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Prove this (periodic function)

  1. May 5, 2009 #1
    plz prove this (periodic function)

    1. The problem statement, all variables and given/known data

    if f is periodic continuous function with period 1 then show there exists x such that f(x+pi)=f(x)

    2. Relevant equations



    3. The attempt at a solution
    i am trying in this way,considering interval [pi,pi+1],and taking g(x)=f(x+pi)-f(x).and trying to use intermediate value theorem...but stuck on that
     
  2. jcsd
  3. May 5, 2009 #2
    Re: plz prove this (periodic function)

    Sine and cosine are cyclic functions...
     
  4. May 5, 2009 #3
    Re: plz prove this (periodic function)

    r u tryin to use fourier expansion
     
  5. May 5, 2009 #4
    Re: plz prove this (periodic function)

    sayan2009, I like your function g(x), and I like that you are using the IVT, but your interval doesn't work. You need numbers a and b where g(a) will be positive and g(b) will be negative (or vice versa). I bet you will have good luck if you first consider the fact that f must attain its maximum and minimum values.
     
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