Let $g_{n}(x)=\frac{n x}{1+n^{2} x^{2}}, x \in[0, \infty) .$ Which of
the following is true as $n \rightarrow \infty$ ?
1. $g_{n} \rightarrow 0$ pointwise but not uniformly
2. $g_{n} \rightarrow 0$ uniformly
3. $g_{n}(x) \rightarrow x \quad \forall x \in[0, \infty)$
4. $g_{n}(x) \rightarrow \frac{x}{1+x^{2}} \quad \forall x \in[0, \infty)$