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Q. $\displaystyle\lim _{x \rightarrow 0} \frac{\log \cos x}{x}=$

Limits and Derivatives

Solution:

$\displaystyle\lim _{x \rightarrow 0} \frac{\log \cos x}{x}$
$=\displaystyle\lim _{x \rightarrow 0} \frac{-\tan x}{1}$
(Using L'Hospital's rule)
$=0$