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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.

$$ \lim_{(x,y)\to(1,\pi)} \frac{\cos (xy)}{1-x-\cos y}$$


\textbf{Answer}

\begin{eqnarray*}
\lim_{(x,y)\to(1,\pi)} \frac{\cos (xy)}{1-x-\cos y} & & \\
= \frac{\cos (\pi) }{1-1-\cos (\pi)} & = & -1
\end{eqnarray*}


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