Problem:
Investigate the behavior of the function

f(x) = sin(1/x)

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(1/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) = 0.84147 098
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        0.84147 098
1        0.50000 000        0.90929 743
2        0.25000 000       -0.75680 250
3        0.12500 000        0.98935 825
4        0.06250 000       -0.28790 332
5        0.03125 000        0.55142 668
6        0.01562 500        0.92002 604
7   7.81250 000 e-03        0.72103 771
8   3.90625 000 e-03       -0.99920 803
9   1.95312 500 e-03        0.07951 849
10   9.76562 500 e-04       -0.15853 338

On the evidence of all values of  F  calculated so far,
we estimate  Lim  F(x) =  -2.08027 731
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.