91Ó°ÊÓ

For the following exercises, evaluate each function at the indicated values. $$ W(x, y)=4 x^{2}+y^{2} . \text { Find } W(2,-1), \quad W(-3,6) $$

For the following exercises, evaluate each function at the indicated values. $$ W(x, y)=4 x^{2}+y^{2} . \text { Find } W(2+h, 3+h) $$

The volume of a right circular cylinder is calculated by a function of two variables, \(V(x, y)=\pi x^{2} y,\) where \(x\) is theradius of the right circular-cylinder and \(y\) represents the height of the cylinder. Evaluate \(V(2,5)\) and explain what this means.

An oxygen tank is constructed of a right cylinder of height \(y\) and radius \(x\) with two hemispheres of radius \(x\) mounted on the top and bottom of the cylinder. Express the volume of the cylinder as a function of two variables, \(x\) and \(y,\) find \(V(10,2),\) and explain what this means.

For the following exercises, find the domain of the function. $$ V(x, y)=4 x^{2}+y^{2} $$

For the following exercises, find the domain of the function. $$ f(x, y)=\sqrt{x^{2}+y^{2}-4} $$

For the following exercises, find the domain of the function. $$ f(x, y)=4 \ln \left(y^{2}-x\right) $$

For the following exercises, find the domain of the function. $$ g(x, y)=\sqrt{16-4 x^{2}-y^{2}} $$

For the following exercises, find the domain of the function. $$ z(x, y)=y^{2}-x^{2} $$

For the following exercises, find the domain of the function. $$ f(x, y)=\frac{y+2}{x^{2}} $$