## Problem Statement

Calculate the limit of the function:

$\lim _{x \rightarrow 0}\left(\frac{1+8 x}{2+11 x}\right)^{\frac{1}{x^{2}+1}}$
## Solution

$\lim _{x \rightarrow 0}\left(\frac{1+8 x}{2+11 x}\right)^{\frac{1}{x^{2}+1}}=\left(\frac{1+8 \cdot 0}{2+11 \cdot 0}\right)^{\frac{1}{0^{2}+1}}=\left(\frac{1}{2}\right)^{1}=\frac{1}{2}$

Problem Kuznetsov Limits 18-29