Chapter 1.2, Problem 40ES

Let

$f\left(x\right)=\left\{\begin{array}{cc}\frac{x^2-9}{x+3},& x\ne -3\\ k,& x=-3\end{array}\right.$

(a) Find $k$ so that $f\left(-3\right)={\lim }_{x\to -3}f\left(x\right)$ ,

(b) With $k$ assigned the value ${\lim }_{x\to -3}f\left(x\right)$ , show that $f\left(x\right)$ can be expressed as a polynomial.