MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{\log \cos x}}{x} = $
- ✓$0$
- B$1$
- C$\infty $
- DNone of these
$ = \mathop {\lim }\limits_{x \to 0} \,\,\frac{{ - \,\left[ {2\,{{\sin }^2}\frac{x}{2} + {{\left( {\frac{{2\,{{\sin }^2}\frac{x}{2}}}{2}} \right)}^2} + ......} \right]}}{x} = 0$
Aliter : Apply $L-$ Hospital’s rule,
$\mathop {\lim }\limits_{x \to 0} \,\frac{{\log \cos x}}{x} = \mathop {\lim }\limits_{x \to 0} \,\frac{{ - \tan x}}{1} = 0.$
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