Maple #6 is due Thursday 22 February 2001

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

All plots need to have a title which includes your name, plots
with mulitple functions need legends.

Introduction to maple. 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.

Do the following using maple
0. Enter your name as a comment
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.]
2. Plot the functions 1+x, 1+x+x^2, 1+x+x^2+x^3, and 1+x+x^2+x^3+x^4
with thickness=[1,1,1,3], color=black, linestyle=[2,2,3,1] the same graph
twice. The 1st time limit -2<=x<=2 and -1<=y<=3. The second time limit
with no limit on y, but limit -0.4<=x<=0.4. Don't forget the title or
the legend. [Why this problem? The linear, quadratic and cubic equations
are the series approximations to the final biquartic (fourth degreee).]
3. Let f be 400e^-4x and g be 50e^-x. Make two plots. First plot the
functions f+g, f, and g on the same graph from 0..2. Second plot the
functions ln(f+g), ln(f) and ln(g) on the same graph from 0..5.
for both graphs use same thickness=[3,1,1], and the same colors that
print well.  Don't forget the title or 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.]
4. Plot (plot3d) the surface of revolution when the area between
sin(x), x=0, x=Pi and y=0 is rotated about the x-axis. Also
have Maple compute the volume of solid. [Hint: cut and paste from
the feb06.mws worksheet.]
5. Use the series command to find the Taylor series for n=10 for
tan(x) about x=0, sqrt(x) about x=1, exp(x) about x=e and
exp(-x^2) about x=0.