Engineering Board Exam Reviewer · Fourier Series · medium

Find a1 in the Fourier series of f(x)=|x| on (-π,π).

  1. 1.27
  2. -0.64
  3. -1.27
  4. 0

Answer

C. -1.27

Solution

a1= 1π -ππ|x| x,dx= 2π 0π x x,dx= 2π [x x+ x ]0π= 2π(-1-1)=- 4π -1.27.

More Fourier Series questions

  1. Find the constant term a0/2 of the Fourier series of f(x)=x2 on (-π,π).
  2. The square wave f(x)=-1 on (-π,0) and f(x)=1 on (0,π) has Fourier coefficients bn. Find b3.
  3. Find b3 in the Fourier series of f(x)=x on (-π,π).
  4. Which Fourier coefficients vanish for the odd function f(x)=x on (-π,π)?
  5. The Fourier series of f(x)=x2 on (-π,π) is π2/3+4 n=1∞(-1)n/n2 nx. Evaluate it at x=π to find n=1∞ 1n2.
  6. The half-range sine series of f(x)=x on (0,2) is bn π x/2. Find b2.
  7. The square wave f(x)=-1 on (-π,0) and f(x)=1 on (0,π) has a jump at x=0. To what value does its Fourier series converge at x=0?

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