Let f(x)=| |. then, 1. f(x) is everywhere differentiable. 2. f(x)… - Vidyadip

Question

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

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

✓

Answer

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

Solution:
$\text{f(x)}=|\sin\text{x}|$
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 Differentiability→Differentiability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $f(x)=\frac{1-\cos x}{x^2}$, is continuous at $x=0$, then $f(0)$ equals to:

If $A=\left[\begin{array}{cc}3 & x-1 \\ 2 x+3 & x+2\end{array}\right]$ is a symmetric matrix, then $x=$

Which of the following sets are convex?

$\{(\text{x},\text{y}):\text{x}^2+\text{y}^2\geq1\}$
$\{(\text{x},\text{y}):\text{y}^2\geq\text{x}\}$
$\{(\text{x},\text{y}):3\text{x}^2+4\text{y}^2\geq5\}$
$\{(\text{x},\text{y}):\text{y}\geq2,\text{y}\leq4\}$

The vector equation of a line passing through the point $(1,-1,0)$ and parallel to $Y$-axis is :

If $\text{y}=\text{ax}^{\text{n+1}}+\text{bx}^{-\text{n}}$ Then $\text{x}^2\frac{\text{d}^2\text{y}}{\text{dx}^2} =$

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b for all a, b ∈ T. Then, R is:

Reflexive but not symmetric.
Transitive but not symmetric.
Equivalence.
None of these.

If the function $\text{f}(\text{x})=\cos|\text{x}|-2\text{ax}+\text{b}$ increases along entire number scale, then:

$\text{a}=\text{b}$
$\text{a}=\frac{1}{2}\text{b}$
$\text{a}\leq-\frac{1}{2}$
$\text{a}>-\frac{3}{2}$

If $\text{A}=\begin{vmatrix}\text{a}_{11}&\text{a}_{12}&\text{a}_{13}\\\text{a}_{21}&\text{a}_{22}&\text{a}_{23}\\\text{a}_{31}&\text{a}_{32}&\text{a}_{33}\end{vmatrix}$ and $C_{ij}$ is cofactor of $a_{ij}$ in a, then value of $|A|$ is given by:

Optimization of the objective function is a process of

If inverse of matrix $\left[\begin{array}{ccc}7 & -3 & -3 \\ -1 & 1 & 0 \\ -1 & 0 & 1\end{array}\right]$ is the matrix $\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & \lambda & 3 \\ 1 & 3 & 4\end{array}\right]$, then value of $\lambda$ is