## Problem Statement

Calculate the limit of the function:

$$
\lim _{x \rightarrow 1}\left(\ln ^{2} e x\right)^{\frac{1}{x^{2}+1}}
$$
## Solution

$$
\lim _{x \rightarrow 1}\left(\ln ^{2} e x\right)^{\frac{1}{x^{2}+1}}=\left(\ln ^{2}(e \cdot 1)\right)^{\frac{1}{1^{2}+1}}=\left(1^{2}\right)^{\frac{1}{2}}=1
$$

## Problem Kuznetsov Limits 20-21