Answer
$a.\quad 0$
$b.\quad $Approaching x=3 from the right,
the square root is not defined so the right-sided limit does not exist.
Work Step by Step
$a.\quad $
Approaching x=3 from the left,
both the numerator and denominator of the radicand are negative,
so the root is defined, as the radicand is positive.
Combining the quotient and fractional power rule of Th.2.3,
$\displaystyle \lim_{x\rightarrow 3^{-}}\sqrt{\frac{x-3}{2-x}}=\sqrt{\frac{-0}{-1}}=0$
$b.\quad $
Approaching x=3 from the right, the numerator is positive,
the denominator is negative, so the square root is not defined,
as the radicand is negative.
Thus, the right-sided limit does not exist
