Problem:
Using the TI-85 graphing calculator, give numerical evidence to evaluate

Visualization:

[Press here to see animation again!]

1. Enter the function: Y = (x^2-1)/(x^2+1) and press the ENTER key.
2. Press 2nd MATH and pick MISC by pressing F5.
3. Press F3 to enter seq. Continue to enter the command:

seq(10^I, I, 0, 10, 1) STO x

and press the ENTER key.

4. This creates a list of x-values:

{1 10 100 1000 ... 10000000000}

which are the powers, 10I, for I = 0, 1, ..., 10.

5. Press the EXIT key twice.
6. Type Y and press the ENTER key. On the screen you will then see the list of corresponding y-values using the function you entered above:

IxY
010
110.980198019802
2100.999800019998
31000.999998000002
410000.99999998
5100000.9999999998
61000000.999999999998
7100000001
81000000001
910000000001
1010000000001

It appears that the limit is 1.

7. If you want to round the numbers to fewer decimal places, press the 2nd MATH key again followed by F1 to pick NUM.
8. Press F1 to pick round and complete the command

round(2nd ANS, 4)

and press the ENTER key to round to four decimal places.