48. Visualizing Functions of Two Variables - Part 2 - Level Curves, Contour Maps, and Surfaces

In this video, we look at two more examples of functions of two variables. We sketch contour maps by setting z equal to several values in the range of the function, and then we use those contour maps and our knowledge of surfaces from an earlier chapter to sketch the surfaces in 3 dimensions.

[gauravgoyal]

Find the range of the function f defined by f(x, y) =10 − x^2 − y^2 for all (x, y)
for which x^2 + y^2 ≤9 . Sketch two of its level curves.