Chapter 2.2, Problem 45E

[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?

45. $\underset{a\to 0}{\lim }\frac{1}{a}\cos \left(\frac{\pi }{a}\right)$

a	$\frac{1}{a}\cos \left(\frac{\pi }{a}\right)$
0.1	a.
0.01	b.
0.001	c.
0.0001	d.