Chapter 14.1, Problem 23E

a)

To determine

The domain of the function $f\left(x,y\right)=\frac{1}{\sqrt{16-x^2-y^2}}$.

b)

To determine

The range of the function $f\left(x,y\right)=\frac{1}{\sqrt{16-x^2-y^2}}$.

c)

To determine

To explain: The level curves of the function $f\left(x,y\right)=\frac{1}{\sqrt{16-x^2-y^2}}$.

d)

To determine

The boundary of the domain of the function $f\left(x,y\right)=\frac{1}{\sqrt{16-x^2-y^2}}$.

e)

To determine

Whether the function $f\left(x,y\right)=\frac{1}{\sqrt{16-x^2-y^2}}$ is an open region, a closed region, or neither.

f)

To determine

Whether the domain of the function $f\left(x,y\right)=\frac{1}{\sqrt{16-x^2-y^2}}$ is bounded or unbounded.