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Recent questions tagged continuity
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1
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1
ISI2014DCG29
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
asked
Sep 23, 2019
in
Calculus
by
Arjun
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430k
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36
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isi2014dcg
calculus
continuity
differentiation
+1
vote
1
answer
2
ISI2014DCG37
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 $f(x)$? $\cos x$ $\tan x$ $\tan^{1} x$ $\sin x$
asked
Sep 23, 2019
in
Calculus
by
Arjun
Veteran
(
430k
points)

25
views
isi2014dcg
calculus
functions
limits
continuity
0
votes
0
answers
3
ISI2015MMA69
Consider the function $f(x) = \begin{cases} \int_0^x \{5+ \mid 1y \mid \} dy & \text{ if } x>2 \\ 5x+2 & \text{ if } x \leq 2 \end{cases}$ 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 $x=2$
asked
Sep 23, 2019
in
Calculus
by
Arjun
Veteran
(
430k
points)

18
views
isi2015mma
calculus
continuity
differentiation
definiteintegrals
nongate
0
votes
0
answers
4
ISI2015MMA71
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
asked
Sep 23, 2019
in
Others
by
Arjun
Veteran
(
430k
points)

9
views
isi2015mma
continuity
partialderivatives
nongate
0
votes
0
answers
5
ISI2015DCG57
Let $y=\lfloor x \rfloor$, where $\lfloor x \rfloor$ is greatest integer less than or equal to $x$. Then $y$ is continuous and manyone $y$ is not differentiable and manyone $y$ is not differentiable $y$ is differentiable and manyone
asked
Sep 18, 2019
in
Calculus
by
gatecse
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(
17.4k
points)

11
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isi2015dcg
calculus
continuity
differentiation
0
votes
0
answers
6
ISI2016DCG58
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 manyone. $y$ is not differentiable and manyone. $y$ is not differentiable. $y$ is differentiable and manyone.
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.4k
points)

11
views
isi2016dcg
calculus
continuity
differentiation
functions
0
votes
1
answer
7
ISI2018MMA28
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 $\pm1$.
asked
May 11, 2019
in
Calculus
by
akash.dinkar12
Boss
(
42.3k
points)

75
views
isi2018mma
engineeringmathematics
calculus
continuity
0
votes
0
answers
8
ISI2016PCBA2
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.
asked
Sep 18, 2018
in
Calculus
by
jothee
Veteran
(
105k
points)

20
views
isi2016pcba
calculus
continuity
nongate
descriptive
0
votes
0
answers
9
ISI2017MMA4
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 $[2,3]$ $(2,3]$ $[3,2] \cup [2,3]$ $(\infty,\infty)$
asked
Sep 15, 2018
in
Calculus
by
jothee
Veteran
(
105k
points)

61
views
isi2017mma
engineeringmathematics
calculus
continuity
0
votes
0
answers
10
ISI2016MMA24
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 $x$
asked
Sep 13, 2018
in
Calculus
by
jothee
Veteran
(
105k
points)

12
views
isi2016mmamma
calculus
continuity
differentiation
limits
+2
votes
1
answer
11
ISI2016MMA27
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
asked
Sep 13, 2018
in
Calculus
by
jothee
Veteran
(
105k
points)

19
views
isi2016mmamma
calculus
continuity
differentiation
0
votes
1
answer
12
NIELIT2017 STAsetc119
The function $f(x)=\frac{x^2 1}{x1}$ at $x=1$ is: (A) Continuous and Differentiable (B) Continuous but not Differentiable (C) Differentiable but not Continuous (D) Neither Continuous nor Differentiable
asked
Aug 31, 2018
in
Graph Theory
by
habedo007
Active
(
2.8k
points)

120
views
nielitjuly2017
continuity
differentiation
0
votes
1
answer
13
CalculusSelf Doubt
Is the function $f(x)=\frac{1}{x^{\frac{1}{3}}}$ continous in the interval [1 0) ?
asked
Jul 17, 2018
in
Calculus
by
Ayush Upadhyaya
Boss
(
29k
points)

132
views
engineeringmathematics
calculus
continuity
0
votes
0
answers
14
Differentiable
Why is a function not differentiable at x=k when f'(x) limits to infinity? Limit can be infinite too?
asked
Jun 25, 2018
in
Mathematical Logic
by
bts
(
129
points)

73
views
calculus
differentiation
continuity
engineeringmathematics
+2
votes
1
answer
15
Mathematics GATE 2018 EE: 11
Let $f$ be a realvalued 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} $
asked
Feb 21, 2018
in
Calculus
by
Lakshman Patel RJIT
Veteran
(
58.5k
points)

447
views
gate2018ee
engineeringmathematics
calculus
continuity
differentiation
+5
votes
1
answer
16
Continuity
If the function f(x) defined by $\left\{\begin{matrix} \frac{log(1+ ax)  log(1bx)}{x} &, if x \neq 0\\ k & ,if x = 0 \end{matrix}\right.$ is continuous at x = 0, then value of k is A) b  a B) a  b C) a + b D) a  b
asked
Jan 15, 2018
in
Calculus
by
Mk Utkarsh
Boss
(
36.4k
points)

