Answer
(a) No.
(b) No.
Work Step by Step
(a) With the concept “limit” we only examine the behavior of a function near a point while we are not interested in knowing the value of the function at the point. So, by knowing only $f(2)=4$ we cannot say anything about $\lim_{x \to 2}f(x)$; it may even not exist.
(b) As it was explained in part (a), we are not interested in knowing the value of the function at the point. So, by just knowing $\lim_{x \to 2}f(x)$ we cannot say anything about $f(2)$; it either can be any real number or may not be defined.
