<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[a4paper,12pt]{article}
\newcommand{\ds}{\displaystyle}
\usepackage{epsfig}
\begin{document}
\parindent=0pt

\begin{center}
\textbf{Partial Differentiation}

\textit{\textbf{Limits}}
\end{center}

\textbf{Question}

Evaluate the given limit. If the limit does not
exist, explain why.

$$ \lim_{(x,y)\to(0,1)} \frac{x^2(y-1)^2}{x^2+(y-1)^2}$$


\textbf{Answer}

$\ds \lim_{(x,y)\to(0,1)} \frac{x^2(y-1)^2}{x^2+(y-1)^2}=0$

This is because
$$ 0 \le \left | \frac{x^2(y-1)^2}{x^2+(y-1)^2} \right | \le x^2$$
and $x^2 \to 0$ as $(x,y)\to (0,1)$.


\end{document}













</pre></body></html>