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Let a be contained in C(complex numbers) and p is a polynomial, then p(x)-->p(a) as x-->a.

Since a polynomial is built from constants, x, addition and multiplication, this statement is a corollary of two facts: $\displaystyle \lim_{x\to a}(f(x)+g(x))=\lim_{x\to a}f(x) + \lim_{x\to a}g(x)$, and $\displaystyle \lim_{x\to a}(f(x)\cdot g(x))=(\lim_{x\to a}f(x))\cdot (\lim_{x\to a}g(x))$. (Well, technically, you also need $\displaystyle \lim_{x\to a}c=c$ for a constant $\displaystyle c$ and $\displaystyle \lim_{x\to a}x=a$.) It is suggested that you break a polynomial into a sum of monomials and use the fact about the sum of limits above. Also, it is suggested that you show that $\displaystyle \lim_{x\to a} x^n=a^n$ by induction on $\displaystyle n$ using the fact about the product of limits above.