\( \lim _{x \rightarrow \infty} \frac{\cot ^{-1}(\sqrt{x+1}-\sqrt{x})}{\sec ^{-1}\left\{\left(\f...

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\( \lim _{x \rightarrow \infty} \frac{\cot ^{-1}(\sqrt{x+1}-\sqrt{x})}{\sec ^{-1}\left\{\left(\frac{2 x+1}{x-1}\right)^{x}\right\}} \) is equal to
(a) 1
(b) 0
(c) \( \pi / 2 \)
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