I'm not too sure how to approach this type of question.
Definition of cluster point of $S$: $\forall \epsilon \gt 0$, $(x_0- \epsilon , x_0+ \epsilon ) \cap (S \setminus {x_0}) \neq \phi $
A real number $L$ is called the limit of $f$ at $x_0$ is defined as $\forall \epsilon \gt 0$, $\exists \delta \gt 0$ such that $0 \lt |x-x_0| \lt \delta$, $x \in S$, implies $|f(x)-L| \lt \epsilon$.
We denote this by $\lim_{x\to x_0} f(x)=L$
Essentially, it wants me to prove that there can only exist one $Y$ value for an $X$ value by showing there exists at most one limit given $x_0$ is a cluster point.