Functions of two variables
1. Find the domain and range of each function.
solution
(a) \(\displaystyle{f(x,y)= 2x + 3y-5}
\) (b) \(\displaystyle{g(x,y) = \sqrt{4-x^2-y^2}}
\)
2. Find the domain of each function.
solution
(a) \( \displaystyle{f(x,y)=\frac{y-3}{\sqrt{x+y-2}}}\)
(b) \(\displaystyle{g(x,y) = \frac{\ln(y-x^2)}{x+2}}
\)
3. Draw a contour map of the function showing several level curves.
(a) \( f(x,y)=x^2 - y^2 \) solution (b) \(g(x,y)=\ln(x^2+y^2) \)
solution