After struggling with this limit for a while, I would really, really appreciate your help with solving this problem.
Let be positive real numbers. Without using the l'Hôpital's rule, find the limit
I tried every method of attack known to me, but to no avail; substitution; trying to utilize the identity , ... nothing seemed to work.
Mathematica says the limit should be , but I have no idea how to arrive at that.
I'd be very grateful for any help.