According to L'H?pital's law, lim(x→+∞)f(x)/x is the limit of 0/0 type. Yes, the law of lobida. The numerator and denominator get derivatives respectively, and the limit of derivative division is equal to the original limit.

So lim (x → +∞) (f (x)/x) = lim (x→ +∞) (f' (x)/x') = lim (x→ +∞) f' (x)/lim (x→ +∞)1= 0/.