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Homework on 11 September 2017:

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  1. 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. $\begin{aligned} x &{}= \cos2z\\ y &{}= \sin z-\cos z\\ \end{aligned}$

  2. Let $f\colon\R^2\to\R$ be defined by $f(x,y)=\sqrt{xy-y^3}$. Determine the natural domain for $f$ and sketch it.
  3. Finish the WebWorK assignment, if you haven't already



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Created: 11 Sep 2017
Last modified: Sep 11, 2017 3:00:26 PM
Comments to: dpvc@union.edu
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