Chapter 12.1, Problem 27E

To determine

To find:The limits of a function using graph utility and if limit does not exist, then explain why.

Answer to Problem 27E

Limit of the function at $x=-2$ does not exist..

Explanation of Solution

Given:

  ${\underrightarrow{\lim }}_{x\to -2}\frac{\left|x+2\right|}{x+2}$

  ${\underrightarrow{\lim }}_{x\to -2}\frac{\left|x+2\right|}{x+2}$ be a given function.

And graph of this function is

  

Now limitof this function ${\underrightarrow{\lim }}_{x\to -2}\frac{\left|x+2\right|}{x+2}$ does not exist at $x=-2$ .

Because left hand limit is not equal to right hand limit.

  $\begin{array}{l}\text{left hand limit}\\ f\left(x\right)={\underrightarrow{\lim }}_{x\to -2^{-}}\frac{\left|x+2\right|}{x+2}=-1\\ \text{right hand limit}\\ f\left(x\right)={\underrightarrow{\lim }}_{x\to -2^{+}}\frac{\left|x+2\right|}{x+2}=1\end{array}$

So, limit of the function at $x=-2$ does not exist.