Problem:
Investigate numerically the behavior of the function

for values of x near 0.
Visualization:
Using Limits
(from the University of Arizona):
- After starting up the program, you are prompted "Would you like some
instructions?" Use the arrow keys to move to either Yes or
No and then press
.
- If you choose Yes then read the instructions and press
when you are ready to proceed.
- Use the arrow keys to highlight Function Operations and press
.
- Use the arrow keys to highlight Create Function and press
.
- At the prompt, Enter function:, type
sin(
- A list of items appears at the right of the
screen. Use the arrow keys to move to ?? and press
.
- Finish entering the function by typing
*x)
.
* denotes multiplication and must be included.
- Use the arrow keys to move to Point and
press
. Next we enter the value that
x approaches; however the default is 0 so we just
press
.
- Now use the arrow keys to move to Method and
press
. If we move to No at the
prompt, Select point exactly halfway?, and
press
then we would get a random sequence
of points converging to 0.
- Use arrow keys to move to Two Sided Limit and
press
several times to get the
following table:
