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Recent questions tagged differentiation
+2
votes
1
answer
1
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 24, 2019
in
Calculus
by
Arjun

107
views
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 24, 2019
in
Calculus
by
Arjun

101
views
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 24, 2019
in
Others
by
Arjun

73
views
isi2014dcg
calculus
differentiation
functions
0
votes
1
answer
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 24, 2019
in
Calculus
by
Arjun

73
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 24, 2019
in
Calculus
by
Arjun

45
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 24, 2019
in
Calculus
by
Arjun

49
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 24, 2019
in
Calculus
by
Arjun

40
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 19, 2019
in
Calculus
by
gatecse

40
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 19, 2019
in
Calculus
by
gatecse

36
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 19, 2019
in
Calculus
by
gatecse

50
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 19, 2019
in
Calculus
by
gatecse

163
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 19, 2019
in
Calculus
by
gatecse

51
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 19, 2019
in
Calculus
by
gatecse

42
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 19, 2019
in
Calculus
by
gatecse

72
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

214
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

87
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

44
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

54
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

88
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

42
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

35
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

45
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

188
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

101
views
calculus
differentiation
continuity
engineeringmathematics
+3
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 28, 2018
in
Calculus
by
jjayantamahata

535
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 22, 2018
in
Calculus
by
Lakshman Patel RJIT

624
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

89
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

345
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 20, 2017
in
Calculus
by
MancunianDevil

301
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

259
views
differentiation
continuity
calculus
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