Problem:
Using the TI-85 graphing calculator, investigate numerically the behavior of the function

for values of x near 0.


Visualization:


[Press here to see animation again!]

  1. If you are not familiar with the graphing of functions on the TI-85, then first read the Initial Setup page from Little's Basic Guide to the TI-85.
  2. Press the GRAPH key and then pick y(x)= by pressing the F1 key.
  3. If necessary, keep pressing the F4 key until only y1= appears on the screen.
  4. At the prompt y1=, type in

    ((x^3+8)^(1/3)-2)/x^3

    and press the ENTER key.

  5. The range settings for the initial graph above is  [-1, 1] × [-1, 1]:

  6. Pick GRAPH from the menu by pressing the F5 key.
  7. Pick ZOOM from the menu by pressing the F3 key and then pick ZIN from the menu by pressing the F2 key.
  8. You will now see a flashing tick mark in the middle of the screen and the coordinates of the tick mark at the bottom of the screen. Using the arrow keys, move the tick mark as close as possible to the intersection of the graph with the vertical line which is the y-axis and press the ENTER key.
  9. Repeat the latter step a couple of times to see the following:

    This graph indicates that there may be a problem.

  10. One more zoom in and we get the final graph in the animation above. It appears that the limit does not exist. However, this problem is due to round off error and the limit, in fact, does exist!
Note. The parameters xFact and yFact were both set to 10 in the animation above.