a. Find the least squares approximation to f(x) = xe-2x over the interval -1 ≤ x ≤ 1 from the span of 1, x, x2 using the stan- dard inner product on C[-1,1].
b. Calculate the error in the approximation using the inner product generated norm.
c. Determine the Taylor series expansion for f(x) through the quadratic term. Calculate the error in this approxi- mation and compare to the error in the least squares approximation.