How do you find limits on a graphing calculator?

1 Answer
Jan 27, 2018

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.

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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:

enter image source here

color(green)(Step.2)

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

The image of the graph is below:

enter image source here

color(green)(Step.3)

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

enter image source here

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:

enter image source here

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:

enter image source here

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:

enter image source here

We observe that the color(blue)(-0.09 is an estimate for our limit problem.