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Recent questions tagged differentiation
2
votes
1
answer
61
TIFR-2014-Maths-A-3
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
makhdoom ghaya
asked
in
Calculus
Dec 10, 2015
by
makhdoom ghaya
510
views
tifrmaths2014
differentiation
1
vote
1
answer
62
TIFR-2011-Maths-A-19
The derivative of the function $\int_{0}^{\sqrt{x}} e^{-t^{2}}dt$ at $x = 1$ is $e^{-1}$ .
makhdoom ghaya
asked
in
Calculus
Dec 9, 2015
by
makhdoom ghaya
451
views
tifrmaths2011
calculus
differentiation
1
vote
1
answer
63
TIFR-2011-Maths-A-9
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
makhdoom ghaya
asked
in
Calculus
Dec 9, 2015
by
makhdoom ghaya
367
views
tifrmaths2011
differentiation
2
votes
1
answer
64
TIFR-2011-Maths-A-5
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
makhdoom ghaya
asked
in
Calculus
Dec 9, 2015
by
makhdoom ghaya
352
views
tifrmaths2011
differentiation
non-gate
4
votes
4
answers
65
TIFR2010-Maths-A-8
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 $x=0$.
makhdoom ghaya
asked
in
Calculus
Oct 11, 2015
by
makhdoom ghaya
924
views
tifrmaths2010
calculus
differentiation
continuity
25
votes
2
answers
66
GATE CSE 1996 | Question: 3
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.
Kathleen
asked
in
Calculus
Oct 9, 2014
by
Kathleen
3.6k
views
gate1996
calculus
continuity
differentiation
normal
descriptive
19
votes
3
answers
67
GATE CSE 1996 | Question: 1.6
The formula used to compute an approximation for the second derivative of a function $f$ at a point $X_0$ is $\dfrac{f(x_0 +h) + f(x_0 – h)}{2}$ $\dfrac{f(x_0 +h) - f(x_0 – h)}{2h}$ $\dfrac{f(x_0 +h) + 2f(x_0) + f(x_0 – h)}{h^2}$ $\dfrac{f(x_0 +h) - 2f(x_0) + f(x_0 – h)}{h^2}$
Kathleen
asked
in
Calculus
Oct 9, 2014
by
Kathleen
5.4k
views
gate1996
calculus
differentiation
normal
19
votes
4
answers
68
GATE CSE 2014 Set 1 | Question: 46
The function $f(x) =x \sin x$ satisfies the following equation: $f''(x) + f(x) +t \cos x = 0$The value of $t$ is______.
go_editor
asked
in
Calculus
Sep 28, 2014
by
go_editor
3.9k
views
gatecse-2014-set1
calculus
easy
numerical-answers
differentiation
39
votes
4
answers
69
GATE CSE 2014 Set 1 | Question: 6
Let the function ... $\theta \in (\frac{\pi}{6},\frac{\pi}{3})$ such that $f'(\theta)\neq 0$ I only II only Both I and II Neither I nor II
go_editor
asked
in
Calculus
Sep 26, 2014
by
go_editor
10.3k
views
gatecse-2014-set1
calculus
differentiation
normal
11
votes
4
answers
70
GATE CSE 1998 | Question: 1.4
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
Kathleen
asked
in
Calculus
Sep 26, 2014
by
Kathleen
3.9k
views
gate1998
calculus
continuity
differentiation
easy
14
votes
2
answers
71
GATE CSE 2007 | Question: 1
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.
Kathleen
asked
in
Calculus
Sep 22, 2014
by
Kathleen
4.7k
views
gatecse-2007
calculus
continuity
differentiation
easy
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