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

for values of **x** near **0**.

[Press here to see animation again!]

- Enter the function:
**y1 = (sin 3 x)/x**and press the ENTER key. - Press 2nd MATH and pick
**MISC**by pressing F5. - Press F3 to enter
**seq**. Continue to enter the command:**seq(2^(-N), N, 0, 10, 1) STO x**and press the ENTER key.

- This creates a list of
**x**-values:**{1 .5 .25 .125 .0625 .03125 ... 9.765625E-4}**which are the powers,

**2**, for^{- N}**N = 0, 1, ..., 10**. - 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:N x y1 0 1 .14112000806 1 .5 1.99498997321 2 .25 2.72655504009 3 .125 2.93018023269 4 .0625 2.9824527482 5 .03125 2.99560739954 6 .015625 2.99890148788 7 .0078125 2.99972534934 8 .00390625 2.99993133592 9 .001953125 2.99998283389 10 9.765625E-4 2.99999570847 It appears that the limit is

**3**. - If you want to round the numbers to fewer decimal places, press the
EXIT key followed by F1 to pick
**NUM**. - Press F1 to pick
**round**and complete the command**round(2nd ANS, 4)**and press the ENTER key to round to four decimal places.