(2) Let $G_n(x) = \frac{1}{\pi} \arctan(nx) + \frac{1}{2}$. (3) Show that $\lim_{n \to \infty} G_n(x) = \begin{cases} 1, & x > 0 \\ \frac{1}{2}, & x = 0 \\ 0, & x < 0 \end{cases}$ (4)
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