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Show that the Fourier sine series of the function defined by f(z) =r²-3r on 0

Show that the Fourier sine series of the function defined by f(z) =r²-3r on 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. (a) Show that the Fourier sine series of the function defined by f(x) = r- 3r o 0<r<3 can be written as (2m – 1)az sin 72 f(r) = r - 3r Σ (2m-1)3 (b) Sketch the series on the interval -6 <a< 6. Can this series be differentiated term- by-term? Justify your answer. Find the Fourier cosine series for g(æ) = 2r – 3 on 0<r< 3.
Transcribed Image Text:8. (a) Show that the Fourier sine series of the function defined by f(x) = r- 3r o 0<r<3 can be written as (2m – 1)az sin 72 f(r) = r - 3r Σ (2m-1)3 (b) Sketch the series on the interval -6 <a< 6. Can this series be differentiated term- by-term? Justify your answer. Find the Fourier cosine series for g(æ) = 2r – 3 on 0<r< 3.
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