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{\bf Math 366, Winter `03 \\ Homework 2}
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\noindent{{\bf From Rudin.} pp 239: 6, 7, 8}

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\noindent{{\bf Profs Personal Problems:}}
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\noindent{\bf 1.} Let $f:\R^2\to\R^3$ be given by $f(x,y) = (x^2y, \sin(x-2y-1),
e^y/x)$.  Compute 
\begin{itemize}
\item $f'(1,0)$.
\item The linear approximation of $f$ about $(x,y) = (1,0)$.
\end{itemize}

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\noindent{\bf 2.} Let $f:\R^2\to\R^2$ be given by 
$f(x,y) = (x^2 - 2y, y - x^3 - 1)$.  Let $f_1 = f$, $f_2 = f\circ f$,
$f_3 = f\circ f \circ f$, etc.  Compute $f_8'(-1,1)$.  ({\it Hint: you
really don't want to actually figure out a formula for $f_8$.  Trust me.})
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