Let $f(x)=\frac{x^2-9}{x+3}.$

$($a$)$ Make a table of values of $f$ at the points $x=-3\mathrm{.}1,-3\mathrm{.}01,-3\mathrm{.}001,$ and so on as far as your calculator can go$.$ Then estimate $\underset{x-3}{lim}f(x).$ What estimate do you arrive at if you evaluate $f$ at $x=-2\mathrm{.}9,-2\mathrm{.}99,-2\mathrm{.}999,$ and so on$?$

$($b$)$ Find $\underset{x-3}{lim}f(x)$ algebraically.