Prove that the limit of the functions

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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
 

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  • #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.
 
  • #3
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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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