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