# Pointwise convergence of arctan(nx)

Question 6 section 8.1 of Introduction to real analysis by Bartle and Sherbert.

Show that $lim(Arctan nx) = (pi/2)sgn x$ for $x$ in R, $x>=0$.

I have a final coming up and I've started doing some of the exercises in the book. I'm not sure how to go about proving this. I know I'm trying to show |Arctan(nx)-$(pi/2)sgn| < \epsilon$ but the sgn function is throwing me off. Any help is appreciated.

Hint: Show the problem reduces to determining $\lim_{x \rightarrow \infty} \arctan(x)$ and $\lim_{x \rightarrow -\infty} \arctan(x)$.