Can somebody help me understand this one, please?

I get that the answer is zero, because the numerator goes to infinity due to the

. I also understand that the value of

is always between 0 and 1, which is why we can conclude that the limit overall is zero.

What is a little weird for me is that the limit of

doesn't exist. I can't get past the idea that the limit of a fraction can be defined when the limit of the numerator doesn't exist. What if the numerator was simply

? Then what would the overall limit be (since

can vary between -1 and 1)?

Sorry if I'm being a little dense, but can somebody try to explain this to me?

Thanks.