Calculate the limit:
$ \lim_{x\to\infty}\frac{\ln(x^\frac{5}2+7)}{x^2} $
This is a part of the whole limit that I'm trying to calculate, but it is this part I have a hard time to figure out why this limit is zero.
Any ideas? Is it reasonable to say that the quotient will be zero because of the denominator function grows faster than the nominator?