MT #4 is a Maple Assignment [This needs to be handed in.]
(You can use maple or web-maple (with pdf mode))
MT #4 is due Thursday 27 Sep 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 as an assignment statement like MyName:="Jane Doe";
1. Find both an exact answer and an decimal approximation (scientific
notation) to 100! (! is factorial). (Webmaple needs factorial instead of !)
2. Find the first 3 derivatives of x^2 e^2x. [hint: diff]
3. Find the anti-derivative for x^2 e^2x and the definite integral
from 1 to ln 2 [hint: int]
4. Expand (x+y)^10 and factor 
              5       4         3  2       2  3         4       5
             a  - 10 a  b + 40 a  b  - 80 a  b  + 80 a b  - 32 b
[Hint expand, factor]
5.  Plot the functions, cos x, 1-x^2/2, 1-x^2/2+x^4/24, 1-x^2/2+x^4/24 - x^6/720
on the same graph. limit x to -2pi to 2pi and y to -2 to 2. Use a legend
[Hint: check out: plot([x^2,x^3,x^4],x=0..1,linestyle=[2,3,4],
title="powers of x", legend=["x^2","x^3","x^4"],thickness=[1,2,3],color=black);]
[Hint2: If you are using webmaple you need to reload gifs or use pdfmode.]