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

WBJEEWBJEE 2010Limits and Derivatives

Solution:

$\displaystyle\lim _{x \rightarrow 0} \frac{\sin |x|}{x}$
$LHL =-1, RHL =1$
Limit does not exist.