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**Help! Prove Lim x--infinity cos(nx) = dne**

Hey guys! I am new here however, I have been lurking around for a while. I need some help with a problem that I am currently working on. Here it is:

## Homework Statement

Prove Lim x--infinity cos(nx) = does not exist

## The Attempt at a Solution

As of now, I am not quite sure how to approach the problem. I know that I can say that if x is a multiple of 2π then it will converge to 1 however, if it is not a multiple of 2π then it will simply oscillate until infinity. As such, the limit does not exist. However, I doubt that that is what is required of the problem. I am thinking that there must be some systematic setup that I can use to prove this problem otherwise. Is there such a way or is my reasoning correct?

In our other problems, we used epsilon-delta proofs to prove that certain functions converged to p.

Anythings would help! Thanks guys!