ISI 2016 B.Math Entrance (3)
Calculus
Level
3
Let \(f: \mathbb {R \to R} \) be a non-zero function such that \(\displaystyle \lim_{x \to \infty} \frac{f(xy)}{x^3} \) exists for all \(y>0\). Let \(g(y) = \displaystyle \lim_{x \to \infty} \frac{f(xy)}{x^3}\) and \(g(1)=1\), then what is \(g(y)\) for all \(y>0\)?
by
Md Zuhair