_ x 0 | x| x is equal to - Vidyadip

MCQ

$\lim _{x \rightarrow 0} \frac{|\sin x|}{x}$ is equal to

A
$0$
✓
Does not exist
C
$1$
D
$-1$

✓

Answer

Correct option: B.

Does not exist

Given, $\lim _{x \rightarrow 0} \frac{|\sin x|}{x}$
$ LHL =\lim _{x \rightarrow 0^{-}} \frac{-\sin x}{x}=-1 \quad\left[\because \lim _{x \rightarrow 0} \frac{\sin x}{x}=1\right]$
$RHL =\lim _{x \rightarrow 0^{+}} \frac{\sin x}{x}=1$
$\text{LHL} \neq {RHL,}$ So the limit does not exist.

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