Showing that a sequence of function does not converge uniformly

Question

Let $f_n$ be a sequence of functions defined on $(0,\infty)$ by $f_n=\frac{nx}{1+nx^2}$. Check whether or not this sequence converges uniformly on $(0,\infty)$. The sequence converges to $\frac{1}{x}$ pointwise. But I think it will not converge uniformly near 0 but I don't know how to show it. Note that since the domain is $(0,\infty)$ the limit function is also continuous. So are there any other arguments to show this?