Problem:
Investigate numerically the behavior of the function

for values of x near 0.

Visualization:
Using Microcalc:

1. Choose Beginning Calculus from the initial menu and press .
2. Use the arrow keys to move to the menu item Limit of F(x), press and .
3. At the prompt F(x) =, enter the function
sin(3x)/x
4. At the prompt a = , enter 0 .
5. At the prompt h = , enter 1 .
6. You will then see on the screen F(a+h) = 0.14112 001.
7. Press and use the arrow keys to move to h <<-- 1/2 h and press .
8. If you keep repeating the previous step then you will obtain a table as below:
```__________________________________________________________

N          a + h/2^n       F(a + h/2^n)
----------------------------------------
0        1.00000 000        0.14112 001
1        0.50000 000        1.99498 997
2        0.25000 000        2.72655 504
3        0.12500 000        2.93018 023
4        0.06250 000        2.98245 275
5        0.03125 000        2.99560 740
6        0.01562 500        2.99890 149
7   7.81250 000 e-03        2.99972 535
8   3.90625 000 e-03        2.99993 134
9   1.95312 500 e-03        2.99998 283
10   9.76562 500 e-04        2.99999 571

On the evidence of all values of  F  calculated so far,
we estimate  Lim  F(x) =  3.00000 000
x-ťa+

Press :
________________________________________________________
```
9. If you want to see the behavior for x < 0, press after seeing the values above, use the arrow keys to move to Change h and press .
10. At the prompt h = , type -1 and proceed as above.