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Problem 3 Please prove Thm. 5.6 Differentiation of Fourier Series Let f be continuous on -L, L) and suppose f(L) = f(-L). Let f' be piecewise continuous on [-L, L]. Then f(r) equals its Fourier series for -LS&SL 1 an and, at each point in (-L, L) where f"(a) exists, nx na f'(x)=(-a, sin("") + b, cos("")) L n=1

Problem 3 Please prove Thm. 5.6 Differentiation of Fourier Series Let f be continuous on -L, L) and suppose f(L) = f(-L). Let f' be piecewise continuous on [-L, L]. Then f(r) equals its Fourier series for -LS&SL 1 an and, at each point in (-L, L) where f"(a) exists, nx na f'(x)=(-a, sin("") + b, cos("")) L n=1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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Problem 3 Please prove Thm. 5.6 Differentiation of Fourier Series Let f be continuous on -L, L] and suppose f(L) = f(-L). Let f' be piecewise continuous on [-L, L]. Then f(r) equals its Fourier series for -L≤x≤L, f(x)= ao+a, cos(") +- b, sin( L and, at each point in (-L, L) where f"(a) exists, f'(x) = ( -Σ(-a, sin (¹) + b₂ cos( ᏤᏤᏤᎳᏗ . (HTF)).
Transcribed Image Text:Problem 3 Please prove Thm. 5.6 Differentiation of Fourier Series Let f be continuous on -L, L] and suppose f(L) = f(-L). Let f' be piecewise continuous on [-L, L]. Then f(r) equals its Fourier series for -L≤x≤L, f(x)= ao+a, cos(") +- b, sin( L and, at each point in (-L, L) where f"(a) exists, f'(x) = ( -Σ(-a, sin (¹) + b₂ cos( ᏤᏤᏤᎳᏗ . (HTF)).
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