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Fourier Series - Convergence

  1. Dec 30, 2008 #1
    1. The problem statement, all variables and given/known data

    Please see attached image. From the given information, I am having trouble deriving the left and right hand limits, I just can't figure out what these are...

    [​IMG]

    2. Relevant equations

    None needed.

    3. The attempt at a solution

    In the solution, t is chosen as pi, which I understand. But I just can't figure out how these left and right hand limits are found. Are these limits somehow derived from limits of integration?

    Here is the solution.

    [​IMG]

    Any help will be appreciated.
     
  2. jcsd
  3. Dec 30, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The limits are derived by looking at the original definition of the function. For 0<t<pi, f(t)=t^2. So as t->pi from below f(t)->pi^2. For pi<t<2*pi, f(t)=0. So as t->pi from above f(t)=0.
     
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