# 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 $$y>0$$?

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