Complex Variables : Limits
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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