Author Topic: TUT0701 QUIZ2  (Read 1422 times)

Huyi Xiong

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TUT0701 QUIZ2
« on: January 29, 2020, 07:20:32 PM »
Find the limit at $\infty$ of the given function, or explain why it does not exist.
\begin{align*}
h(z)=\frac{z}{|z|^2}, z \neq 0
\end{align*}

\begin{align}
\lim_{z\to\infty} h(z) &=\lim_{z\to\infty} \frac{z}{|z|^2} \\
&=\lim_{z\to0}\frac{|z|^2}{z} && {\text{since z $\neq 0$}}\\
&=\lim_{z\to0} \frac{z\overline{z}}{z} \\
&=\lim_{z\to0} \overline{z}\\
&=\lim_{(x,y)\to(0,0)}x-iy \\
&=0
\end{align}
« Last Edit: March 03, 2020, 08:15:47 PM by Huyi Xiong »

Victor Ivrii

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Re: TUT0701 QUIZ2
« Reply #1 on: January 30, 2020, 06:39:22 AM »
Wrong reasoning

Huyi Xiong

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Re: TUT0701 QUIZ2
« Reply #2 on: March 03, 2020, 08:17:50 PM »
I've modified my answer now  ;D