Chapter 1 - Functions and Limits - 1.6 Calculating Limits Using the Limit Laws - 1.6 Exercises - Page 71: 47

(i) $1$ (ii)$-1$ (iii)$DNE$ (iv) $1$

Looking at the graph we see that: (i) $\lim\limits_{x \to 0^{+}}sgn(x) = 1$ (ii)$\lim\limits_{x \to 0^{-}}sgn(x) = -1$ (iii)$\lim\limits_{x \to 0}sgn(x) = DNE$ because $-1\ne1$ (iv) $\lim\limits_{x \to 0}|sgn(x)| = 1$ because $|-1|=|1|$ so the limit of the absolute value of the function does exist