1. Some Calc I problems are ugly enough that even though you know perfectly well how to do them, it's much more reasonable to let Mathematica do the messy part. Use Mathematica to find the derivative of f(x) =  [Stewart, Problems Plus p. 180 #13b].
 
 

2. You probably don't need to be told that the same goes for some Calc II problems. Use Mathematica to find  [Stewart, Section 7.6 p.472 #66]. The most natural way to do this one by hand involves using a substitution, a property of logs, integration by parts, long division, and finally a trig substitution.
 
 

3. Consider the function f(x,y) = 10x²y - 5x² - 4y² -x⁴ -2y⁴. This function has three local maxima (sort of hilltop-looking things). Produce a graph that clearly shows all three of these maxima.
 
 

4. See what output Mathematica gives to the command Plot3D[(x^2+y^2)E^(-x^2-y^2), {x,-10,10}, {y,-10,10}]. Although this graph gives a pretty good idea of the overall behavior of this surface -- a flat plain with a big "bump" in the middle -- it's deceptive about the details of this "bump". Experiment with different commands to get a better idea of what's really going on near the origin, and briefly explain why the first graph looked the way it did and how your improvement fixed it.
 
 

5. See what output Mathematica gives to the command Plot3D[Sin[x]Sin[y], {x,-7Pi,7Pi}, {y,-7Pi,7Pi}]. Is this actually a good depiction of the function? Explain what's going on, and find a command that produces a better graph.
 
 

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." (5) If it works properly, delete the output again and e-mail it to Jon.