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Calculate the limit of the series

  1. Apr 14, 2009 #1
    need to calculate the limit of the series

    (cos(a/n))^(n^3) n goes to infinity and a=!0


    i try that :

    e^L


    L= the limit of (n^3)*ln(cos(a/n))


    what now ???


    TNX !
     
  2. jcsd
  3. Apr 14, 2009 #2

    Dick

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    Re: limit

    L has the form 0*infinity. Use l'Hopital's theorem on it to try and figure out the limit. You may have to use l'Hopital more than once.
     
  4. Apr 14, 2009 #3
    Re: limit

    hello Dick !

    first of all tnx.

    i cant use l'Hopital's theorem cause n =1,2,3.....

    so F(n) not differentiable .
     
  5. Apr 14, 2009 #4

    Dick

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    Re: limit

    f(x)=ln(cos(a/x))*x^3 is differentiable. If you know the limit of f(x) as x->infinity, then you know the limit of L as n->infinity.
     
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