The Fourier series of the function $f ( x ) = | x |$ on $[ - 2,2 ]$ is Select all that apply.
A) contains cosine terms
B) contains sine terms
C) contains sine and cosine terms
D) contains a constant term
E) contains sine, cosine, and constant terms

Question

Quizplus · Accepted Answer

The Fourier series of $f(x) = |x|$ on $[-2,2]$ is an even function, which means it will only contain cosine terms and possibly a constant term. Sine terms are associated with odd functions, which $f(x) = |x|$ is not.

The Fourier Series of the Function f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣

The Fourier Series of the Function $f ( x ) = | x |$