JEE MATHEMATICS MCQ: LIMITS

1 Easy

1 of 1

Analyzing +4 | -1

\lim \limits_{{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

View answer and explanation

Correct option: A

Option A (1) is correct because as x approaches infinity, the numerator approaches

\cot^{-1}(0) = \frac{\pi}{2}

and the denominator approaches

\sec^{-1}(\infty) = \frac{\pi}{2}

, resulting in a limit of 1.

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