MT #5 is a Maple Assignment [This needs to be handed in.]
(You can use maple or web-maple (with pdf mode))
MT #5 is due Thursday 4 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 as an assignment statement like MyName:="Jane Doe";
1. Find both an exact answer and an decimal approximation (scientific
notation) to 3/2 to the 100th power.
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. Make Maple find the anti-derivatives to both x^10 e^2x and x^10 sin 2x.
4. 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.]
5.  Plot the functions, arctan x, x-x^3/3, x-x^3/3+x^5/5, x-x^3/3+x^5/5 - x^7/7
on the same graph. limit x to -3 to 3 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.]

[Future observation (not required but for insight): try taylor(cos(x),x=0,7)
and taylor(arctan(x),x=0,8) with Maple or use the taylor function in your
calculator. This will show you where the polynomials are coming from.]