Maple #4 is due Thursday 8 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. Make Maple find the anti-derivative to x^10 e^2x and x^20 e^2x.
[hint: maple will screw up x^10 e^2x for 3 or 4 reasons.]
2. Find both an exact answer and an decimal approximation (scientific
notation) for the binomial coefficient `100 choose 20' which is usually
written somewhat like the below.

  /100\      100!     100*99*98* ... *81
 (     )  = ------- = ------------------
  \ 20/     20! 80!    20*19*18* ... * 1

3. Plot the functions e^-x xe^-x x^2e^-x and x^3e^-x on the
same graph. limit x to 0 to 10. Use a legend (in plot command) and use
color, thickness or linestyle to clearly identify which curve is which
WHEN PRINTED. Don't forget the title. [hint maple will screw up x^3e^-x
for 3 reasons.]
4. Maple allows plots to range from x=1..infinity as well as ranges
like 1..100. Make two plots, one with x=1..infinity the other with
x=1..100. Both plots should plot both functions 1/square root x and
1/x^2. [Hint title, legend.]
5. The cubic equation x^3-x+3 has one real root and two complex roots.
Find both an exact answer and an decimal approximation for the real
root. [Hints, solve(...) will give all 3 roots, use `solve(...)[n]'
to pick off the root you want (n=1 gives the first root, n=2 the
second, etc). An alternate way of finding a numberical approximation
is the fsolve command. Although not required you might plot the function
to gain insight.]