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. Enter the function: y1 = (sin 3 x)/x 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(2^(-N), N, 0, 10, 1) STO x

and press the ENTER key.

4. This creates a list of x-values:

{1 .5 .25 .125 .0625 .03125 ... 9.765625E-4}

which are the powers, 2- N, for N = 0, 1, ..., 10.

5. Type y1 and press the ENTER key. On the screen you will then see the list of corresponding y-values using the function you entered above:

Nxy1
01.14112000806
1.51.99498997321
2.252.72655504009
3.1252.93018023269
4.06252.9824527482
5.031252.99560739954
6.0156252.99890148788
7.00781252.99972534934
8.003906252.99993133592
9.0019531252.99998283389
109.765625E-42.99999570847

It appears that the limit is 3.

6. If you want to round the numbers to fewer decimal places, press the EXIT key followed by F1 to pick NUM.
7. Press F1 to pick round and complete the command

round(2nd ANS, 4)

and press the ENTER key to round to four decimal places.