Recall that the first three Legendre polynomials are Xo(x) = 1 X₁(x) = x X₂(x) = x² oj where - These are orthogonal on [-1, 1] with respect to the weight function w(x) = 1. (a) Confirm that ¹₁ \₁(x)\2(x)w(x) dx = 0 (b) Find the values of 1 3 = = [₁ A₂ (2)²³w(x)dx, j = 0, 1, 2. (c) Let f(x) = cos(x). Find the least squares cubic polynomial P(x) with respect to the weight function w(x) = 1 on [-1, 1] minimising [_(f(x) – P(x))³²w(a)dr P(x) = aoλo(x) + α₁λ₁(x) + a₂λ₂ (x). Recall that the theorem from class gave that the coefficients are given by aj = === [ f(x)\; (x)w(x)dx. σj

Recall that the first three Legendre polynomials are Xo(x) = 1 X₁(x) = x X₂(x) = x² oj where - These are orthogonal on [-1, 1] with respect to the weight function w(x) = 1. (a) Confirm that ¹₁ \₁(x)\2(x)w(x) dx = 0 (b) Find the values of 1 3 = = [₁ A₂ (2)²³w(x)dx, j = 0, 1, 2. (c) Let f(x) = cos(x). Find the least squares cubic polynomial P(x) with respect to the weight function w(x) = 1 on [-1, 1] minimising [_(f(x) – P(x))³²w(a)dr P(x) = aoλo(x) + α₁λ₁(x) + a₂λ₂ (x). Recall that the theorem from class gave that the coefficients are given by aj = === [ f(x)\; (x)w(x)dx. σj

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 92E

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