- Generate a surface plot and contour plot for the following functions on the given domains:
- for and .
- for and .

- What does the contour plot look like in the regions where the surface plot has a steep incline? What does it look like where the surface plot is almost flat?
- What can you say about the surface plot in a region where the contour plot looks like a series of nested circles?

- Generate a surface plot and contour plot for the following functions on the given domains:
- Generate a surface plot for the following functions on the domains given.
- for and . Use cylindrical coordinates.
- for and . Use spherical coordinates.

- Consider the following function for and which looks like a deep valley with a mountain opposite it. Is it possible to find a path from the point to such that the value of is always between and ? You do not have to find a formula for your path, but you must present convincing evidence that it exists. For example, you might want to sketch your path in by hand on an appropriate countour plot.

2005-09-06