Chapter 12, Problem 47RE

To determine

The graph and then limit of the function if exist using the corresponding one sided limit.

Explanation of Solution

Given:

The expression is given as:

  $\underset{x\to 2}{\lim }\frac{2}{x^2-4}$

Using the T1-83 calculator, graphing the given function:

Pressing Y= and then enter the equation:

  

Now pressing the Zoom option and then choosing the appropriate zoom function and drawing the graph as shown below:

  

Referring to the above graph, the function is behaving as the unbounded when it is approaching 2 either the left side or the right side.

Hence, the one sided limit is evaluated as:

  $\begin{array}{l}\underset{x\to 2^{-}}{\lim }\frac{2}{x^2-4}=-\infty \\ \underset{x\to 2^{+}}{\lim }\frac{2}{x^2-4}=-+\end{array}$

Since, the left side and the right side of the functions are not equal, thus the limit will not exist.