Chapter 12, Problem 48RE

To determine

The limit if exist.

Answer to Problem 48RE

Limit exist and value of limit is 0.077

Explanation of Solution

Given:

Limit is given as ;

  $\underset{x\to 3}{\lim }\frac{1}{x^2+9}$

Let the function is $f\left(x\right)=\frac{1}{x^2+9}$

Now plot the function using Ti -83 graphing calculator.

Steps for plotting the function are;

Press y = and then enter the given equation.

  

Now, after pressing ZOOM choose the suitable zooming function.

  

Now, press trace and the give the value of x on which y has to be found.

  

From the graph it is clear that function converge to 0.077

Hence, the one sided limits are;

  $\begin{array}{l}\underset{x\to 2^{-}}{\lim }\frac{1}{x^2+9}=0.077\\ \underset{x\to 2^{+}}{\lim }\frac{1}{x^2+9}=0.077\end{array}$

Therefore, limit exists.