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Ex.1 Let f(x) be a 27-periodic and odd function, coinciding with the function (x) = x² in the interval [0, 7), and such that ƒ(k) = 0, Vk = Z. The Fourier series of f is: (A) not converging in quadratic norm to f(x) on [-π,π] pointwise converging to f(x) on R ∞ 2π2 (C) in the form 3 +Σak cos(kx), ak #0 k=1 ∞ 2π2 (D) in the form 3 +Σ bk sin(kx), bk 0 k=1

Ex.1 Let f(x) be a 27-periodic and odd function, coinciding with the function (x) = x² in the interval [0, 7), and such that ƒ(k) = 0, Vk = Z. The Fourier series of f is: (A) not converging in quadratic norm to f(x) on [-π,π] pointwise converging to f(x) on R ∞ 2π2 (C) in the form 3 +Σak cos(kx), ak #0 k=1 ∞ 2π2 (D) in the form 3 +Σ bk sin(kx), bk 0 k=1

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.5: Applications Of Inner Product Spaces
Problem 89E
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Ex.1 Let f(x) be a 27-periodic and odd function, coinciding with the function (x) = x² in the interval [0, 7), and such that ƒ(k) = 0, Vk = Z. The Fourier series of f is: (A) not converging in quadratic norm to f(x) on [-π,π] pointwise converging to f(x) on R ∞ 2π2 (C) in the form 3 +Σak cos(kx), ak #0 k=1 ∞ 2π2 (D) in the form 3 +Σ bk sin(kx), bk 0 k=1
Transcribed Image Text:Ex.1 Let f(x) be a 27-periodic and odd function, coinciding with the function (x) = x² in the interval [0, 7), and such that ƒ(k) = 0, Vk = Z. The Fourier series of f is: (A) not converging in quadratic norm to f(x) on [-π,π] pointwise converging to f(x) on R ∞ 2π2 (C) in the form 3 +Σak cos(kx), ak #0 k=1 ∞ 2π2 (D) in the form 3 +Σ bk sin(kx), bk 0 k=1
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