Lets say we want to know what the limit approaches for the function
Now we know oscillates between and
So we can say:
(We know the value of the limit must be somewhere between these two values.)
But the original question asks for
So multiply throughout the equation with
We are given that approaches
Now observe, the value must be 0. It lies between 0 and... well uhm... 0 So it must be 0 itself.
And so we have calculated the limit!
(The proof behind it will be in your textbook, go through it again now that I've shown you the idea behind the theorem.)