# Prove that the limit of the functions

## Main Question or Discussion Point

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
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.

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.
$$\lim_{x \rightarrow \infty} e^{(i-1)x}$$