Homework for Class 3

Of course, you may start on the homework during class if you have time!

1. A Maple puzzle

   Take a look at Exercise 12 on page 46 of Chapter 3 of the CalcLabs with Maple V manual:

   A cylindrical can with a top and bottom is to contain 1000 cubic centimeters. Find the dimensions of the can if its surface area is 600 square centimeters.
   Note: there are two answers.

   Consider the following alleged Maple solution to the problem.

   Let r and h denote the radius and the height of the cylinder. We set up a pair of simultaneous equations and solve them for r and h.

     > eq1:=Pi*r^2*h=1000; eq2:=2*Pi*r^2+2*Pi*r*h=600; fsolve({eq1,eq2},{r,h});
   
     eq1 := Pi*r^2*h = 1000
   
     eq2 := 2*Pi*r^2+2*Pi*r*h = 600
   
     {r = -11.13867027, h = 2.565567417}
          

   Obviously something is wrong here, because it does not make sense for the radius to be negative!

   Write a Maple worksheet, addressed to an audience of first-year calculus students, that explains the error and exhibits a correct solution. Use Maple's Print feature to get hard copy, and turn it in at the next class.

   A requirement of this assignment is that your paper include an appropriate Maple plot. (That's also a hint: look at a suitable graph to see what is going on.) To get a plot into a Maple V Release 3 worksheet, select ``Edit'' and ``Copy'' from the plot window, move the cursor back into the main Maple window, and select ``Edit'' and ``Paste.'' The new Maple V Release 4 (currently available on the PCs in the university PC labs) is capable of displaying plots inside the worksheet automatically: on the ``Options'' drop-down menu, select ``Plot Display'' and then ``Inline.''

2. Make a signature file

   Intelligent mail programs can automatically include a ``signature'' file into each mail message you send. (For instance, pine, emacs, and the Netscape mailer have this capability; mailtool, as far as I know, does not.) Use a text editor to make yourself a signature file. I change my signature file from time to time; currently it looks like this:

   Harold P. Boas                         mailto:boas@tamu.edu
     World-Wide Web URL:     /~Harold.Boas/
   --
          

   Generally, a signature file should contain your name and some contact information. Some people include little ASCII pictures or witty sayings. It is recommended that your signature file not exceed four lines. (If you send mail from within Netscape, it may complain if your signature file exceeds four lines, even if some of the lines are blank.)

   Save your signature file as .signature (that file name starts with a period). Then open a terminal window and use the command chmod a+r .signature to make the file world readable. Now try sending yourself mail to see if the signature does get included in your mail message.

Comments to Harold P. Boas.
Created Sep 17, 1996. Last modified Sep 18, 1996.