Question

Can l' hospital rule be applied to function giving (infinity/infinity) form?

Answer 1

YES.
L'hospital rule can be applied to function giving (infinity/infinity) form.
This is one common use of L'Hôpital's Rule.
If you are finding a limit of a fraction, where the limits of both the numerator and the denominator are infinite, then l'Hôpital's Rule says that the limit of the fraction is the same as the limit of the fraction of the derivatives