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  4. Let undersetx arrow ∞ textLim ( cot -1 x)(1/x)=L; then L is

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Q. Let $\underset{x \rightarrow \infty}{\text{Lim}} \left(\cot ^{-1} x\right)^{\frac{1}{x}}=L$; then $L$ is

Continuity and Differentiability

Solution:

$L= e ^{\operatorname{Lim}_{x \rightarrow \infty} \frac{\ln \cot ^{-1} x}{x}}$ (L'Hospital rule)
$\therefore L = e ^{-\infty}=0$