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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.

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.