Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook