The function f(x)=| | is : - Vidyadip

MCQ

The function $\text{f(x)}=|\cos\text{x}|$ is :

A
Everywhere continuous and differentiable.
✓
Everywhere continuous but not differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
C
Neither continuous nor differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
D
None of these.

✓

Answer

Correct option: B.

Everywhere continuous but not differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$

As $\cos x$ is even function it is continuous everywhere but not differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
$\cos\Big[(2\text{n}+1)\frac{\pi}{2}=\cos\Big(\text{n}\pi+\frac{\pi}{2}\Big)\Big]=-\sin\text{n}\ \pi$
For $n$ as an integer
$\Rightarrow\sin\text{n}\ \pi=0$
For $n$ as rational
$\Rightarrow\sin\text{n}\ \pi=-1$

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

Let $\mathrm{X}$ be the set of all five digit numbers formed using $1,2,2,2,4,4,0$. For example, $22240$ is in $\mathrm{X}$ while $02244$ and $44422$ are not in $X$. Suppose that each element of $X$ has an equal chance of being chosen. Let $\mathrm{p}$ be the conditional probability that an element chosen at random is a multiple of $20$ given that it is a multiple of $5$ . Then the value of $38 p $ is equal to

For the curve $\sqrt{\text{x}}+\sqrt{\text{y}}=1,\frac{\text{dy}}{\text{dx}}$ at $\Big(\frac{1}{4},\frac{1}{4}\Big)$ is:

Let $\text{f(x)}=\begin{vmatrix}\cos\text{x}&\text{x}&1\\2\sin\text{x}&\text{x}&2\text{x}\\\sin\text{x}&\text{x}&\text{x}\end{vmatrix},$ then $\lim_\limits{\text{x}\rightarrow0}\frac{\text{f(x)}}{\text{x}^2}$ is equal to:

Can $\frac{1}{\sqrt{3}},\frac{2}{\sqrt{3}},\frac{-2}{\sqrt{3}}$ be the direction cosines of any directed line:

Given the differential equation
$
\frac{d y}{d x}=\frac{6 x^2}{2 y+\cos y} ; y(1)=\pi \text {. }
$
Which of the following statements is correct?

If $\text{A}=\begin{bmatrix}1&0&0\\0&1&0\\\text{a}&\text{b}&-1\end{bmatrix},$ then $A^2$ is equal to:

$\int_0^2 {\sqrt {\frac{{2 + x}}{{2 - x}}} } \,dx = $

The area of the region between the curve $y^2=4 a x$, line $y=2 a$ and $y$-axis is :

If $ A$ is a square matrix, then which of the following matrices is not symmetric

Let $X$ denote the number of times heads occur in $n$ tosses of a fair coin. If $P(X = 4), P(X = 5)$ and $P(X = 6)$ are in $AP,$ the value of $n$ is :