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Prove this (periodic function)

  • Thread starter sayan2009
  • Start date
  • #1
14
0
plz prove this (periodic function)

Homework Statement



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

Homework Equations





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
 

Answers and Replies

  • #2
65
0


Sine and cosine are cyclic functions...
 
  • #3
14
0


r u tryin to use fourier expansion
 
  • #4
392
0


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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