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

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


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