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**Quiz 2 / TUT0301 Quiz2**

« **on:**February 03, 2020, 12:24:25 PM »

Question: Find the limit of the function at the given point, or explain why it doesn't exsit.

Answer:

f(z)=(1−Imz)

^{-1}at z_{0}=8 and then at z_{0}=8+i.Answer:

- When z
_{0}= 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 z
_{0}= 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 z_{0}= 8+i does not exist.