I just want to make sure I'm on the right path with the problem. The problem is as follows:
I rewrote it as follows:
Now $\sin(x)^2$ does oscillate as $x$ approaches infinity and therefore a limit does not exist. However it oscillates between the numbers $-1$ and $1$. Since the denominator would increase without bound and the numerator would only move between $-1$ and $1$, part of me wants to say that the limit is zero.
However a smarter part of me wants to say that the limit does not exist due to the numerator. Could someone shed some light on this problem?