Two young mathematicians consider a way to compute limits using derivatives.

Check out this dialogue between two calculus students (based on a true story):
Devyn
Riley! I think I have a problem!
Riley
What kind?
Devyn
I was calculating some limits last night.
Riley
Fun times.
Devyn
I realized something. L’Hôpital’s Rule lets us deal with and forms.
Riley
Right!
Devyn
But what about all the other indeterminate forms? Like this one: .
Riley
So and . This is a -form, not or .
Devyn
EXACTLY! L’Hôpital’s Rule only works on those fraction forms, not on this product form.
Riley
Can you take and write it like a fraction?
Devyn
Oh, like how ?
Riley
Yes, because then .
Devyn
Great! That means my limit is the same as which is a -form!
By L’Hôpital’s Rule,
Write the function as a fraction with a numerator of .
Write the function as a fraction with a numerator of .