Consider the surface in $R^3$ given by $z=\frac{16}{x^2{y}^2}.$

$($a$)$ What is the range of $z$ for this surface?

Enter your answer as an interval using interval notation. For example $[-3,2)$ for the interval

If you need to enter infinity, you can either copy and paste the symbol $$ or type infinity

Answer: $$

$($b$)$ The equation of the level curve for this surface when $z=64$ is

$($c$)$ The level curve for this surface when $z=64$ is a circle of radius $\frac{1}{4}$

a circle of radius $\frac{1}{2}$

a hyperbola

a single point

something else

does not exist.

$($d$)$ The equation of the cross section in the $xz-$plane is: $z=$

$($e$)$ Which of the following could be a sketch of the surface?

You can click on any of the images to view a larger version