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 Write each of the following systems of equations as a single function (using the full function notation we developed in class). For each, indicate the spaces (i.e., the $\R^n$) where you would find the level sets, image, and graph of your function.
a. $\displaystyle w = x^2y + yz  3xy^2z^3$ b. $y = x\ln x$ c. $\begin{aligned} x &{}= \cos u \cos v\\ y &{}= \cos u \sin v\\ z &{}= \sin u \end{aligned}$ d. $\begin{aligned} x &{}= \cos2z\\ y &{}= \sin z\cos z\\ \end{aligned}$  Let $f\colon\R^2\to\R$ be defined by $f(x,y)=\sqrt{xyy^3}$. Determine the natural domain for $f$ and sketch it.
 Finish the WebWorK assignment, if you haven't already

