Math Help - Domain and Level sets

1. Domain and Level sets

Lecturer decided to do an R3 domain whereas I would be used to the R2. Any suggestions?

2. Re: Domain and Level sets

I don't know what you mean by "decided to use the R2" The domain is not a "choice"! The problem says "f(x, y, z)" so f depends upon the three variables x, y, and z. The domain of the function is a subset of $R^3$. Of course to be able to take that square root we must have $z- x^2- y^2\ge 0$. What is that set?

The "level sets" of levels 0 and 2 are the graphs of $\sqrt{z- x^2- y^2}= 0$ and $\sqrt{z- x^2- y^2}= 2$ which are equivalent to $z= x^2+ y^2$ and $z= x^2+ y^2+ 2$. What are those graphs?

3. Re: Domain and Level sets

Domain is the lecturer's choice I meant!

4. Re: Domain and Level sets

Originally Posted by kangaruaidhri
Domain is the lecturer's choice I meant!
Hmm...
Originally Posted by HallsofIvy
The domain is not a "choice"!