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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

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

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

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

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

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

3.6k views

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

5.4k views

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

3.9k views

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

10.3k views

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

3.9k views

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

4.7k views

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Recent questions tagged differentiation