Find the limit, if it exists. Limit as x approaches -8 of (8 - absolute x)/(8 + x).


Find the limit, if it exists.

{eq}\lim_{x\rightarrow -8}\frac{8 - \left | x \right |}{8 + x} {/eq}.

Limits with Absolute Values:

To find limits involving absolute values, we must be careful to keep our right and left limits straight. Thankfully, our limit is easy to work with, so all we need to do is think about our situation and get rid of the absolute value.

Answer and Explanation: 1

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Note that as we approach the function at {eq}x=-8 {/eq} from either side, we have {eq}x < 0 {/eq}, so {eq}|x| = -x {/eq}. Then the limit is


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Limits with Absolute Value


Chapter 6 / Lesson 7

While limits in calculus can be evaluated in many different ways, those involving absolute value can be especially tricky. In this lesson, we'll use plenty of examples to show you how to compute limits in calculus with absolute value using a graph or algebra.

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