19.2.2.6 Convergence in normed spaces

Problem: Find out the character of the convergence of the sequence of the function: \[ f_{n}(x)=\operatorname{tg}^{-1} \frac{\pi}{2 n} x \] a) on the set \( \mathbb{R}, b) \) on the segment \( [0 ; 1] \).