## Problem Statement

Calculate the limit of the function:
$\lim _{x \rightarrow 0}\left(\frac{x^{3}+4}{x^{3}+9}\right)^{\frac{1}{x+2}}$
## Solution

$\lim _{x \rightarrow 0}\left(\frac{x^{3}+4}{x^{3}+9}\right)^{\frac{1}{x+2}}=\left(\frac{0^{3}+4}{0^{3}+9}\right)^{\frac{1}{0+2}}=\left(\frac{4}{9}\right)^{\frac{1}{2}}=\sqrt{\frac{4}{9}}=\frac{2}{3}$

## Problem Kuznetsov Limits 18-31