I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 12.5 : Functions of Several Variables
1. Find the domain of the following function.
\[f\left( {x,y} \right) = \sqrt {{x^2} - 2y} \] Show SolutionThere really isn’t all that much to this problem. We know that we can’t have negative numbers under the square root and so the we’ll need to require that whatever \(\left( {x,y} \right)\) is it will need to satisfy,
\[{x^2} - 2y \ge 0\]Let’s do a little rewriting on this so we can attempt to sketch the domain.
\[{x^2} \ge 2y\hspace{0.5in} \Rightarrow \hspace{0.5in}y \le \frac{1}{2}{x^2}\]So, it looks like we need to be on or below the parabola above. The domain is illustrated by the green area and red line in the sketch below.
