(0) Thẻ Legendre's polynomials are defined on the interval [-1,1]. They are orthogonal with respect to inner product (p,q) = | p(x)q(x)dx -1 The recursion relation for Chebychev polynomials is given by (n + 1)Pn+1(x) = (2n+ 1)xP,(x) – nPn-1 (x) given that Po(x) = 1, P1(x) = x. (i) Find linear least squares approximation to f(x) = e2x. (ii) Calculate the absolute error at x = 0.5. %3D

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