Chapter 1.R, Problem 45E

Let

$f\left(x\right)=\{\begin{array}{l}\sqrt{-x}\text{ if }x<0\\ 3-x\text{ if 0}\le x<3\\ {\left(x-3\right)}^2\text{ if }x>3\end{array}$

(a) Evaluate each limit, if it exists.

(i) $\underset{x\to 0^{+}}{{\displaystyle \lim }}f\left(x\right)$

(ii) $\underset{x\to 0^{-}}{{\displaystyle \lim }}f\left(x\right)$

(iii) $\underset{x\to 0}{{\displaystyle \lim }}f\left(x\right)$

(iv) $\underset{x\to 3^{-}}{{\displaystyle \lim }}f\left(x\right)$

(v) $\underset{x\to 3^{+}}{{\displaystyle \lim }}f\left(x\right)$

(vi) $\underset{x\to 3}{{\displaystyle \lim }}f\left(x\right)$

(b) Where is f discontinuous?

(c) Sketch the graph of f.