LeL $f: (0, \infty)\to R$ be continuous and $f(x)\leq f(nx)$ prove $\lim\limits_{x\to\infty} f(x)$ exists
$f\colon(0,\infty)\to \mathbb R$ be continuous ; $f(x)\le f(nx) , \forall n \in \mathbb N , \forall x >0$ , then $\lim_{x\to \infty} f(x)$ exists?