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Recent questions tagged continuity
0
votes
1
answer
1
ISI2018MMA28
Consider the following functions $f(x)=\left\{\begin{matrix} 1 &, if\ x \leq 1 \\ 0 & ,if\ x>1 \end{matrix}\right.$ ... at $ 1$ $h_2$ is continuous everywhere and $h_1$ has discontinuity at $ 2$ $h_1$ has discontinuity at $ 2$ and $h_2$ has discontinuity at $ 1$.
asked
May 11
in
Calculus
by
akash.dinkar12
Boss
(
41.4k
points)

53
views
isi2018
engineeringmathematics
calculus
continuity
0
votes
0
answers
2
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
(
99.6k
points)

49
views
isi2017
engineeringmathematics
calculus
continuity
0
votes
1
answer
3
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
(
2.4k
points)

111
views
nielitjuly2017
continuity
differentiability
0
votes
1
answer
4
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
(
25.9k
points)

127
views
engineeringmathematics
calculus
continuity
0
votes
0
answers
5
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
(
119
points)

66
views
calculus
differentiability
continuity
engineeringmathematics
+2
votes
1
answer
6
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
Boss
(
46.5k
points)

387
views
gate2018ee
engineeringmathematics
calculus
continuity
differentiability
+5
votes
1
answer
7
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
(
34.9k
points)

177
views
calculus
continuity
+1
vote
1
answer
8
MadeEasy Test Series: Calculus  Differentiability
At the point x = 1, the function
asked
Jan 6, 2018
in
Calculus
by
Kuldeep Pal
Active
(
1.4k
points)

56
views
madeeasytestseries
calculus
differentiability
continuity
+2
votes
0
answers
9
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
(
18.1k
points)

287
views
limits
continuity
function
calculus
0
votes
0
answers
10
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)

255
views
calculus
imits
continuity
differentiability
+3
votes
1
answer
11
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
(
661
points)

224
views
differentiability
continuity
calculus
0
votes
1
answer
12
Test Series
https://gateoverflow.in/?qa=blob&qa_blobid=4549376166631720003
asked
Jan 14, 2017
in
Calculus
by
Shreya Roy
Active
(
4.4k
points)

146
views
continuity
+1
vote
1
answer
13
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
(
114k
points)

365
views
calculus
continuity
+2
votes
1
answer
14
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
(
38.3k
points)

304
views
calculus
engineeringmathematics
continuity
+11
votes
3
answers
15
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)

1k
views
calculus
gate2010me
engineeringmathematics
continuity
+3
votes
1
answer
16
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
(
29.6k
points)

198
views
tifrmaths2015
calculus
continuity
+2
votes
1
answer
17
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
(
29.6k
points)

125
views
tifrmaths2015
functions
continuity
+3
votes
1
answer
18
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
(
29.6k
points)

191
views
tifrmaths2015
continuity
differentiability
+1
vote
0
answers
19
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
(
29.6k
points)

112
views
tifrmaths2014
continuity
+1
vote
0
answers
20
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
(
29.6k
points)

86
views
tifrmaths2014
continuity
+1
vote
0
answers
21
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
(
29.6k
points)

77
views
tifrmaths2014
continuity
+1
vote
0
answers
22
TIFR2011MathsB4
A bounded continuous function on $\mathbb{R}$ is uniformly continuous.
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
29.6k
points)

87
views
tifrmaths2011
calculus
continuity
+3
votes
1
answer
23
TIFR2011MathsA25
The function $f(x) = \begin{cases} 0 & \text{if x is rational} \\ x& \text{if x is irrational} \end{cases}$ is not continuous anywhere on the real line.
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
29.6k
points)

139
views
tifrmaths2011
calculus
continuity
+1
vote
0
answers
24
TIFR2011MathsA21
Any continuous function from the open unit interval $(0, 1)$ to itself has a fixed point.
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
29.6k
points)

100
views
tifrmaths2011
continuity
+1
vote
1
answer
25
TIFR2011MathsA14
$\log x$ is uniformly continuous on $( \frac{1}{2}, \infty)$.
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
29.6k
points)

213
views
tifrmaths2011
continuity
+4
votes
3
answers
26
TIFR2010MathsA8
Let $f(x)= x^{3/2}, x \in \mathbb{R}$. Then $f$ is uniformly continuous. $f$ is continuous, but not differentiable at $x=0$. $f$ is differentiable and $f ' $ is continuous. $f$ is differentiable, but $f ' $ is discontinuous at $x=0$.
asked
Oct 11, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
29.6k
points)

410
views
tifrmaths2010
calculus
differentiability
continuity
+24
votes
7
answers
27
GATE2015226
Let $f(x)=x^{\left(\frac{1}{3}\right)}$ and $A$ denote the area of region bounded by $f(x)$ and the Xaxis, when $x$ varies from $1$ to $1$. Which of the following statements is/are TRUE? $f$ is continuous in $[1, 1]$ $f$ is not bounded in $[1, 1]$ $A$ is nonzero and finite II only III only II and III only I, II and III
asked
Feb 12, 2015
in
Calculus
by
jothee
Veteran
(
99.6k
points)

4.5k
views
gate20152
continuity
functions
normal
+13
votes
2
answers
28
GATE19963
Let $f$ be a function defined by $f(x) = \begin{cases} x^2 &\text{ for }x \leq 1\\ ax^2+bx+c &\text{ for } 1 < x \leq 2 \\ x+d &\text{ for } x>2 \end{cases}$ Find the values for the constants $a$, $b$, $c$ and $d$ so that $f$ is continuous and differentiable everywhere on the real line.
asked
Oct 9, 2014
in
Calculus
by
Kathleen
Veteran
(
52.1k
points)

1.2k
views
gate1996
calculus
continuity
differentiability
normal
descriptive
+39
votes
6
answers
29
GATE2014147
A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = 1$ and $f(1) = 1$. Which one of the following statements must be true? There exists a $y$ in the interval $(0,1)$ such that $f(y) = f(y+1)$ For every $y$ in the interval ... of the function in the interval $(0,2)$ is $1$ There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $f(2y)$
asked
Sep 28, 2014
in
Calculus
by
jothee
Veteran
(
99.6k
points)

5.4k
views
gate20141
calculus
continuity
normal
+5
votes
4
answers
30
GATE19981.4
Consider the function $y=x$ in the interval $[1, 1]$. In this interval, the function is continuous and differentiable continuous but not differentiable differentiable but not continuous neither continuous nor differentiable
asked
Sep 26, 2014
in
Calculus
by
Kathleen
Veteran
(
52.1k
points)

983
views
gate1998
calculus
continuity
differentiability
easy
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