\( \lim _{x \rightarrow \infty} \frac{\cot ^{-1}(\sqrt{x+1}-\sqrt{x})}{\sec ^{-1}\left\{\left(\f...
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0\( \lim _{x \rightarrow \infty} \frac{\cot ^{-1}(\sqrt{x+1}-\sqrt{x})}{\sec ^{-1}\left\{\left(\frac{2 x+1}{x-1}\right)^{x}\right\}} \)
(A) 1
(B) 0
(C) \( \frac{\pi}{2} \)
(D) does not exist
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