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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
122
views
continuity
calculus
0
votes
0
answers
2
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
missing-videos
go-classroom
free-videos
video-links
continuity
13
votes
2
answers
3
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
gatecse-2021-set2
numerical-answers
calculus
continuity
1-mark
0
votes
0
answers
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
tifrmaths2018
true-false
calculus
continuity
0
votes
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
nielit2017dec-assistanta
engineering-mathematics
calculus
continuity
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
isi2014-dcg
calculus
continuity
differentiation
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
isi2014-dcg
calculus
functions
limits
continuity
0
votes
1
answer
8
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
isi2015-mma
calculus
continuity
differentiation
definite-integral
non-gate
1
vote
1
answer
9
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
isi2015-mma
continuity
partial-derivatives
non-gate
0
votes
1
answer
10
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
by
gatecse
244
views
isi2015-dcg
calculus
continuity
differentiation
0
votes
0
answers
11
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
by
gatecse
185
views
isi2016-dcg
calculus
continuity
differentiation
functions
1
vote
2
answers
12
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
isi2018-mma
engineering-mathematics
calculus
continuity
0
votes
1
answer
13
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
by
go_editor
294
views
isi2016-pcb-a
calculus
continuity
non-gate
descriptive
0
votes
2
answers
14
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
by
go_editor
816
views
isi2017-mma
engineering-mathematics
calculus
continuity
0
votes
0
answers
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
by
go_editor
274
views
isi2016-mmamma
calculus
continuity
differentiation
limits
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
by
go_editor
299
views
isi2016-mmamma
calculus
continuity
differentiation
0
votes
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
by
habedo007
984
views
nielit-july-2017
engineering-mathematics
calculus
continuity
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
engineering-mathematics
calculus
continuity
0
votes
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
calculus
differentiation
continuity
engineering-mathematics
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
gate2018-ee
engineering-mathematics
calculus
continuity
differentiation
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
by
Mk Utkarsh
601
views
calculus
continuity
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
by
Kuldeep Pal
270
views
made-easy-test-series
calculus
differentiation
continuity
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
by
Shubhanshu
738
views
limits
continuity
function
calculus
0
votes
0
answers
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
calculus
imits
continuity
differentiation
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
by
firki lama
579
views
differentiation
continuity
calculus
0
votes
1
answer
26
Test Series
https://gateoverflow.in/?qa=blob&qa_blobid=4549376166631720003
Shreya Roy
asked
in
Calculus
Jan 14, 2017
by
Shreya Roy
317
views
continuity
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
by
srestha
1.6k
views
calculus
continuity
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
calculus
engineering-mathematics
continuity
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
calculus
gate2010me
engineering-mathematics
continuity
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