Unknown theorem in my textbook for solving limit problems

[midododo11]

Has anybody heard of this theorem before? because it's in my school book and it works with most limit problems but I can't find its name or even find it in any reference book

Any help or guidance would be appreciated, thanks

 

[jbunniii]

(x - a) is a factor of both the numerator and the denominator. Try canceling it and see what results.

 

[Dick]

Or l'Hopital's theorem proves it easily. It's easy enough to prove that I don't think it rates it's own name or a place in reference books.