# Approximating polynomials

## Homework Statement

find closest function a+bx3 to x2 on the iterval [-1,1]
(we consider standard inner product (f,g) = integral(-1 to 1):fgdx

So, here is my attempt, but I got a suspicious result:

[(1,1) (1,x3)] [a]
[(1,x3) (x3,x3)]
=
[(1,x2)]
[x3, x2)]

then after I've done all the integration I came up with this:
[2 0] [a]
[0 2/7]
=
[1/3]
[0]
which means that x3 term disappears....

## Answers and Replies

Dick
Science Advisor
Homework Helper
I can't help you fix it. Because you are completely correct. Why do you think that is suspicious? Find ways to check yourself.

Dick
Science Advisor
Homework Helper
You are approximating an even function over a symmetric interval. Can adding part of an odd function help you?