Question

Evaluate $\underset{x\to 0}{lim}\frac{\log \cos x}{x}$

Answer 1

Now

$\underset{x\to 0}{lim}\frac{\log \cos x}{x}$ $\left(\frac{0}{0}\right)$ form.

Now applying L'Hospital's rule we get

$=\underset{x\to 0}{lim}\frac{-\tan x}{1}$

$=0$