Assume that f is continuous on $[0,\infty)$ and $\lim_{x\to \infty} f(x)=0$ then f is uniformly continuous

Question

Assume that f is continuous on $[0,\infty)$ and $\lim_{x\to \infty} f(x)=0$ then f is uniformly continuous

since given $\lim_{x\to \infty} f(x)=0$ then

$\forall \epsilon 0, \exists M>0, \forall x>M,|f(x)|<\epsilon $

i did't get any ideal any help .thank you...