Question

Find the limit, if it exists. (If an answer does not exist, enter DNE.)

Answer 1

Note that your function can be written as

$\begin{cases}\frac{2-(-x)}{2+x}&\text{if } x0\end{cases} = \begin{cases}\frac{2+x}{2+x}&\text{if } x0\end{cases} = \begin{cases}1&\text{if } x0\end{cases}$

So, if x is negative, your function is identically equal to 1. In particular, the limit as x approaches -2 will be 1 as well.