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Recent questions tagged continuity
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Memory Based GATE DA 2024 | Question: 30
Consider the function \( F(x) \) defined as follows: \[ F(x) = \left\{ \begin{array}{cc} -x & \text{if } x < -2 \\ ax^2 + bx + c & \text{if } x \in [-2, 2] \\ x & \text{if } x > 2 \end{ ... \] \noindent Determine the values of \( a, b, \) and \( c \) such that \( F(x) \) is continuous and differentiable over its entire domain.
GO Classes
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in
Calculus
Feb 4
by
GO Classes
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gate2024-da-memory-based
goclasses
calculus
continuity
0
votes
1
answer
2
LIMIT AND CONTINUITY
1.Evaluate the following definite integral $\int^{130}_{130}\frac{x^{3}-x\sin(x)+\cos(x)}{x^{^{2}}+1}dx$
Hailemariam
asked
in
Others
Jun 1, 2023
by
Hailemariam
283
views
limits
continuity
integration
0
votes
0
answers
3
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
237
views
continuity
calculus
0
votes
0
answers
4
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 ... 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
203
views
missing-videos
go-classroom
free-videos
video-links
continuity
16
votes
3
answers
5
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
6.1k
views
gatecse-2021-set2
numerical-answers
calculus
continuity
1-mark
0
votes
0
answers
6
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 29, 2020
by
soujanyareddy13
205
views
tifrmaths2018
true-false
calculus
continuity
1
vote
3
answers
7
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
admin
asked
in
Calculus
Mar 31, 2020
by
admin
1.1k
views
nielit2017dec-assistanta
engineering-mathematics
calculus
continuity
0
votes
2
answers
8
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
714
views
isi2014-dcg
calculus
continuity
differentiation
2
votes
2
answers
9
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
557
views
isi2014-dcg
calculus
functions
limits
continuity
0
votes
2
answers
10
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
814
views
isi2015-mma
calculus
continuity
differentiation
definite-integral
non-gate
1
vote
1
answer
11
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
395
views
isi2015-mma
continuity
partial-derivatives
non-gate
0
votes
2
answers
12
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
422
views
isi2015-dcg
calculus
continuity
differentiation
0
votes
0
answers
13
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
368
views
isi2016-dcg
calculus
continuity
differentiation
functions
1
vote
4
answers
14
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
1.2k
views
isi2018-mma
engineering-mathematics
calculus
continuity
0
votes
2
answers
15
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
416
views
isi2016-pcb-a
calculus
continuity
non-gate
descriptive
0
votes
2
answers
16
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
1.2k
views
isi2017-mma
engineering-mathematics
calculus
continuity
0
votes
1
answer
17
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
475
views
isi2016-mmamma
calculus
continuity
differentiation
limits
2
votes
3
answers
18
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
536
views
isi2016-mmamma
calculus
continuity
differentiation
1
vote
1
answer
19
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 30, 2018
by
habedo007
1.4k
views
nielit-july-2017
engineering-mathematics
calculus
continuity
0
votes
1
answer
20
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
678
views
engineering-mathematics
calculus
continuity
0
votes
0
answers
21
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
386
views
calculus
differentiation
continuity
engineering-mathematics
3
votes
1
answer
22
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 Bhaiya
asked
in
Calculus
Feb 21, 2018
by
Lakshman Bhaiya
3.0k
views
gate2018-ee
engineering-mathematics
calculus
continuity
differentiation
6
votes
1
answer
23
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
982
views
calculus
continuity
2
votes
1
answer
24
MadeEasy Test Series: Calculus - Differentiability
At the point x = 1, the function
Kuldeep Pal
asked
in
Calculus
Jan 6, 2018
by
Kuldeep Pal
535
views
made-easy-test-series
calculus
differentiation
continuity
3
votes
1
answer
25
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
968
views
limits
continuity
function
calculus
0
votes
0
answers
26
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 ... 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
846
views
calculus
imits
continuity
differentiation
3
votes
0
answers
27
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
701
views
differentiation
continuity
calculus
0
votes
1
answer
28
Test Series
https://gateoverflow.in/?qa=blob&qa_blobid=4549376166631720003
Shreya Roy
asked
in
Calculus
Jan 14, 2017
by
Shreya Roy
538
views
continuity
1
vote
1
answer
29
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 28, 2016
by
srestha
2.3k
views
calculus
continuity
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