This from my textbook
I understand that the domain of a function need to be real numbers to apply l’Hôpital’s Rule.
But the textbook also provides a theorem below.
It looks like to me that we can apply l’Hôpital’s Rule every time by coming up with a function first, then apply it to the sequence. Or we can only apply l’Hôpital’s Rule to see if the limit exists, if it exists, fine, the limit of sequence is the same limit. But if a function's limit doesn't exist, there no point to use l’Hôpital’s Rule?