## Problem Statement

Calculate the limit of the function:

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

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

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

## Problem Kuznetsov Limits 20-8