Proving that cosine diverges as x->infinity. Not sure on how to go about this

I've to prove that as we take the limit of cosine as x goes to + infinity, the limit DNE. I've looked on different forums and sites, but all have methods I barely understand. I'm not very familiar with the Delta-Epsilon definition of limits. I've tried to look at the sticky at the top and try to understand but this is due tomorrow and I won't learn it at the moment unless it's the only way.

What's a good way to start off a proof like this? I know the reasons why it doesn't exist, as it oscillates between -1 and 1, but I need to have a proof.

Thanks

Re: Proving that cosine diverges as x->infinity. Not sure on how to go about this

Quote:

Originally Posted by

**LightningZI** I've to prove that as we take the limit of cosine as x goes to + infinity, the limit DNE. I've looked on different forums and sites, but all have methods I barely understand. I'm not very familiar with the Delta-Epsilon definition of limits. I've tried to look at the sticky at the top and try to understand but this is due tomorrow and I won't learn it at the moment unless it's the only way.

What's a good way to start off a proof like this? I know the reasons why it doesn't exist, as it oscillates between -1 and 1, but I need to have a proof.

Thanks

Are you familiar with the sequential characterization of limits?

It states that if a limit exists it is independant of the sequence used to approch the point.

Translation. For any two sequences

So if you can find two different seqences that go to infinity, but

that will show that the limit does not exist.