI2017-MMA-4
Let $S\subseteq \mathbb{R}$. Consider the statement “There exists a continuous function $f:S\rightarrow S$ such that $f(x) \neq x$ for all $x \in S.$ ” This statement is false if $S$ equals $[2,3]$ $(2,3]$ $[-3,-2] \cup [2,3]$ $(-\infty,\infty)$

go_editor asked in Calculus Sep 15, 2018

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15

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

274 views

2 votes

2 answers

16

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

299 views

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1 answer

17

NIELIT2017 STA-set-c-119
The function $f(x)=\frac{x^2 -1}{x-1}$ at $x=1$ is: Continuous and Differentiable Continuous but not Differentiable Differentiable but not Continuous Neither Continuous nor Differentiable

habedo007 asked in Calculus Aug 31, 2018

984 views

0 votes

1 answer

18

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

Ayush Upadhyaya asked in Calculus Jul 17, 2018

by Ayush Upadhyaya

418 views

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0 answers

19

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

274 views

3 votes

1 answer

20

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

5 votes

1 answer

21

Continuity
If the function f(x) defined by $\left\{\begin{matrix} \frac{log(1+ ax) - log(1-bx)}{x} &, if x \neq 0\\ k & ,if x = 0 \end{matrix}\right.$ is continuous at x = 0, then value of k is A) b - a B) a - b C) a + b D) -a - b

Mk Utkarsh asked in Calculus Jan 15, 2018

601 views

1 vote

1 answer

22

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

Kuldeep Pal asked in Calculus Jan 6, 2018

270 views

2 votes

1 answer

23

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.

Shubhanshu asked in Calculus Dec 31, 2017

738 views

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24

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

618 views

3 votes

0 answers

25

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

579 views

0 votes

1 answer

26

Test Series
https://gateoverflow.in/?qa=blob&qa_blobid=4549376166631720003

Shreya Roy asked in Calculus Jan 14, 2017

317 views

1 vote

1 answer

27

Continuity
Function f(x) = |cos x| is (A) Continuous only in [0, π/2] (B) Continuous only in [−π/2, π/2] (C) Continuous only in [−π, π] (D) None

srestha asked in Set Theory & Algebra Dec 29, 2016

1.6k views

2 votes

1 answer

28

Continuity
What should be the value of a,b and c such that the function defined below is continuous at x=0 ? $f\left ( x \right )=\begin{Bmatrix} \left ( 1+ax \right )^{\frac{1}{x}} & x<0 & \\ b & x=0& \\ \frac{(x+c)^{\frac{1}{3}}-1}{x} &x>0 & \end{Bmatrix}$

ManojK asked in Calculus Dec 20, 2016

by ManojK

749 views

22 votes

4 answers

29

GATE2010 ME
The function $y=|2 - 3x|$ is continuous $∀ x ∈ R$ and differentiable $∀ x ∈ R$ is continuous $∀ x ∈ R$ and differentiable $∀ x ∈ R$ except at $x=\frac{3}{2}$ is continuous $∀ x ∈ R$ and differentiable $∀ x ∈ R$ except at $x=\frac{2}{3}$ is continuous $∀ x ∈ R$ except $x=3$ and differentiable $∀ x ∈ R$

Anuraag Nayak asked in Calculus Mar 20, 2016

by Anuraag Nayak

4.5k views

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Recent questions tagged continuity