Answer
If the limit is $0$, pros include offering a real value for the limit that is equivalent to the value of the function at $0$. Cons include neglecting to consider that the limit from the left does not exist, and therefore, ignoring the definition of a limit.
Work Step by Step
If the limit is undefined, pros include following the definition of a limit where the left and right limits exist and are equal to each other. Cons include offering limited information about the nature of the function near $x=0$.
