$[10$ pts$.]$

$5.$ Use the THREE part definition of continuity and analytically show how$/$why each part passes or fails, to determine if $f(x)$ is continuous at $x=3.$ If you decide that it's discontinuous, clearly state which part of thre definition fails and whether the discontinuity is removable or non$-$removable.

$($a$)f(x)=\{\begin{array}{ccc}-x^2-5x& 12if& x3\\ 4cos(\frac{}{3})-8& if& x>3\end{array}$

$($b$)f(x)=\frac{x^3-27}{x-3}$

$(15$ pes.$)$

$6.$