Chapter 2.3, Problem 52E

l.et

$g(x)=\{\begin{array}{l}x\text{if}x<1\\ 3\text{if}x=1\\ 2-x\text{if}1<x\le 2\\ x-3\text{if}x>2\end{array}$

(a) Evaluate each of the following, if it exists.

(i) $\underset{x\to 1^{-}}{\lim }g(x)$

(ii) $\underset{x\to 1}{\lim }g(x)$

(iii) $g(1)$

(iv) $\underset{x\to 2^{-}}{\lim }g(x)$

(v) $\underset{x\to 2^{+}}{\lim }g(x)$

(vi) $\underset{x\to 2}{\lim }g(x)$

(b) Sketch the graph of g.