Prove that the limit of the functions

[eljose]

how do you prove that the limit of the functions cos(x) ,sen(x), e^{ix} is 0 when x\rightarrow\infty

another question what would be the limit of (1+x)^i tending x to infinite?..thanx

 

[Zurtex]

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

Same goes for your other problem as well.

 

[TOKAMAK]

Note that
e^{ix}
is bounded:
e^{ix} = \cos(x) + i\sin(x)
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:
\lim_{x \rightarrow \infty} e^{(i-1)x}
the e^{-x} part forces the whole thing to go to zero.