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Recent questions tagged continuity
1
votes
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answer
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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.
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] \\...
GO Classes
234
views
GO Classes
asked
Feb 4
Calculus
gate2024-da-memory-based
goclasses
calculus
continuity
+
–
0
votes
1
answer
2
LIMIT AND CONTINUITY
1.Evaluate the following definite integral $\int^{130}_{130}\frac{x^{3}-x\sin(x)+\cos(x)}{x^{^{2}}+1}dx$
1.Evaluate the following definite integral $\int^{130}_{130}\frac{x^{3}-x\sin(x)+\cos(x)}{x^{^{2}}+1}dx$
Hailemariam
286
views
Hailemariam
asked
Jun 1, 2023
Others
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
For f(x)=√x x€[0,b] the number c satisfying mean value therom is c=1
Katyayani0306
240
views
Katyayani0306
asked
Sep 21, 2022
Calculus
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
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 pla...
makhdoom ghaya
211
views
makhdoom ghaya
asked
Aug 15, 2022
Study Resources
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 __________
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 fo...
Arjun
6.3k
views
Arjun
asked
Feb 18, 2021
Calculus
gatecse-2021-set2
numerical-answers
calculus
continuity
1-mark
+
–
1
votes
1
answer
6
GATE Overflow Test Series | Calculus | Test 1 | Question: 26
Which of the following function(s) is/are continuous at $x = 3?$ ... $f(x) = \left\{ \begin{matrix} \frac{1}{\sqrt{x^3- 27}}; & \text{when } x<3 \end{matrix} \right.$
Which of the following function(s) is/are continuous at $x = 3?$ (Mark all the appropriate choices)$f(x) = \left\{\begin{matrix}2; & \text{when } x = 3 \\x-1; & \text{whe...
gatecse
95
views
gatecse
asked
Dec 28, 2020
Calculus
go2025-calculus-1
continuity
multiple-selects
+
–
0
votes
0
answers
7
TIFR-2018-Maths-A: 5
True/False Question : The function $f\left ( x \right )=cos\left ( e^{x} \right )$ is not uniformly continuous on $\mathbb{R}$.
True/False Question :The function $f\left ( x \right )=cos\left ( e^{x} \right )$ is not uniformly continuous on $\mathbb{R}$.
soujanyareddy13
212
views
soujanyareddy13
asked
Aug 29, 2020
Calculus
tifrmaths2018
true-false
calculus
continuity
+
–
1
votes
3
answers
8
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
The function $f\left ( x \right )=\dfrac{x^{2}-1}{x-1}$ at $x=1$ is :Continuous and differentiableContinuous but not differentiableDifferentiable but not continuousNeith...
admin
1.1k
views
admin
asked
Mar 31, 2020
Calculus
nielit2017dec-assistanta
engineering-mathematics
calculus
continuity
+
–
0
votes
2
answers
9
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
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$$f(x)$ is differentiable at $x=0$, and $f’(0) \neq 0$...
Arjun
721
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
continuity
differentiation
+
–
2
votes
2
answers
10
ISI2014-DCG-37
Let $f: \bigg( – \dfrac{\pi}{2}, \dfrac{\pi}{2} \bigg) \to \mathbb{R}$ be a continuous function, $f(x) \to +\infty$ as $x \to \dfrac{\pi^-}{2}$ and $f(x) \to – \infty$ as $x \to -\dfrac{\pi^+}{2}$. Which one of the following functions satisfies the above properties of $f(x)$? $\cos x$ $\tan x$ $\tan^{-1} x$ $\sin x$
Let $f: \bigg( – \dfrac{\pi}{2}, \dfrac{\pi}{2} \bigg) \to \mathbb{R}$ be a continuous function, $f(x) \to +\infty$ as $x \to \dfrac{\pi^-}{2}$ and $f(x) \to – \infty...
Arjun
580
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
functions
limits
continuity
+
–
0
votes
2
answers
11
ISI2015-MMA-69
Consider the function $f(x) = \begin{cases} \int_0^x \{5+ \mid 1-y \mid \} dy & \text{ if } x>2 \\ 5x+2 & \text{ if } x \leq 2 \end{cases}$ Then $f$ is not continuous at $x=2$ $f$ is continuous and differentiable everywhere $f$ is continuous everywhere but not differentiable at $x=1$ $f$ is continuous everywhere but not differentiable at $x=2$
Consider the function $$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}$$ Then$f$ is not continuous at...
Arjun
826
views
Arjun
asked
Sep 23, 2019
Calculus
isi2015-mma
calculus
continuity
differentiation
definite-integral
non-gate
+
–
1
votes
1
answer
12
ISI2015-MMA-71
Let $f(x,y) = \begin{cases} 1, & \text{ if } xy=0, \\ xy, & \text{ if } xy \neq 0. \end{cases}$ Then $f$ is continuous at $(0,0)$ and $\frac{\partial f}{\partial x}(0,0)$ exists $f$ is not continuous at $(0,0)$ ... $f$ is not continuous at $(0,0)$ and $\frac{\partial f}{\partial x}(0,0)$ does not exist
Let $$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)...
Arjun
407
views
Arjun
asked
Sep 23, 2019
Others
isi2015-mma
continuity
partial-derivatives
non-gate
+
–
0
votes
2
answers
13
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
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-o...
gatecse
433
views
gatecse
asked
Sep 18, 2019
Calculus
isi2015-dcg
calculus
continuity
differentiation
+
–
0
votes
0
answers
14
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.
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...
gatecse
386
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
continuity
differentiation
functions
+
–
1
votes
4
answers
15
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$.
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}.$ and $g(x)=\begin{cases} 1, & \te...
akash.dinkar12
1.2k
views
akash.dinkar12
asked
May 11, 2019
Calculus
isi2018-mma
engineering-mathematics
calculus
continuity
+
–
0
votes
2
answers
16
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.
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...
go_editor
427
views
go_editor
asked
Sep 18, 2018
Calculus
isi2016-pcb-a
calculus
continuity
non-gate
descriptive
+
–
0
votes
2
answers
17
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 $[2,3]$ $(2,3]$ $[-3,-2] \cup [2,3]$ $(-\infty,\infty)$
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 ...
go_editor
1.2k
views
go_editor
asked
Sep 15, 2018
Calculus
isi2017-mma
engineering-mathematics
calculus
continuity
+
–
0
votes
1
answer
18
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 $x$
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 $...
go_editor
494
views
go_editor
asked
Sep 13, 2018
Calculus
isi2016-mmamma
calculus
continuity
differentiation
limits
+
–
2
votes
3
answers
19
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
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 eve...
go_editor
546
views
go_editor
asked
Sep 13, 2018
Calculus
isi2016-mmamma
calculus
continuity
differentiation
+
–
1
votes
1
answer
20
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
The function $f(x)=\frac{x^2 -1}{x-1}$ at $x=1$ is:Continuous and Differentiable Continuous but not DifferentiableDifferentiable but not ContinuousNeither Continuous nor ...
habedo007
1.4k
views
habedo007
asked
Aug 30, 2018
Calculus
nielit-july-2017
engineering-mathematics
calculus
continuity
+
–
0
votes
1
answer
21
Calculus-Self Doubt
Is the function $f(x)=\frac{1}{x^{\frac{1}{3}}}$ continous in the interval [-1 0) ?
Is the function $f(x)=\frac{1}{x^{\frac{1}{3}}}$ continous in the interval [-1 0) ?
Ayush Upadhyaya
698
views
Ayush Upadhyaya
asked
Jul 17, 2018
Calculus
engineering-mathematics
calculus
continuity
+
–
0
votes
0
answers
22
Differentiable
Why is a function not differentiable at x=k when f'(x) limits to infinity? Limit can be infinite too?
Why is a function not differentiable at x=k when f'(x) limits to infinity? Limit can be infinite too?
bts
392
views
bts
asked
Jun 25, 2018
Mathematical Logic
calculus
differentiation
continuity
engineering-mathematics
+
–
3
votes
1
answer
23
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} $
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...
Lakshman Bhaiya
3.0k
views
Lakshman Bhaiya
asked
Feb 21, 2018
Calculus
gate2018-ee
engineering-mathematics
calculus
continuity
differentiation
+
–
6
votes
1
answer
24
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
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 v...
Mk Utkarsh
1.0k
views
Mk Utkarsh
asked
Jan 15, 2018
Calculus
calculus
continuity
+
–
2
votes
1
answer
25
MadeEasy Test Series: Calculus - Differentiability
At the point x = 1, the function
At the point x = 1, the function
Kuldeep Pal
580
views
Kuldeep Pal
asked
Jan 6, 2018
Calculus
made-easy-test-series
calculus
differentiation
continuity
+
–
3
votes
1
answer
26
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.
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 Differen...
Shubhanshu
983
views
Shubhanshu
asked
Dec 31, 2017
Calculus
limits
continuity
function
calculus
+
–
0
votes
0
answers
27
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.
#CalculusLet f(x)= |x|^3/2, x€R thenA.f is uniformly continuousB.f is Continous but not differentiable ar x=0C. f is differentiable and f' is continuousD. f is differen...
MancunianDevil
860
views
MancunianDevil
asked
Apr 19, 2017
Calculus
calculus
imits
continuity
differentiation
+
–
3
votes
0
answers
28
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
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 ...
firki lama
707
views
firki lama
asked
Mar 1, 2017
Calculus
differentiation
continuity
calculus
+
–
0
votes
1
answer
29
Test Series
https://gateoverflow.in/?qa=blob&qa_blobid=4549376166631720003
https://gateoverflow.in/?qa=blob&qa_blobid=4549376166631720003
Shreya Roy
556
views
Shreya Roy
asked
Jan 14, 2017
Calculus
continuity
+
–
1
votes
1
answer
30
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
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
2.3k
views
srestha
asked
Dec 28, 2016
Set Theory & Algebra
calculus
continuity
+
–
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