190
views
calculus
continuity
+1
vote
1
answer
17
MadeEasy Test Series: Calculus  Differentiability
At the point x = 1, the function
asked
Jan 6, 2018
in
Calculus
by
Kuldeep Pal
Active
(
1.5k
points)

67
views
madeeasytestseries
calculus
differentiation
continuity
+2
votes
0
answers
18
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) = $x1^{3/2}$ Check for Differentiability and Continuity. I am getting Cont and Differentiable both. 3) Find the value of $f(x) = \int_{2}^{2}1x^4dx$. I am getting 8/5, but answer is 12.
asked
Dec 31, 2017
in
Calculus
by
Shubhanshu
Boss
(
18.3k
points)

299
views
limits
continuity
function
calculus
0
votes
0
answers
19
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.
asked
Apr 19, 2017
in
Calculus
by
MancunianDevil
(
15
points)

260
views
calculus
imits
continuity
differentiation
+3
votes
1
answer
20
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
asked
Mar 1, 2017
in
Calculus
by
firki lama
Junior
(
681
points)

231
views
differentiation
continuity
calculus
0
votes
1
answer
21
Test Series
https://gateoverflow.in/?qa=blob&qa_blobid=4549376166631720003
asked
Jan 14, 2017
in
Calculus
by
Shreya Roy
Active
(
4.5k
points)

148
views
continuity
+1
vote
1
answer
22
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
asked
Dec 29, 2016
in
Set Theory & Algebra
by
srestha
Veteran
(
118k
points)

389
views
calculus
continuity
+2
votes
1
answer
23
Continuity
What should be the value of a,b and c such that the function defined below is continuous at x=0 ? $f\left ( x \right )=\begin{Bmatrix} \left ( 1+ax \right )^{\frac{1}{x}} & x<0 & \\ b & x=0& \\ \frac{(x+c)^{\frac{1}{3}}1}{x} &x>0 & \end{Bmatrix}$
asked
Dec 20, 2016
in
Calculus
by
ManojK
Boss
(
38.6k
points)

317
views
calculus
engineeringmathematics
continuity
+12
votes
3
answers
24
GATE2010ME
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 $∀ x ∈ R$
asked
Mar 20, 2016
in
Calculus
by
Anuraag Nayak
(
47
points)

1.2k
views
calculus
gate2010me
engineeringmathematics
continuity
+3
votes
1
answer
25
TIFR2015MathsA8
Let $f(x)=\frac{e^{\frac{1}{x}}}{x}$, where $x \in (0, 1)$. Then on $(0, 1)$. $f$ is uniformly continuous. $f$ is continuous but not uniformly continuous. $f$ is unbounded. $f$ is not continuous.
asked
Dec 19, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
30.6k
points)

205
views
tifrmaths2015
calculus
continuity
+2
votes
1
answer
26
TIFR2015MathsA7
Let $f$ and $g$ be two functions from $[0, 1]$ to $[0, 1]$ with $f$ strictly increasing. Which of the following statements is always correct? If $g$ is continuous, then $f ∘ g$ is continuous. If $f$ is continuous, then $f ∘ g$ is ... $f ∘ g$ are continuous, then $g$ is continuous. If $g$ and $f ∘ g$ are continuous, then $f$ is continuous.
asked
Dec 19, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.6k
points)

130
views
tifrmaths2015
functions
continuity
+3
votes
1
answer
27
TIFR2015MathsA5
Let $f : \mathbb{R} \rightarrow \mathbb{R}$ denote the function defined by $f(x)= (1x^{2})^{\frac{3}{2}}$ 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.
asked
Dec 19, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
30.6k
points)

198
views
tifrmaths2015
continuity
differentiation
+1
vote
0
answers
28
TIFR2014MathsA6
Let $f:\left[0, 1\right]\rightarrow \mathbb{R}$ be a continuous function. Which of the following statements is always true? $\int_{0}^{1} f^{2}(x) \text{d}x = (\int_{0}^{1} f(x) \text{d}x)^{2}$ $\int_{0}^{1} f^{2}(x) \text{d}x \leq (\int_{0}^{1} f(x) \text{d}x)^{2}$ ... $\int_{0}^{1} f^{2}(x) \text{d}x ≰ (\int_{0}^{1} f(x) \text{d}x)^{2}$
asked
Dec 14, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
30.6k
points)

116
views
tifrmaths2014
continuity
+1
vote
0
answers
29
TIFR2014MathsA4
Let $f$ be the real valued function on $[0, \infty)$ defined by $f(x) = \begin{cases} x^{\frac{2}{3}}\log x& \text {for x > 0} \\ 0& \text{if x=0 } \end{cases}$ Then $f$ is discontinuous at $x = 0$ $f$ ... $f$ is uniformly continuous on $[0, \infty)$ $f$ is not uniformly continuous on $[0, \infty)$, but uniformly continuous on $(0, \infty)$.
asked
Dec 10, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
30.6k
points)

92
views
tifrmaths2014
continuity
+1
vote
0
answers
30
TIFR2014MathsA2
Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous bounded function, then: $f$ has to be uniformly continuous There exists an $x \in \mathbb{R}$ such that $f(x) = x$ $f$ cannot be increasing $\lim_{x \rightarrow \infty} f(x)$ exists.
asked
Dec 10, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.6k
points)

81
views
tifrmaths2014
continuity
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