Answer
See below.
Work Step by Step
The problem arises when $f(a)$ is not defined, but the limit at $x=a$ exists.
For example, consider
$f(x)=\displaystyle \frac{(x-1)(x-2)}{(x-1)}$
which is not defined for $x=a=1$, but the graph of $f$ looks exactly like the graph of $y=x-2$, excluding the point $(1,-1)$.
The limit is
$\displaystyle \lim_{x\rightarrow 1}f(x)=-1$
but Fiona could not find it.
Another example:
$f(x)=\displaystyle \frac{xe^{x}}{x}$
which is not defined for $x=0$, but
$\displaystyle \lim_{x\rightarrow 0}f(x)=e^{0}=1$
