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Question
`\lim_{x \to \pi/2} \frac{a^\cot x - a^\cos x}{\cot x - \cos x}`
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Solution
`lim_{x \to \frac{\pi}{2}} \left[ \frac{a^\cot x - a^\cos x}{\cot x - \cos x} \right`
= `\lim_{x \to \frac{\pi}{2}} \left[ \frac{a^\cos x \left( a^\cot x - \cos x - 1 \right)}{\cot x - \cos x} \right]`
\[ x \to \frac{\pi}{2}\]
\[ \therefore \cot x - \cos x \to 0\]
` \Rightarrow a^\cos \frac{\pi}{2} \times \log a`
\[ = a^0 \times \log a\]
\[ = \log a\]
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