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Prove that the limit of the functions

  1. Jul 20, 2005 #1
    how do you prove that the limit of the functions [tex] cos(x) ,sen(x), e^{ix} [/tex] is 0 when [tex] x\rightarrow\infty [/tex]

    another question what would be the limit of [tex] (1+x)^i [/tex] tending x to infinite?..thanx
     
  2. jcsd
  3. Jul 20, 2005 #2

    Zurtex

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    I don't know what sen is but cos(x) and eix have no limit as x approches infinity.

    Same goes for your other problem as well.
     
  4. Jul 20, 2005 #3
    Note that
    [tex] e^{ix} [/tex]
    is bounded:
    [tex] e^{ix} = \cos(x) + i\sin(x) [/tex]
    so, for large, or arbitrary x, e^{ix}, the imaginary part will never be greater than 1, and the real part will never be greater than 1.
    Thus, if you had:
    [tex] \lim_{x \rightarrow \infty} e^{(i-1)x} [/tex]
    the e^{-x} part forces the whole thing to go to zero.
     
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