MCQ
The $\mathop {\lim }\limits_{x \to 0} {(\cos x)^{\cot x}}$ is
- A$-1$
- B$0$
- ✓$1$
- DNone of these
Taking $log$ on both sides,
==> $\log y = \mathop {\lim }\limits_{x \to 0} \,\,\cot x\log \cos x$
==> $\log y = \mathop {\lim }\limits_{x \to 0} \frac{{\log \cos x}}{{\tan x}}$,$\left( {\frac{0}{0} \,\, {\rm{form}}} \right)$
Applying $L-$ Hospital’s rule,
==> $\log y = \mathop {\lim }\limits_{x \to 0} \frac{{ - \tan x}}{{{{\sec }^2}x}}$= 0
==> $y = {e^0}$ ==> $y = 1$.
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