Determine the convergence being, Be,
$$f(x)=\lim_{n\rightarrow+\infty}\frac{x}{1+x^{n}},\hspace{5mm}\forall x\geq0$$
what I want is to graph that function, but as I do analytically, because for $ n = 0 $ and $ n = 1 $ are a line and a hyperbole, but then while the $ n \rightarrow \infty $ 'apparently' $ f (x) \rightarrow0 $

Recall that for $x \ge 0$ we have
$$\lim_{n\to\infty} x^n = \begin{cases}
0,  & \text{if $x < 1$} \\
1, & \text{if $x = 1$} \\
+\infty, & \text{if $x > 1$} \\
\end{cases}$$
Now clearly $$\lim_{n\to\infty} \frac{x}{1+x^n} =  \begin{cases}
x,  & \text{if $x < 1$} \\
\frac12, & \text{if $x = 1$} \\
0, & \text{if $x > 1$} \\
\end{cases}$$
