Chapter 1.4, Problem 120E

Signum Function The signum function is defined by

$\mathrm{sgn}(x)=\{\begin{array}{cc}-1,& x<0\\ 0,& x=0\\ 1,& x>0\end{array}$

Sketch a graph of sgn(x) and find the following (if possible).

(a) $\underset{x\to 0}{\lim }\mathrm{sgn}(x)$

(b) $\underset{x\to 0^{+}}{\lim }\mathrm{sgn}(x)$

(c) $\underset{x\to 0}{\lim }\mathrm{sgn}(x)$