# Toronto Math Forum

## MAT334--2020S => MAT334--Tests and Quizzes => Quiz 2 => Topic started by: Aoqi Xie on February 03, 2020, 12:24:25 PM

Title: TUT0301 Quiz2
Post by: Aoqi Xie 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.

• 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.