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Convergence in C[a,b]

  1. Dec 21, 2011 #1
    Folks,

    For C[0,2*pi] and given a function f(x)=sin(x) the supremum |f(x)|=max|f(x)| for x in [a,b]

    I calculate the sup|f(x)| to be = 0 but my notes say 1. The latter answer would be the case if f(x) was cos(x)....right?
     
  2. jcsd
  3. Dec 21, 2011 #2

    micromass

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    With both sin(x) and cos(x), the supremum is 1. Can you explain how you found 0 as answer??
     
  4. Dec 21, 2011 #3
    I thought you take the highest evaluation resulting from either sin(0) and sin(2*pi)? Both are 0...?
     
  5. Dec 21, 2011 #4

    micromass

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    No, you take |f(x)| for all values in [itex][0,2\pi][/itex]. And you take the maximum for all those values x. So the maximum can also occur at 1/2 or 1 or whatever.
     
  6. Dec 21, 2011 #5
    ahh right...you consider all values from 0 to 2pi on the real line and it is sin(pi/2) in this case?

    Thanks
     
  7. Dec 21, 2011 #6

    micromass

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    Yes, both at [itex]\pi/2[/itex] as at [itex]3\pi/2[/itex] is the maximum reached.
     
  8. Dec 21, 2011 #7
    Thanks,

    Warning noted.
     
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