Math Help - Limit- Evaluation

1. Limit- Evaluation

Hi there..

can someone help me determine that limit for the following function, as x --> -2?

2. Originally Posted by ty2391
Hi there..

can someone help me determine that limit for the following function, as x --> -2?

Note that $\left|x\right|=\left\{\begin{array}{rl} x, & \text{ if } x\geq0\\ {\color{red}-x}, & \text{ if } x<0\end{array}\right.$

So $\lim_{x\to-2}\frac{2-\left|x\right|}{2+x}=\lim_{x\to-2}\frac{2-(-x)}{2+x}=\lim_{x\to-2}\frac{2+x}{2+x}=1$

Does this make sense?

3. That makes sense. However, do you not have to evaluate the left and right hand limits and equate them to prove that the limit exists? In that case, how would you evaluate the right hand limit?