Math 115H (Assignments)

# Homework on 11 September 2017:

[Not to be turned in]

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

 Math 115H (Fall 2017) web pages Created: 11 Sep 2017 Last modified: Sep 11, 2017 3:00:26 PM Comments to: dpvc@union.edu