A) \[\log a\]
B) \[\log 2\]
C) a
D) log x
Correct Answer: A
Solution :
\[\underset{x\to \pi /2}{\mathop{\text{lim}}}\,\,\left( \frac{{{a}^{\cot x}}-{{a}^{\cos x}}}{\cot x-\cos x} \right)\]\[=\underset{x\to \pi /2}{\mathop{\text{lim}}}\,{{a}^{\cos x}}\left( \frac{{{a}^{\cot x-\cos x}}-1}{\cot x-\cos x} \right)\] \[={{a}^{\cos (\pi /2)}}\underset{x\to \pi /2}{\mathop{\text{lim}}}\,\left( \frac{{{a}^{\cot x-\cos x}}-1}{\cot x-\cos x} \right)\]\[=1.\log a=\log a\].
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