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Recent questions tagged continuity
+2
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1
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1
GATE 2018 Maths  11(Electrical Engineering)
asked
Feb 21
in
Calculus
by
Lakshman Patel RJIT
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7.7k
points)

139
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gate2018
engineeringmathematics
calculus
continuity
differentiability
+5
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1
answer
2
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
in
Calculus
by
Mk Utkarsh
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12.6k
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126
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calculus
continuity
+2
votes
0
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3
Continuity and Differentiability of root mod function
asked
Dec 31, 2017
in
Calculus
by
Shubhanshu
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15k
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146
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limits
continuity
function
calculus
0
votes
0
answers
4
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
(
17
points)

201
views
calculus
#limits
limits
continuity
differentiability
+2
votes
0
answers
5
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
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873
points)

173
views
differentiability
continuity
calculus
+1
vote
1
answer
6
Maths: Limits Que03
given answer is (B) why continuous and differential on 0 ONLY?
asked
Jan 28, 2017
in
Calculus
by
Vijay Thakur
Boss
(
17.1k
points)

245
views
engineeringmathematics
calculus
differentiability
continuity
0
votes
1
answer
7
Test Series
https://gateoverflow.in/?qa=blob&qa_blobid=4549376166631720003
asked
Jan 14, 2017
in
Calculus
by
Shreya Roy
Active
(
4.3k
points)

127
views
continuity
+1
vote
1
answer
8
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
(
86.9k
points)

250
views
calculus
continuity
+2
votes
1
answer
9
Maths: Continuity and Differntiability
The function f(x) = 1/(1+x) is____ (A) Differntiable and Continuous (B) Not Differntiable and Not Continuous (C) Continuous but not Differntiable I know this is continuous everywhere because X will always be a positive value, how to check if it's differntiable or not?
asked
Dec 26, 2016
in
Calculus
by
Vijay Thakur
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(
17.1k
points)

859
views
calculus
engineeringmathematics
continuity
0
votes
1
answer
10
Maths: Differentiability
The function y=23x is not differential at x=2/3, please prove it.
asked
Dec 26, 2016
in
Calculus
by
Vijay Thakur
Boss
(
17.1k
points)

387
views
calculus
engineeringmathematics
continuity
+1
vote
1
answer
11
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
(
38.7k
points)

251
views
calculus
engineeringmathematics
continuity
+9
votes
3
answers
12
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
(
53
points)

694
views
calculus
gate2010me
engineeringmathematics
continuity
+3
votes
1
answer
13
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
(
40k
points)

157
views
tifrmaths2015
calculus
continuity
+2
votes
1
answer
14
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 $f ∘ g$ ... and $f ∘ g$ 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
(
40k
points)

99
views
tifrmaths2015
functions
continuity
+3
votes
1
answer
15
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
(
40k
points)

135
views
tifrmaths2015
continuity
differentiability
+1
vote
0
answers
16
TIFR2014MathsA6
Let $f:\left[0, 1\right]\rightarrow \mathbb{R}$ be a continuous function. Which of the following statements is always true? $\int_{0}^{1} f^{2}(x) \text{d}x = (\int_{0}^{1} f(x) \text{d}x)^{2}$ $\int_{0}^{1} f^{2}(x) \text{d}x \leq (\int_{0}^{1} f(x) \text{d}x)^{2}$ ... ^{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
(
40k
points)

76
views
tifrmaths2014
continuity
+1
vote
0
answers
17
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 $x = 0$ $f$ is continuous on $[0, \ ... )$ $f$ 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
(
40k
points)

73
views
tifrmaths2014
continuity
+1
vote
0
answers
18
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
(
40k
points)

56
views
tifrmaths2014
continuity
+1
vote
0
answers
19
TIFR2011MathsB4
A bounded continuous function on $\mathbb{R}$ is uniformly continuous.
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
40k
points)

63
views
tifrmaths2011
calculus
continuity
+3
votes
1
answer
20
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
(
40k
points)

105
views
tifrmaths2011
calculus
continuity
+1
vote
0
answers
21
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
(
40k
points)

65
views
tifrmaths2011
continuity
+1
vote
1
answer
22
TIFR2011MathsA14
$\log x$ is uniformly continuous on $( \frac{1}{2}, \infty)$.
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
40k
points)

108
views
tifrmaths2011
continuity
+4
votes
3
answers
23
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
(
40k
points)

324
views
tifrmaths2010
calculus
differentiability
continuity
+16
votes
6
answers
24
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
(
98.5k
points)

3k
views
gate20152
continuity
functions
normal
+8
votes
2
answers
25
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
(
59.4k
points)

778
views
gate1996
calculus
continuity
differentiability
normal
descriptive
+30
votes
6
answers
26
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
(
98.5k
points)

3.5k
views
gate20141
calculus
continuity
normal
+4
votes
4
answers
27
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
(
59.4k
points)

591
views
gate1998
calculus
continuity
differentiability
easy
+6
votes
3
answers
28
GATE201322
Which one of the following functions is continuous at $x = 3?$ $f(x) = \begin{cases} 2,&\text{if $x = 3$ } \\ x1& \text{if $x > 3$}\\ \frac{x+3}{3}&\text{if $x < 3$ } \end{cases}$ $f(x) = \begin{cases} 4,&\text{if $x = 3$ } \\ 8x& \ ... \\ x4& \text{if $x > 3$} \end{cases}$ $f(x) = \begin{cases} \frac{1}{x^327}&\text{if $x \neq 3$ } \end{cases}$
asked
Sep 24, 2014
in
Calculus
by
Arjun
Veteran
(
349k
points)

1.2k
views
gate2013
calculus
continuity
normal
+5
votes
2
answers
29
GATE20071
Consider the following two statements about the function $f(x)=\left\vert x\right\vert$: P. $f(x)$ is continuous for all real values of $x$. Q. $f(x)$ is differentiable for all real values of $x$ . Which of the following is TRUE? $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are true. Both $P$ and $Q$ are false.
asked
Sep 22, 2014
in
Calculus
by
Kathleen
Veteran
(
59.4k
points)

1k
views
gate2007
calculus
continuity
differentiability
easy
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