Limit- Evaluation

**ty2391** · October 4th 2009, 11:39 AM

Hi there..

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

**Chris L T521** · October 4th 2009, 11:45 AM

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?

**ty2391** · October 4th 2009, 01:18 PM

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?

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