Use the L2 inner product

to answer the following:
(a) Find the "angle" between the functions 1 and x. Are they orthogonal?
(b) Verify the Cauchy-Schwarz and triangle inequalities for these two functions.
(c) Find all quadratic polynomials p(x) = α + bx + cx2 that are orthogonal to both of these functions.

Transcribed Image Text:

(f, g)= 1 f(x) g(x) dx