Each problem is worth 3 points.
 

1. Integrating and differentiating functions can be tedious.

Mathematica makes it quick and easy. Pick the ugliest derivative (your choice) from exercises 17-44 on pp. 175-176 of Stewart and the ugliest integral (again your choice) from exercises 9-68 on pp. 497-498 of Stewart and use Mathematica to compute them.
 
 

2. Why is z = x² - y² called a hyperbolic paraboloid?

Use Mathematica to look at the shapes of traces of vertical and horizontal planes in the surface and explain (in coherent English) why the name makes sense.
 
 

3. So for those surfaces where the limits are weird but you can't show it by approaching along lines, how can you tell what curve to approach along?

[Putz, "The CAS in Multivariable Calculus"]

Use Mathematica to investigate the shape of f(x,y) = . Figure out what curve of approach to use to show that  does not exist.
 
 

4. So are these 3D graphs always the easy way to answer Calc IV problems?

Graphs alone can be deceptive, and learning to read them carefully is itself a serious skill. Investigate the graphs of g₁(x,y) = cos x cos y and g₂(x,y) = cos x + cos y. At a casual glance someone might say they're pretty much the same thing. Find three different ways of demonstrating to someone (using coherent English and possibly pictures) how you know the surfaces are different. You'll probably have to do more than just look at the standard graph to do this well.
 
 

5. So aside from the frustrations, what drawbacks does Mathematica have?

Lots, but some are more important than others to be aware of. In particular, often what you most want to see is what it's hardest to get Mathematica to give you a good look at. Investigate the family of functions h(x,y) = ln(ax² + y² + c). What effect do different values of a and c have on the shapes of the graphs? Be specific about this -- "bigger" is a start, but to answer this well you'll need to be precise about how much bigger. Again, explain yourself in coherent English.
 
 

Turn this assignment in to Jon by e-mail (JJWhite@OU.Edu). Delete all output before e-mailing. Tip: To make sure that the document Jon gets will do what you want it to do, (1) Delete all output, (2) Save the file, (3) Quit Mathematica, (4) Open the notebook and "Evaluate Notebook." (4) If it works properly, delete the output again and e-mail it to Jon.