Toronto Math Forum

MAT334--2020S => MAT334--Tests and Quizzes => Quiz 2 => Topic started by: Huyi Xiong on January 29, 2020, 07:20:32 PM

Title: TUT0701 QUIZ2
Post by: Huyi Xiong 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}
Title: Re: TUT0701 QUIZ2
Post by: Victor Ivrii on January 30, 2020, 06:39:22 AM
Wrong reasoning
Title: Re: TUT0701 QUIZ2
Post by: Huyi Xiong on March 03, 2020, 08:17:50 PM
I've modified my answer now  ;D