For the function \(f(x,y)=x^2+3xy-y^2\), find \(f(2,-1)\).

State the domain of \(f(x,y)=\sqrt{9-x^2-y^2}\) as a set of ordered pairs.

Find the range of \(f(x,y)=x^2+y^2\) for all real \(x\) and \(y\).

Describe the level curve \(f(x,y)=4\) for \(f(x,y)=x^2+y^2\).

For \(f(x,y)=\ln(x-y)\), state the domain in terms of \(x\) and \(y\).

Let \(f(x,y)=2x-y\). Find the equation of the level curve through the point \((3,1)\).

Evaluate \(g(r,\theta)=r\cos\theta\) at \(r=4\) and \(\theta=\pi/3\).

For \(f(x,y)=\frac{1}{x^2+y^2-1}\), state the domain.

For \(f(x,y)=xy\), compare the paths \(y=x\) and \(y=2x\) as \((x,y)\) approaches \((0,0)\). What limit value do both path expressions approach?

Find a formula for the cross-section of \(z=f(x,y)=x^2+y^2\) in the plane \(y=3\).