MCQ
$\mathop {\lim }\limits_{x \to \pi /2} \frac{{{a^{\cot x}} - {a^{\cos x}}}}{{\cot x - \cos x}} = $
- ✓$\log a$
- B$\log 2$
- C$a$
- D$log\ x$
$ = \mathop {{\rm{lim}}}\limits_{x \to \pi /2} {a^{\cos x}}\left( {\frac{{{a^{\cot x - \cos x}} - 1}}{{\cot x - \cos x}}} \right)$
$ = {a^{\cos (\pi /2)}}\mathop {{\rm{lim}}}\limits_{x \to \pi /2} \left( {\frac{{{a^{\cot x - \cos x}} - 1}}{{\cot x - \cos x}}} \right)$$ = 1.\log a = \log a$.
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