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$\lim _{x \rightarrow 0} \frac{|\sin x|}{x}$ is equal to
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Does not exist
Let $l=\lim _{x \rightarrow 0} \frac{[\sin x]}{x} ; \mathrm{RHL}=\lim _{x \rightarrow 0^{+}} \frac{\sin x}{x}=1$
$\mathrm{LHL}=\lim _{x \rightarrow 0^{-}}\left(\frac{-\sin x}{x}\right)=-\left(\lim _{x \rightarrow 0^{-}} \frac{\sin x}{x}\right)=-1$
$\left[|x|=\begin{array}{c}x \text { if } x \geq 0 \\ -x \text { if } x \leq 0\end{array}\right]$
As, LHL $\neq$ RHL Hence, limit $l$.does not exist.
$\mathrm{LHL}=\lim _{x \rightarrow 0^{-}}\left(\frac{-\sin x}{x}\right)=-\left(\lim _{x \rightarrow 0^{-}} \frac{\sin x}{x}\right)=-1$
$\left[|x|=\begin{array}{c}x \text { if } x \geq 0 \\ -x \text { if } x \leq 0\end{array}\right]$
As, LHL $\neq$ RHL Hence, limit $l$.does not exist.
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