what is $e^{ix}$ as $x \to \infty$

Question

What is the value of the following?

$$\lim_{x \to \infty} e^{-ix}$$

I have looked at a few criteria for convergence, such as the simple ratio test, or the integral test.

In this case the expression $e^{ix}$ rotates around a unit circle as $x$ grows.

Answer 1

Yes it "rotates clockwise around a unit circle" as $x$ grows and therefore the limit doesn't exist.