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.

enter image source here

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.