Labware - MA35 Multivariable Calculus - Polar Coordinate Labs



Domain, Range & Function Graphs


The domain of a function of two variables in polar coordinates is a subset of the polar coordinate plane { (r,θ) | r ∈ R \mbox{and} 0 {leq} θ < 2π.

The range of a real-valued function f is the collection of all real numbers f(p) where p is in the domain of f.

The graph of a function of two variables is the collection of points (x,y,f(x,y)) in 3-space where (x,y) is in the domain of f. When we write the domain in polar coordinates, the graph is said to be in cylindrical coordinates.



  • What is the range of the function f(x,y) = -x4 + 2x2 - y2 over a unit disc domain centered at the origin (i.e. the set of all points (x,y) such that 0 ≤ r ≤ 1)?
  • Describe the graph of f(x,y) = 2xy/(x2 + y2) for all values of x, y other than (0,0) where the function is not defined.