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Let f:R→Rf: \mathbb {R \to R} f:R→R be a non-zero function such that limx→∞f(xy)x3\displaystyle \lim_{x \to \infty} \frac{f(xy)}{x^3} x→∞limx3f(xy) exists for all y>0y>0y>0. Let g(y)=limx→∞f(xy)x3g(y) = \displaystyle \lim_{x \to \infty} \frac{f(xy)}{x^3}g(y)=x→∞limx3f(xy) and g(1)=1g(1)=1g(1)=1, then what is g(y)g(y)g(y) for all y>0y>0y>0?
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