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 - 5) 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(5-10^(-I), I, 0, 10, 1) STO x

    and press the ENTER key.

  4. This creates a list of x-values:

    {4 4.9 4.99 4.999 ... 4.9999999999}

    which are numbers which are getting close to 5 on the left-hand side of 5.

  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
    04-17
    14.9-250.1
    24.99-2590.01
    34.999-25990.001
    44.9999-259990.0001
    54.99999-2599990.00001
    64.999999-25999990
    74.9999999-259999990
    84.99999999-2599999990
    94.999999999-25999999990
    104.9999999999-259999999990

    It appears that the limit is - infinity.