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\leftline{Mathematics 241 -- Multivariable Calculus}
\leftline{Quiz 5 -- October 22, 2010}
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\leftline{Your Name: $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$}
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\noindent
A) Let 
$$f(x,y) = \cases{ {xy \over x^2 + y^2} + x & if $(x,y) \ne (0,0)$\cr
                          0 & if $(x,y) = (0,0)$.\cr}
$$
\item{(1)} (5) Find ${\partial f\over \partial x}(x,y)$ if $(x,y) \ne (0,0)$.
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\item{(2)} (5) Does ${\partial f\over \partial x}(0,0)$ exist?  If so, what is its 
value; if not, why not?
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\noindent
B) (10)  Sketch the set $S = \{(x,y) \in {\bf R}^2 \mid |x| < 1, |y| \le 2\}$
Is S open, closed, or neither?  Explain. 
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