10. Let f be a continuous function with period 27. If f is an even function (that is, ƒ(x) = f(−x) for every x), and ∞ ao + Σ(an cos nt + b₂ sin nt) n=1 is the Fourier series for f, then bn = :0 for every n.

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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is the following statement true or false ? 

10. Let f be a continuous function with period 27. If ƒ is an even function (that
is, f(x) = f(-x) for every x), and
∞
+ Σ(an cos nt + bn sin nt)
2
n=1
ao
is the Fourier series for f, then bn
=
0 for every n.
Transcribed Image Text:10. Let f be a continuous function with period 27. If ƒ is an even function (that is, f(x) = f(-x) for every x), and ∞ + Σ(an cos nt + bn sin nt) 2 n=1 ao is the Fourier series for f, then bn = 0 for every n.
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