The Fourier Series of a Function $f ( x ) = x$

question 16

Multiple Choice

The Fourier Series of a function $f ( x ) = x$ defined on $[ - 1,1 ]$ is $f ( x ) = a _ { 0 } / 2 + \sum _ { n - 1 } ^ { \infty } \left( a _ { n } \cos ( n \pi x ) + b _ { n } \sin ( n \pi x ) \right)$ where Select all that apply.

• A) \(a _ { 0 } = 1\)
• B) \(a _ { n } = 0\)
• C) \(a _ { n } = \int _ { - 1 } ^ { 1 } x \sin ( n \pi x ) d x\)
• D) \(b _ { n } = 0\)
• E) \(b _ { n } = \int _ { - 1 } ^ { 1 } x \sin ( n \pi x ) d x\)