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Finding a limit of a sequence or proving it diverges

  1. Dec 2, 2012 #1
    1. The problem statement, all variables and given/known data

    Given is a sequence: sin(1), cos(sin(1)), sin(cos(sin(1))) etc. Find the limit of the sequence or prove it diverges.


    2. Relevant equations

    ?

    3. The attempt at a solution

    One way to prove a sequence diverges is to find two subsequences which converge to different limits, but I could not find such.


    I would be thankful for any idea :)
     
  2. jcsd
  3. Dec 2, 2012 #2

    Dick

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    If there is a limit L, then it must satisfy both sin(L)=L and cos(L)=L, mustn't it?
     
  4. Dec 2, 2012 #3

    haruspex

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    Suppose it does converge to some value. What equations could you deduce regarding that value?
    [Dick beat me to the Submit, and was a little more generous with the hint.]
     
  5. Dec 2, 2012 #4

    Dick

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    Yeah, probably too generous in retrospect. I like yours better as a starter hint.
     
    Last edited: Dec 2, 2012
  6. Dec 3, 2012 #5
    Yes, it is true, it must satisfy both sin(L)=L and cos(L)=L, from which follows that the sequence diverges :)

    Thank you very much to both for the help :)
     
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