Maple #7 is due Thursday 1 March 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
1-4. Lets build our own density function like that of problem #4
on page 413. Our bell shape curve is
exp(-(x-mu)^2/(2*sigma^2))/(sigma*sqrt(2*Pi). Problem graph looks like
the `normalized sum of two bell curves'. The first has mean (mu) 20 and
sigma 20, the second has mean (mu) 50 and sigma of 2. Call the
first one bellflat and the second bellpeak. If a, b are positive
and a+b = 1, then bellboth = a*bellflat+b*bellpeak will be a prob density
function cause the integral -infinity..infinity will still be one.
Find a and b so that a+b = 1 and so the resulting graph of has the
peak at 50 exactly twice the peak at 20. Use your density to find
the percent of students which have a grade between 48 and 52. Compare
with the percent of students with grades 15-25 with those between 45-55.
Find the precent of funny scores for your graph, Those with negative
scores or scores above 100.

5. Use the series command to find the Taylor series(no big Oh term)
for (deg) n=10 for arccot(x) about x=Pi, 
int(exp(-t^2),t=0..x) about x=0, int(sin(t)/t,t=0..x) about x=0,
and BesselJ(1,x) about x=0. [Maple knows about Bessel Functions, they
are solutions to a particular Differential Equation. You might enjoy
looking at a plot and comparing it to sin(x).]