Chapter 2.2, Problem 44E

[T] In the following exercises, set up a table of values and round to eight significant digits. Based on the table of values, make a guess about what the limit is. Then, use a calculator to graph the function and determine the limit. Was the conjecture correct? If not, why does the method of tables fail?

44. $\underset{\theta \to 0}{\lim }\sin \left(\frac{\pi }{\theta }\right)$

$\theta$	$\sin \left(\frac{\pi }{\theta }\right)$	$\theta$	$\sin \left(\frac{\pi }{\theta }\right)$
-0.1	a.	0.1	e.
-0.01	b.	0.01	f.
-0.001	c.	0.001	g.
-0.0001	d.	0.0001	f.