Function Limits of Quotients of Polynomials
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Problem:
Prove that
lim
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.
