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.