$g_n(x)=\frac{\frac{x}{n\:}}{1+\frac{x^2}{n^2}\:}$ proving uniform convergence

Question

$$g_n(x)=\frac{\frac{x}{n\:}}{1+\frac{x^2}{n^2}\:}$$

I have to show that it converges uniformly in $[0,\infty)$, I already got that it converges pointwise to $\frac{1}{2}$ but I am just stuck on uniformly proving it.

I have tried using Weierstrass M-Test and Abel's Uniform Convergence Test, but I always reach something not logical.

Answer 1

$g_n$ does not converge uniformly. It converges pointwise to 0 and $g_n(n)=\frac 1 2$ so it does not converge uniformly.