Let p0, p1, and p2 be the orthogonal polynomials described below, where the inner product on P4 is given by evaluation at -2, -1, 0, 1, 2. Find the othogonal projection of 3t^(3) onto Span{p0,p1,p2}. p0(t) = 4
p1(t) = 3t
p2(t) = t^(2) -2

Step-by-step explanation:

Let W =  be orthogonal polynomials which is equal to , which defines the inner products as

Now, we find the orthogonal projection of on W.

So the projection is

Therefore,

step-by-step explanation:

f(gx)=f(1/x+2)

=(1/x+2)+2

=(1+2x)/2+2

=(1+2x+4)/2

= (2x+5)/2

the answer is $23.63