MAT334--2020S > Quiz 2

TUT0301 Quiz2

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Aoqi Xie:
Question: Find the limit of the function at the given point, or explain why it doesn't exsit.
f(z)=(1−Imz)-1 at z0=8 and then at z0=8+i.
Answer:

* When z0 = 8,  $$\lim_{z\to 8}f(z)=\lim_{z\to 8}(1- Im[8])^{-1} = \lim_{z\to 8}\frac{1}{1-0} = 1$$
* When z0 = 8+i, $$\lim_{z\to 8+i}f(z)=\lim_{z\to 8+i}(1- Im[8+i])^{-1} = \lim_{z\to 8+i}\frac{1}{1-1}$$, since the denominator cannot be zero, so the limit when z0 = 8+i does not exist.

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