Function Limits of Quotients of Polynomials
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Problem:
Prove that
\begin{equation}
\lim_{x\to a}\,\frac{P_n(x)}{Q_m(x)}=\frac{P_n(a)}{Q_m(a)}
\end{equation}
where $P_n(x)$ and $Q_m(x)$ are arbitrary polynomials of degrees $n$ and $m$, respectively, and $Q_m(a)\neq 0$.
Answer:
It is true that \begin{equation} \lim_{x\to a}\,\frac{P_n(x)}{Q_m(x)}=\frac{P_n(a)}{Q_m(a)} \end{equation} where $P_n(x)$ and $Q_m(x)$ are arbitrary polynomials of degrees $n$ and $m$, respectively, and $Q_m(a)\neq 0$.
