A3 Find the half-range Fourier cosine series expansion for the function f(x) = x(Lx), for 0 < x < L. By considering x = L 듬, use your result to show that (-1) k2 12 k=1 Sketch the graph of the even periodic extension (period 2L).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 65E
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A3 Find the half-range Fourier cosine series expansion for the function
f(x) = x(L − x), for 0 < x < L.
By considering x = 플,
use your result to show that
(−1)
k2
+2
12°
k=1
Sketch the graph of the even periodic extension (period 2L).
Transcribed Image Text:A3 Find the half-range Fourier cosine series expansion for the function f(x) = x(L − x), for 0 < x < L. By considering x = 플, use your result to show that (−1) k2 +2 12° k=1 Sketch the graph of the even periodic extension (period 2L).
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