Question Number 159130 by metamorfose last updated on 13/Nov/21
$${f}\:\in\:\mathcal{C}^{\mathrm{0}} \left(\mathbb{R},\mathbb{R}\right)\:,\:\frac{{f}\left({x}\right)}{{x}}\underset{{x}\rightarrow+\infty} {\rightarrow}\mathrm{0} \\ $$$${Does}\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:{f}\left({x}+\mathrm{1}\right)\:−\:{f}\left({x}\right)\:{exist}? \\ $$