I'm trying to prove that the limit of sin x as x->infinity is not equal to 1/2. I know that this is true, but I can't seen to figure out how to prove it using the precise definition of a limit.
What I have so far is this,
abs(sin x - 1/2)<e whenever x>M
I also think that I can use the fact that,
abs(sin x)<=1 for all x
But I don't know for sure. I've also seen some really extensive proofs for stuff like sin x/x (ref 1). So I may be doing this completely wrong.
Thanks for any help.