Consider the function

$f(x)=\{\begin{array}{ccc}sin(x)& if& x0\\ 2^x& if& x>0\end{array}$

$($a$)$ Is $f$ continuous at $x=3?$ Use the definition of continuity to justify.

$($b$)$ Is $f$ continuous at $x=0?$ Use the definition of continuity to justify.