### Author Topic: Quiz#2 Lec0101 B  (Read 234 times)

#### Xun Zheng

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##### Quiz#2 Lec0101 B
« on: October 02, 2020, 11:15:53 AM »
Question: Find the limit of each function at the given point, or explain why it does not exsit.
f(z)=(1−Im z)-1 at z0=8
and then at
\begin{equation*}
z_{0}=8+i.
\end{equation*}

• When z0 = 8, we have  $$\lim_{z\to 8}f(z)=\lim_{z\to 8}\frac{1}{1- Im[8]} = \lim_{z\to 8}\frac{1}{1-0} = 1$$
• When z0 = 8+i, we have $$\lim_{z\to 8+i}f(z)=\lim_{z\to 8+i}\frac{1}{1- Im(8+i)} = \lim_{z\to 8+i}\frac{1}{1-1}$$ Since the denominator cannot be zero, hence when z0 = 8+i, the limit does not exist.