# Complex Variables : Limits

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3. Let n be a positive integer and let P(z) and Q(z) be polynomials, where Q(z0) ≠ 0. Find the following limits. (Please explain by using relevant theorem.)

(a) lim 1/ zn (z0 ≠ 0)

z→z0

(b) lim (iz3 -1) / (z + i)

z→i

(c) lim P(z) / Q(z)

z→z0

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First, I solve the problem (c) and use this result to solve (a) and (b).

For polynomials and , if , then we have .

Proof:

We ...

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