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( /(16 x))
The two keys and must be pressed at the same time. This will give the Greek letter pi.
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) = 0.19509 032
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        0.19509 032
1        0.50000 000        0.38268 343
2        0.25000 000        0.70710 678
3        0.12500 000        1.00000 000
4        0.06250 000       -0.00000 000
5        0.03125 000        0.00000 000
6        0.01562 500        0.00000 000
7   7.81250 000 e-03        0.00000 000
8   3.90625 000 e-03        0.00000 000
9   1.95312 500 e-03        0.00000 000
10   9.76562 500 e-04        0.00000 000

On the evidence of all values of  F  calculated so far,
we estimate  Lim  F(x) =  -3.89125 750 e-08
x->a+

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.