## Problem Statement

Calculate the limit of the function:

$\lim _{x \rightarrow 1}(\sqrt{x}+1)^{\frac{\pi}{\operatorname{arctg} x}}$
## Solution

$\lim _{x \rightarrow 1}(\sqrt{x}+1)^{\frac{\pi}{\operatorname{arctg} x}}=(\sqrt{1}+1)^{\frac{\pi}{\operatorname{arctg} 1}}=2^{\frac{\pi}{\left(\frac{\pi}{4}\right)}}=2^{4}=16$

## Problem Kuznetsov Limits 20-22