Chapter 14.1, Problem 26E

a)

To determine

The domain of the function $f\left(x,y\right)=e^{-\left(x^2+y^2\right)}$.

b)

To determine

The range of the function $f\left(x,y\right)=e^{-\left(x^2+y^2\right)}$.

c)

To determine

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

d)

To determine

The boundary of the domain of the function $f\left(x,y\right)=e^{-\left(x^2+y^2\right)}$.

e)

To determine

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

f)

To determine

To choose: Whether the domain of the function $f\left(x,y\right)=e^{-\left(x^2+y^2\right)}$ is bounded or unbounded.