Let o, 1 Let (r) (1) For any polynomial p(x) of degree n + 1, n...

Transcribed Image Text:

Let o, 1 Let (r) (1) For any polynomial p(x) of degree n + 1, n be distinct real numbers and 1(r) be the Lagrange's basis function. II(-k). Prove that = n 1 p(x) - ΣP(Tr)lk(x) = p(n+1)(x)(x). (n+1)! (2) If further xo,...,n are Gauss-Legendre points in the interval [-1, 1], then LL(x k=0 l(r)l, (x) dx = 0 for i‡j. Let o, 1 Let (r) (1) For any polynomial p(x) of degree n + 1, n be distinct real numbers and 1(r) be the Lagrange's basis function. II(-k). Prove that = n 1 p(x) - ΣP(Tr)lk(x) = p(n+1)(x)(x). (n+1)! (2) If further xo,...,n are Gauss-Legendre points in the interval [-1, 1], then LL(x k=0 l(r)l, (x) dx = 0 for i‡j.