Exercises

1. Generate the contours for the following functions and describe what you see.
   1. .
   2. .
   3. .
   4. .
   5. .
   6. .
2. The contours that Maple plots are generated at equally-spaced values of z. Can you relate the distance between the contours in a two-dimensional contour plot to (average) rates of change of the function?

3. Can you distinguish between the two-dimensional contour plots of and ? If so, how? If not, how would you overcome this problem?

4. Report the values of a, b, , and used in the first three examples of the SurfLoop command. Explain how these choices generated the slices described there. Try to explain graphically why the directional derivatives have the values given.

5. Consider the function . Compute the directional derivatives for the following values of a, b, and .
   1. a=-1, , .
   2. a=-1, , and in the direction of .
   3. a=1, , and in the direction of .