# How do you find limits on a graphing calculator?

Jan 27, 2018

See the explanation.

#### Explanation:

We will consider the following example:

$\text{ L = } {\lim}_{x \to \left(- 2\right)} \left[\frac{{x}^{3} + 2 {x}^{2} - 1}{5 - 3 x}\right]$

We will create an EXCEL table of values for x" and $y$ to estimate the limit and verify using a calculator.

For $x ,$ we will consider values closer to the limit, and $y$ is the rational expression in our problem. We can easily observe the the limit is approaching $\left(\textcolor{b l u e}{- 0.09}\right)$

Next we will find out how to use a calculator to find the limit.

The calculator I am going to use is a Texas Instruments Graphical Display Calculator (Model TI-84 Plus Silver Edition):

$\textcolor{g r e e n}{S t e p .1}$

Press color(blue)(y= button and enter our expression as shown: $\textcolor{g r e e n}{S t e p .2}$

Hit the Graph Key to draw the graph of our rational expression.

The image of the graph is below: $\textcolor{g r e e n}{S t e p .3}$

Press color(red)(2nd key followed by calc key and choose Option.1 for Value to get the screen below: $\textcolor{g r e e n}{S t e p .4}$

Enter the first value of $\textcolor{red}{x}$ from the table above. i.e., color(red)((-2.1) and press Enter to get: $\textcolor{g r e e n}{S t e p .5}$

Enter the next value of $\textcolor{red}{x}$ from the table above. i.e., color(red)((-2.01) and press Enter to get: Continue to enter the rest of the values for $\textcolor{red}{x}$ from the table above, to get the rest of the values for $\textcolor{red}{y}$

$\textcolor{g r e e n}{S t e p .6}$

Enter the calculator results in the Excel table to compare results: We observe that the color(blue)(-0.09 is an estimate for our limit problem.