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Finding a limit of a sequence or proving it diverges

  • Thread starter nikolafmf
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  • #1
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Homework Statement



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


Homework Equations



?

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 :)
 

Answers and Replies

  • #2
Dick
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Homework Statement



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


Homework Equations



?

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 :)
If there is a limit L, then it must satisfy both sin(L)=L and cos(L)=L, mustn't it?
 
  • #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.]
 
  • #4
Dick
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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.]
Yeah, probably too generous in retrospect. I like yours better as a starter hint.
 
Last edited:
  • #5
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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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