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Recent questions tagged differentiability
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GATE 2018 Maths  11(Electrical Engineering)
asked
Feb 21
in
Calculus
by
Lakshman Patel RJIT
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gate2018
engineeringmathematics
calculus
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differentiability
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2
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
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Calculus
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MancunianDevil
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17
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195
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calculus
#limits
limits
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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
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Mar 1, 2017
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Calculus
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firki lama
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873
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168
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differentiability
continuity
calculus
+10
votes
3
answers
4
GATE2017210
If $f(x) = R \: \sin ( \frac{\pi x}{2}) + S. f’(\frac{1}{2}) = \sqrt{2}$ 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 $\frac{16}{\pi}$
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Feb 14, 2017
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Calculus
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Madhav
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2k
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1.7k
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gate20172
engineeringmathematics
calculus
differentiability
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1
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5
Maths: Limits Que03
given answer is (B) why continuous and differential on 0 ONLY?
asked
Jan 28, 2017
in
Calculus
by
Vijay Thakur
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17k
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239
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engineeringmathematics
calculus
differentiability
continuity
0
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1
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6
Diffrentiability+Limits
how to solve diffrentiability with standard procedure of f(a+h).
asked
Dec 9, 2016
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Calculus
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Rahul Jain25
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11.5k
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185
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calculus
engineeringmathematics
differentiability
+14
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4
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7
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
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2.1k
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gate20162
calculus
normal
numericalanswers
differentiability
+3
votes
1
answer
8
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
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39.9k
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132
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tifrmaths2015
continuity
differentiability
+2
votes
1
answer
9
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
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39.9k
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128
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tifrmaths2014
differentiability
+1
vote
0
answers
10
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
(
39.9k
points)

89
views
tifrmaths2011
calculus
differentiability
+1
vote
1
answer
11
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
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(
39.9k
points)

99
views
tifrmaths2011
differentiability
+2
votes
1
answer
12
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
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39.9k
points)

87
views
tifrmaths2011
differentiability
nongate
+4
votes
3
answers
13
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
(
39.9k
points)

315
views
tifrmaths2010
calculus
differentiability
continuity
+8
votes
2
answers
14
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
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(
59.4k
points)

751
views
gate1996
calculus
continuity
differentiability
normal
+6
votes
1
answer
15
GATE19961.6
The formula used to compute an approximation for the second derivative of a function $f$ at a point $X_0$ is $\dfrac{f(x_0 +h) + f(x_0 – h)}{2}$ $\dfrac{f(x_0 +h)  f(x_0 – h)}{2h}$ $\dfrac{f(x_0 +h) + 2f(x_0) + f(x_0 – h)}{h^2}$ $\dfrac{f(x_0 +h)  2f(x_0) + f(x_0 – h)}{h^2}$
asked
Oct 9, 2014
in
Calculus
by
Kathleen
Veteran
(
59.4k
points)

668
views
gate1996
calculus
differentiability
normal
+6
votes
4
answers
16
GATE2014146
The function $f(x) =x \sin x$ satisfies the following equation: $$f''(x) + f(x) +t \cos x = 0$$. The value of $t$ is______.
asked
Sep 28, 2014
in
Calculus
by
jothee
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98.4k
points)

796
views
gate20141
calculus
easy
numericalanswers
differentiability
+15
votes
2
answers
17
GATE201416
Let the function $$f(\theta) = \begin{vmatrix} \sin\theta & \cos\theta & \tan\theta \\ \sin(\frac{\pi}{6}) & \cos(\frac{\pi}{6}) & \tan(\frac{\pi}{6}) & \\ \sin(\frac{\pi}{3}) & \cos(\frac{\pi}{3}) & \tan(\frac{\pi}{3}) \ ... 0$ There exists $\theta \in (\frac{\pi}{6},\frac{\pi}{3})$ such that $f'(\theta)\neq 0$ I only II only Both I and II Neither I Nor II
asked
Sep 26, 2014
in
Calculus
by
jothee
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(
98.4k
points)

2.3k
views
gate20141
calculus
differentiability
normal
+4
votes
4
answers
18
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)

566
views
gate1998
calculus
continuity
differentiability
easy
+5
votes
2
answers
19
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)

988
views
gate2007
calculus
continuity
differentiability
easy
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