Question

How do you find limits on a graphing calculator?

Answer 1

See the explanation.

Explanation:

We will consider the following example:

`" L = "lim_(x to (-2))[[x^3+2x^2-1)/(5-3x)]`

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 `(color(blue)(-0.09))`

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):

`color(green)(Step.1)`

Press `color(blue)(y=` button and enter our expression as shown:

`color(green)(Step.2)`

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

The image of the graph is below:

`color(green)(Step.3)`

Press `color(red)(2nd` key followed by calc key and choose Option.1 for Value to get the screen below:

`color(green)(Step.4)`

Enter the first value of `color(red)x` from the table above. i.e., `color(red)((-2.1)` and press Enter to get:

`color(green)(Step.5)`

Enter the next value of `color(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 `color(red)x` from the table above, to get the rest of the values for `color(red)y`

`color(green)(Step.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.