Hang on to your hats, folks. We're going to play!Originally Posted bydahbch

Take a look at the numerator. This can be thought of as the difference between the square of two numbers, and 1. So

In a similar fashion, the denominator is the difference between two cubes: and 1. The factorization here is so

Putting these together gives:

=

And now you can take your limit.

-Dan

BTW Thank you for this problem. I haven't had this much fun doing a limit in ages!