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\textbf{Partial Differentiation}

\textit{\textbf{Functions of more than one variable}}
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\textbf{Question}

If each level curve $f(x,y)=C$ is a circle with centre $(0,0)$ and the
given radius, find $f(x,y)$
\begin{description}
\item{(a)}
$C$
\item{(b)}
$C^2$
\item{(c)}
$\sqrt{c}$4
\item{(d)}
$\ln C$
\end{description}

\textbf{Answer}

\begin{description}

\item{(a)}
$f(x,y)=C$ is $x^2+y^2=C^2$ implies that $f(x,y)=\sqrt{x^2+y^2}$.

\item{(b)}
$f(x,y)=C$ is $x^2+y^2=C^4$ implies that $f(x,y)=(x^2+y^2)^(1/4)$.

\item{(c)}
$f(x,y)=C$ is $x^2+y^2=C$ implies that $f(x,y)=x^2+y^2$.

\item{(d)}
$f(x,y)=C$ is $x^2+y^2=(\ln C)^2$ implies that
$f(x,y)=e^{\sqrt{x^2+y^2}}$.

\end{description}

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