$($a$)(6$ points$)\underset{n1}{lim}f(x).$ DNE

$($b$)$ points$)\underset{e8}{lim}f(x)=4$

$\underset{x{2}^{-}}{lim}f(x)=-2\frac{\underset{?}{lim}f(x)}{x{2}^{}}=0$

$\underset{x{4}^{}}{lim}f(x)=4\underset{x{4}^{}}{lim}f(x),4$

$($c$)(8$ points$)$ Is $f$ continuous at $x=0?$ Explain. $($d$)(5$ points$)$ Is $f$ continuous at $x=3?$ Explain.

The fuction busteredimucos.

$14.$ Furtion is aid continums.

$f(0)=$ pec.

$\underset{x{0}^{}}{lim}f(x)=\frac{1}{\underset{x{0}^{}}{lim}}f(x)=2$

$f(3)=2$

$\underset{x{5}^{}}{lim}f(x)7=\underset{x{3}^{}}{lim}f(x)=x$

$($e$)(6$ points$)$ Identify one removable discootinuity for $f.$ Then einther redefine $f$ at that $x-$value or define $f$ at that $x-$value such that $f$ is coelinuous at that $x-$value.

$x=2$ remourbu Draoulaity

$f(z)=1$