Chapter 12, Problem 47RE

To determine

To find the limit (if it exists) by evaluating the corresponding one-sided limits..

Answer to Problem 47RE

Limit does not exist.

Explanation of Solution

Given information:

Graph the function. Determine the limit (if it exists) by evaluating the corresponding one-sided limits.

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

Calculation:

The limit of given function is,

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

Let plot the given function.

To calculate the model graphically use graphic utility TI-83calculator,

Press Y key and enter the equation,

  

Press zoom and plot window button,

  

  

From the graph we observe that the function goes unbounded as it approaches $2$ from both sides left and right.

Therefore one sided limit are,

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

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

Hence limit does not exist.