1. (Chebyshev) This problem is a continuation of the example from class involving the Chebyshev polynomials. These Chebyshev polynomials, T. (r) are easily generated by the recursion relationship: To (r) = 1 T(x) = x Tn+1(x) = 2xTn(x) - Tn-1(x) n = 2, 3,... (1) (a) Write out the first six Chebyshev polynomials (To, T,...,T5) using the recursion relationship (1). (b) Apply the Gram-Schmidt orthogonalization procedure to represent the basis set {To(x), T(x), T(x), T3(x), T(x), T5(x)} as an orthogonal set. Let the inner product be defined as we did in class with the interval from a = -1 to b = 1. That is, (51, 52) = (T,T;) = | T;(2)T; (x) dx (2)