**Example 3.** Compare
the "discrete least squares approximation" and "continuous least
squares approximation," on the interval .

**3 (a).** Use the
function .

**Solution 3 (a).**

We are done.

Let us investigate the linear system involved in this example.

We are really done.

**Aside.** We can
calculate the coefficients by
directly setting up the matrix
vector . This
is just for fun !

This is the same as we obtained previously.

(c) John H. Mathews 2005