f(x)/x tinde la 0

[Adrian Zahariuc]

Fie \( f: (0,\infty) \to (0,\infty) \) continua astfel incat
\( \lim_{x \to \infty}f\left(x+\frac{f(x)}{x}\right)-f(x) =0. \)
Sa se arate ca
\( \lim_{x \to \infty}\frac{f(x)}{x}=0. \)