<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.

$$ \lim_{(x,y)\to(0,0)} \frac{x^2y^2}{x^2+y^4}$$


\textbf{Answer}

\begin{eqnarray*}
x^2 &amp; \le &amp; x^2 + y^4\\
\Rightarrow \frac{x^2y^2}{x^2+y^4} &amp; \le &amp; y^2 \to 0\\
\textrm{as } y &amp; \to &amp; 0
\end{eqnarray*}

$$\Rightarrow \ds \lim_{(x,y)\to(0,0)} \frac{x^2y^2}{x^2+y^4}=0$$


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