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Recent questions tagged differentiability
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1
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
in
Calculus
by
Arjun
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425k
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9
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isi2015mma
calculus
continuity
differentiability
definiteintegration
nongate
0
votes
0
answers
2
ISI2015MMA72
The map $f(x) = a_0 \cos \mid x \mid +a_1 \sin \mid x \mid +a_2 \mid x \mid ^3$ is differentiable at $x=0$ if and only if $a_1=0$ and $a_2=0$ $a_0=0$ and $a_1=0$ $a_1=0$ $a_0, a_1, a_2$ can take any real value
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
425k
points)

5
views
isi2015mma
calculus
differentiability
trigonometry
0
votes
0
answers
3
ISI2015MMA73
$f(x)$ is a differentiable function on the real line such that $\underset{x \to \infty=}{\lim} f(x) =1$ and $\underset{x \to \infty=}{\lim} f’(x) =\alpha$. Then $\alpha$ must be $0$ $\alpha$ need not be $0$, but $\mid \alpha \mid <1$ $\alpha >1$ $\alpha < 1$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
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425k
points)

7
views
isi2015mma
calculus
limits
differentiability
0
votes
0
answers
4
ISI2015MMA74
Let $f$ and $g$ be two differentiable functions such that $f’(x)\leq g’(x)$for all $x<1$ and $f’(x) \geq g’(x)$ for all $x>1$. Then if $f(1) \geq g(1)$, then $f(x) \geq g(x)$ for all $x$ if $f(1) \leq g(1)$, then $f(x) \leq g(x)$ for all $x$ $f(1) \leq g(1)$ $f(1) \geq g(1)$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
425k
points)

5
views
isi2015mma
calculus
differentiability
0
votes
0
answers
5
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
in
Calculus
by
gatecse
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16.8k
points)

5
views
isi2016dcg
calculus
continuity
differentiability
functions
0
votes
1
answer
6
ISI2018DCG24
Let $[x]$ denote the largest integer less than or equal to $x.$ The number of points in the open interval $(1,3)$ in which the function $f(x)=a^{[x^2]},a\gt1$ is not differentiable, is $0$ $3$ $5$ $7$
asked
Sep 18
in
Calculus
by
gatecse
Boss
(
16.8k
points)

8
views
isi2018dcg
calculus
differentiability
0
votes
0
answers
7
ISI2018DCG29
Let $f(x)=(x1)(x2)(x3)g(x); \: x\in \mathbb{R}$ where $g$ is twice differentiable function. Then there exists $y\in(1,3)$ such that $f’’(y)=0.$ there exists $y\in(1,2)$ such that $f’’(y)=0.$ there exists $y\in(2,3)$ such that $f’’(y)=0.$ none of the above is true.
asked
Sep 18
in
Calculus
by
gatecse
Boss
(
16.8k
points)

9
views
isi2018dcg
calculus
differentiability
0
votes
1
answer
8
Gate 2002  ME
Which of the following functions is not differentiable in the domain $[1,1]$ ? (a) $f(x) = x^2$ (b) $f(x) = x1$ (c) $f(x) = 2$ (d) $f(x) = Maximum (x,x)$
asked
May 4
in
Calculus
by
balchandar reddy san
Active
(
3.2k
points)

79
views
engineeringmathematics
usergate2002
usermod
calculus
differentiability
0
votes
0
answers
9
Testbook Test Series: Calculus  Differentiability
If $y = f(x)$ is a solution of $ d^2y/dx^2 = 0$ , with boundary conditions $y=8$ at $x=0$ and $dy/dx =4$ at $x=16$, Find the value of $f(2)$ When they say, $y = f(x)$ is a solution of $ d^2y/dx^2 = 0$ What does that mean?
asked
Dec 18, 2018
in
Mathematical Logic
by
shreyansh jain
Active
(
2.2k
points)

65
views
testbooktestseries
differentiability
calculus
0
votes
0
answers
10
ISI2017MMA13
An even function $f(x)$ has left derivative $5$ at $x=0$. Then the right derivative of $f(x)$ at $x=0$ need not exist the right derivative of $f(x)$ at $x=0$ exists and is equal to $5$ the right derivative of $f(x)$ at $x=0$ exists and equal to $5$ none of the above is necessarily true
asked
Sep 15, 2018
in
Numerical Ability
by
jothee
Veteran
(
105k
points)

16
views
isi2017mma
engineeringmathematics
calculus
differentiability
+2
votes
1
answer
11
ISI2016MMA8
Let $g: \mathbb{R} \rightarrow \mathbb{R}$ be differentiable with $g'(x^2)=x^3$ for all $x>0$ and $g(1) =1$. Then $g(4)$ equals $64/5$ $32/5$ $37/5$ $67/5$
asked
Sep 13, 2018
in
Calculus
by
jothee
Veteran
(
105k
points)

35
views
isi2016mmamma
calculus
differentiability
0
votes
0
answers
12
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)

7
views
isi2016mmamma
calculus
continuity
differentiability
limits
+2
votes
1
answer
13
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)

13
views
isi2016mmamma
calculus
continuity
differentiability
0
votes
1
answer
14
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
(
2.5k
points)

115
views
nielitjuly2017
continuity
differentiability
0
votes
0
answers
15
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)

66
views
calculus
differentiability
continuity
engineeringmathematics
+2
votes
3
answers
16
ISI2017MMA13
An even function $f(x)$ has left derivative $5$ at $x=0$. Then the right derivative of $f(x)$ at $x=0$ need not exist the right derivative of $f(x)$ at $x=0$ exists and is equal to $5$ the right derivative of $f(x)$ at $x=0$ exists and is equal to $5$ none of the above is necessarily true
asked
Mar 27, 2018
in
Calculus
by
jjayantamahata
Active
(
1.5k
points)

303
views
isi2017mma
engineeringmathematics
calculus
differentiability
+2
votes
1
answer
17
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
(
54.8k
points)

413
views
gate2018ee
engineeringmathematics
calculus
continuity
differentiability
+1
vote
1
answer
18
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)

60
views
madeeasytestseries
calculus
differentiability
continuity
+1
vote
1
answer
19
TIFR2018A5
Which of the following id the derivative of $f(x)=x^{x}$ when $x>0$ ? $x^{x}$ $x^{x} \ln \;x$ $x^{x}+x^{x}\ln\;x$ $(x^{x}) (x^{x}\ln\;x)$ $\text{None of the above;function is not differentiable for }x>0$
asked
Dec 10, 2017
in
Calculus
by
Arjun
Veteran
(
425k
points)

213
views
tifr2018
calculus
differentiability
0
votes
0
answers
20
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)

257
views
calculus
imits
continuity
differentiability
+3
votes
1
answer
21
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)

227
views
differentiability
continuity
calculus
+13
votes
2
answers
22
GATE2017210
If $f(x) = R \: \sin ( \frac{\pi x}{2}) + S, f’\left(\frac{1}{2}\right) = \sqrt{2}$ and $\int_0^1 f(x) dx = \frac{2R}{\pi}$, then the constants $R$ and $S$ are $\frac{2}{\pi}$ and $\frac{16}{\pi}$ $\frac{2}{\pi}$ and 0 $\frac{4}{\pi}$ and 0 $\frac{4}{\pi}$ and $\frac{16}{\pi}$
asked
Feb 14, 2017
in
Calculus
by
Madhav
Active
(
1.6k
points)

2.4k
views
gate20172
engineeringmathematics
calculus
differentiability
0
votes
1
answer
23
Diffrentiability+Limits
how to solve diffrentiability with standard procedure of f(a+h).
asked
Dec 9, 2016
in
Calculus
by
Rahul Jain25
Boss
(
11.1k
points)

247
views
calculus
engineeringmathematics
differentiability
+17
votes
5
answers
24
GATE2016202
Let $f(x)$ be a polynomial and $g(x)=f'(x)$ be its derivative. If the degree of $(f(x)+f(x))$ is $10$, then the degree of $(g(x)  g(x))$ is __________.
asked
Feb 12, 2016
in
Calculus
by
Akash Kanase
Boss
(
41.5k
points)

3.2k
views
gate20162
calculus
normal
numericalanswers
differentiability
+2
votes
1
answer
25
MadeEasy Test Series: Calculus  Differentiability
Q.64 A function f (x) is differentiated twice such that its differential equation λ2f (x) – 2λf ′(x) + f ′′(x) = 0 provides two equal value of λ for all x. It f (0) = 1, f′(0) = 2, then f(x) at x = 1 will be _________. Given ans > 7.39 (7.00  7.80)
asked
Dec 19, 2015
in
Calculus
by
Akash Kanase
Boss
(
41.5k
points)

155
views
madeeasytestseries
calculus
differentiability
+3
votes
1
answer
26
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
(
30.2k
points)

194
views
tifrmaths2015
continuity
differentiability
+2
votes
1
answer
27
TIFR2014MathsA3
Let $f: \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $\displaystyle \lim_{x \to +\infty} f'(x)=1$, then $f$ is bounded $f$ is increasing $f$ is unbounded $f'$ is bounded.
asked
Dec 10, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
30.2k
points)

171
views
tifrmaths2014
differentiability
+1
vote
1
answer
28
TIFR2011MathsA19
The derivative of the function $\int_{0}^{\sqrt{x}} e^{t^{2}}dt$ at $x = 1$ is $e^{1}$ .
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
30.2k
points)

151
views
tifrmaths2011
calculus
differentiability
+1
vote
1
answer
29
TIFR2011MathsA9
The function $f(x)$ defined by $f(x) = \begin{cases} ax+b & \text{x ≥ 1 } \\ x^{2}+3x+3& \text{x ≤ 1} \end{cases}$ is differentiable For a unique value of a and infinitely many values of $b$. For a unique value of $b$ and infinitely many values of $a$. For infinitely many values of $a$ and $b$. None of the above.
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
30.2k
points)

142
views
tifrmaths2011
differentiability
+2
votes
1
answer
30
TIFR2011MathsA5
The differential equation $\frac{dy}{dx}= y^{1/3}, y(0)=0$ has A unique solution No nontrivial solution Finite number of solutions. Infinite number of solutions.
asked
Dec 9, 2015
in
Calculus
by
makhdoom ghaya
Boss
(
30.2k
points)

128
views
tifrmaths2011
differentiability
nongate
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