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Recent questions tagged differentiation
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ISI2014DCG13
Let the function $f(x)$ be defined as $f(x)=\mid x1 \mid + \mid x2 \:\mid$. Then which of the following statements is true? $f(x)$ is differentiable at $x=1$ $f(x)$ is differentiable at $x=2$ $f(x)$ is differentiable at $x=1$ but not at $x=2$ none of the above
asked
Sep 23, 2019
in
Calculus
by
Arjun
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431k
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61
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isi2014dcg
calculus
differentiation
0
votes
1
answer
2
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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431k
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42
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isi2014dcg
calculus
continuity
differentiation
0
votes
1
answer
3
ISI2014DCG49
Let $f(x) = \dfrac{x}{(x1)(2x+3)}$, where $x>1$. Then the $4^{th}$ derivative of $f, \: f^{(4)} (x)$ is equal to $ \frac{24}{5} \bigg[ \frac{1}{(x1)^5}  \frac{48}{(2x+3)^5} \bigg]$ ... $\frac{64}{5} \bigg[ \frac{1}{(x1)^5} + \frac{48}{(2x+3)^5} \bigg]$
asked
Sep 23, 2019
in
Others
by
Arjun
Veteran
(
431k
points)

42
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isi2014dcg
calculus
differentiation
functions
0
votes
0
answers
4
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
(
431k
points)

21
views
isi2015mma
calculus
continuity
differentiation
definiteintegrals
nongate
0
votes
0
answers
5
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, 2019
in
Calculus
by
Arjun
Veteran
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431k
points)

13
views
isi2015mma
calculus
differentiation
0
votes
0
answers
6
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, 2019
in
Calculus
by
Arjun
Veteran
(
431k
points)

16
views
isi2015mma
calculus
limits
differentiation
0
votes
0
answers
7
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, 2019
in
Calculus
by
Arjun
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431k
points)

12
views
isi2015mma
calculus
differentiation
0
votes
0
answers
8
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
Boss
(
17.5k
points)

14
views
isi2015dcg
calculus
continuity
differentiation
0
votes
0
answers
9
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
(
17.5k
points)

15
views
isi2016dcg
calculus
continuity
differentiation
functions
0
votes
2
answers
10
ISI2017DCG30
If $f(x)=e^{5x}$ and $h(x)=f’’(x)+2f’(x)+f(x)+2$ then $h(0)$ equals $38$ $8$ $4$ $0$
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

20
views
isi2017dcg
calculus
differentiation
functions
+1
vote
1
answer
11
ISI2018DCG9
Let $f(x)=1+x+\dfrac{x^2}{2}+\dfrac{x^3}{3}...+\dfrac{x^{2018}}{2018}.$ Then $f’(1)$ is equal to $0$ $2017$ $2018$ $2019$
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

53
views
isi2018dcg
calculus
functions
differentiation
0
votes
1
answer
12
ISI2018DCG10
Let $f’(x)=4x^33x^2+2x+k,$ $f(0)=1$ and $f(1)=4.$ Then $f(x)$ is equal to $4x^43x^3+2x^2+x+1$ $x^4x^3+x^2+2x+1$ $x^4x^3+x^2+2(x+1)$ none of these
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

22
views
isi2018dcg
calculus
differentiation
polynomials
0
votes
1
answer
13
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, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

15
views
isi2018dcg
calculus
differentiation
0
votes
0
answers
14
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, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

17
views
isi2018dcg
calculus
differentiation
0
votes
1
answer
15
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, 2019
in
Calculus
by
balchandar reddy san
Active
(
3.3k
points)

95
views
engineeringmathematics
usergate2002
usermod
calculus
differentiation
0
votes
0
answers
16
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)

69
views
testbooktestseries
differentiation
calculus
0
votes
0
answers
17
ISI2017PCBA4
Let $\lceil x \rfloor$ denote the integer nearest to $x$. For example, $\lceil 1.1 \rfloor =1, \lceil 1.5 \rfloor =1$ and $\lceil 1.6 \rfloor$ =2. Draw the graph of the function $y= \mid x  \lceil x \rfloor \mid$ for $0 \leq x \leq 4$. Find all the points $x, \: 0 \leq x \leq 4$, where the function is not differentiable. Justify your answer.
asked
Sep 19, 2018
in
Calculus
by
jothee
Veteran
(
105k
points)

19
views
isi2017pcba
differentiation
0
votes
0
answers
18
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)

17
views
isi2017mma
engineeringmathematics
calculus
differentiation
+2
votes
1
answer
19
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)

50
views
isi2016mmamma
calculus
differentiation
0
votes
0
answers
20
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)

15
views
isi2016mmamma
calculus
continuity
differentiation
limits
+1
vote
0
answers
21
ISI2016MMA26
Let $x$ and $y$ be real numbers satisfying $9x^2+16y^2=1$. Then $(x+y)$ is maximum when $y=9x/16$ $y=9x/16$ $y=4x/3$ $y=4x/3$
asked
Sep 13, 2018
in
Others
by
jothee
Veteran
(
105k
points)

13
views
isi2016mma
differentiation
nongate
+2
votes
1
answer
22
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)

23
views
isi2016mmamma
calculus
continuity
differentiation
0
votes
1
answer
23
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)

121
views
nielitjuly2017
continuity
differentiation
0
votes
0
answers
24
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)

78
views
calculus
differentiation
continuity
engineeringmathematics
+2
votes
3
answers
25
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)

343
views
isi2017mma
engineeringmathematics
calculus
differentiation
+2
votes
1
answer
26
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
(
59.3k
points)

456
views
gate2018ee
engineeringmathematics
calculus
continuity
differentiation
+1
vote
1
answer
27
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)

70
views
madeeasytestseries
calculus
differentiation
continuity
+3
votes
1
answer
28
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
(
431k
points)

265
views
tifr2018
calculus
differentiation
0
votes
0
answers
29
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)

261
views
calculus
imits
continuity
differentiation
+3
votes
1
answer
30
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)

234
views
differentiation
continuity
calculus
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