Multivariable calculus: Exercises

06 Functions of multiple variables, part 2

Exercise 1: Plotting using cross sections

Plot the graphs of the following functions using cross sections.

  1. \(f(x,y) =-x^2 - y^2\)
  2. \(g(x,y) = y^3 + xy\)
  3. \(h(x,y) = \sqrt{1-x^2-y^2}\)
  4. \(k(x,y) = e^{-x^2-y^2}\)
  5. \(m(x,y) = x^2\)

Check your plots using Desmos.

Exercise 2: Plotting using contour diagrams

Plot contour diagrams of the following functions.

  1. \(f(x,y) =y-x^2\)
  2. \(g(x,y) = x^2+2y^2\)