Problem:
Investigate numerically the behavior of the function

for values of x near 0.


Visualization:
Using Limits (from the University of Arizona):

  1. 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 .
  2. If you choose Yes then read the instructions and press when you are ready to proceed.
  3. Use the arrow keys to highlight Function Operations and press .
  4. Use the arrow keys to highlight Create Function and press .
  5. At the prompt, Enter function:, type
    sin(3*x)/x .
  6. 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 .
  7. 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.
  8. Use arrow keys to move to Two Sided Limit and press several times to get the following table: