Let f(x)=| |. then, - Vidyadip

MCQ

Let $\text{f(x)}=|\sin\text{x}|.$ then,

A
f(x) is everywhere differentiable.
✓
f(x) is everywhere continuous but not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}$
C
f(x) is everywhere continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}.$
D
None of these.

✓

Answer

Correct option: B.

f(x) is everywhere continuous but not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}$

$\text{f(x)}=|\sin\text{x}|$

Given function is continuous and differentiable on $(2\text{n}\pi,(2\text{n}+1)\pi)$

But not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}.$

As $\sin\text{n}\pi=0$ for $\text{n}\in\text{Z}.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

What is the general solution of the differential equation $x\ dy - y\ dx\ y^2 ?$

$ \begin{bmatrix}1 & \text{x} & \text{x}^2 \\1 & \text{y} & \text{y}^2 \\1 & \text{z} & \text{z}^2\end{bmatrix}$

If $A$ is a skew symmetric matrix, then $∣A∣$ is:

If a line makes angles $\alpha,\beta,\gamma,\delta$ with four diagonals of a cube, then $\cos^2\alpha+\cos^2\beta+\cos^2\gamma+\cos^2\delta$ is equal to:

Maximize Z = 3x + 5y, subject to constraints: $\text{x}+4\text{y}\leq24,3\text{x}+\text{y}\leq21,\text{x}+\text{y}\geq9,\text{x}\geq0,\text{y}\geq0.$

Let $A =\{2,3,4,5, \ldots ., 30\}$ and $^{\prime} \simeq ^{\prime}$ be an equivalence relation on $A \times A ,$ defined by $(a, b) \simeq (c, d),$ if and only if $a d=b c .$ Then the number of ordered pairs which satisfy this equivalence relation with ordered pair $(4,3)$ is equal to :

Find values of $\mathrm{k}$ if area of triangle is $4$ square units and vertices are $(\mathrm{k}, 0),(4,0),(0,2)$

Choose the correct answer from the given four options.
If $\text{P}(\text{A})=\frac{3}{10},\text{P}(\text{B})=\frac{2}{5}$ and $\text{P}(\text{A}\cup\text{B})=\frac{3}{5},$ then $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)+\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)$ equas:

Point $A$ lies at a distance of $6$ units from the point $(1 ,0, 1)$ , on the line $\frac{{x - 1}}{2} = \frac{y}{2} = \frac{{z - 1}}{1}$ , in $-ve\ z$ direction, then co-ordinates of $A$ are

If matrix $\text{A}=\big[\text{a}_{\text{ij}}\big]_{2\times2'}$ where $\text{a}_\text{ij}=\begin{cases}1,&\text{if }\text{i }\neq\text{j}\\0,&\text{if }\text{i }=\text{j}\end{cases},$ then $A^2$ is equal to: