Toronto Math Forum
MAT3342020S => MAT334Tests and Quizzes => Quiz 2 => Topic started 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)}xiy \\
&=0
\end{align}

Wrong reasoning

I've modified my answer now ;D