MT #6 is a Maple Assignment [This needs to be handed in.]
(You can use maple or web-maple (with pdf mode))
MT #6 is due Thursday 11 Oct 2001

Papers which are not STAPLED will not be acepted
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

All plots need to have a title which includes your name, (eventually plots
might have multiple functions and plots with mulitple functions need legends.)
Be sure to answer the questions as Maple comments. One can add
titles to plots like
 plot(sin(x),x=0..2*Pi,title="Catch the Wave");

Introduction to Syntax. Note often the expressions below are not given
in a format exceptable to Maple. For example, Maple does not understand
3x as 3*x, one must enter 3*x. Maple uses Pi for pi and does not know 
about e (either use exp(x) for e^x, or define e:=exp(1) before using it).

Typing ?diff into webmaple will give you help on the the diff command

Do the following using maple
0. Enter your name(s) as an assignment statement like MyName:="Jane Doe";
or OurNames:="Gwyneth Paltrow and Ben Affleck";
1. Find both an exact answer and an decimal approximation (scientific
notation) for both cos(pi/8) and cos(pi/16). [Hint cos^2 x = (1+cos 2x)/2
and remember to trash any extra roots. Remember to use the exact value
for cos(pi/8) to compute the exact value of cos(pi/16).]
2&3. Let f:=x^2*exp(-x) [and not f:=x->x^2*exp(-x)]. Use maple to find
the critical points of f and use eval or subs to find the value of f
at the critical points.
4. Use the series or taylor command to find the Taylor series for n=10 for
tan(x) about x=0, sqrt(x) about x=1, ln(x) about x=1 and
exp(-x^2) about x=0. [remember that maple's n is not the text's n,
so in maple you need to use 10+1 for n.]
5. Let f be 400e^-4x and g be 50e^-x. Make a plot with two plots. The
first plot is of the functions f+g, f, and g on the same graph from
0..2. The second plot the functions ln(f+g), ln(f) and ln(g) on the
same graph from x=0..2.  for both graphs use same thickness=[3,1,1],
and the same colors or linestyles that print well.  Don't forget the
title, don't forget the legend.  [hint maple will screw up 100e^-2x for
several reasons.] [Why this problem?  it is both a solution to
differential equation and what you would observe from a mixture of two
radioactive isotopes. The log graph has the initial slope of the first
isotope, and the final slope of the second isotope.  The good doctor
actually did this experiment in a radiation biology lab.]

[How to get 2 plots on the same webmaple: 1st you need `with(plots):'
(you can use the `:' to surpress the output, or you can use the `;'
and see all the functions. You create two plots assigning them each
a name like F:=plot(sin(x),x=0..2*Pi): and G:=plot(cos(x),x=0..2*Pi):.
Now here the `:' is more important. If you leave off you will get
about a page of meaningless output. (Well it has meaning and contains
a list of the points plotted, but I don't want to see this on your
answer sheets. Neither of the assignments will produce a picture, but
the command `display(array([F,G]));' will. Careful `display([F,G])'
will combine the two plots into one and if the scales are not close
you might only see one of the graphs.]