Maple #3 is due Thursday 25 January 2001

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

All plots need to have a title which includes your name.

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 or as maple text.
1. Find both an exact answer and an decimal approximation (scientific
notation) to 100! (! is factorial).
2. Plot the function f:=x^4-10x^2+9 together with its derivative and
its second derivative on the on the same graph. limit x to -5 to 5 and
y to -25 to 25. Use a legend and use color, thickness or linestyle to
clearly identify which curve is which WHEN PRINTED.
3. Plot the functions f:=1/((x-1)(x+1)), 1/(x-1) and -1/(x+1) on the
same graph. limit x to -2 to 2 and y to -20 to 20. Use a legend and use
color, thickness or linestyle to clearly identify which curve is which
WHEN PRINTED.
ALSO USE MAPLE to convert f to PARTIAL FRACTIONS.
[hint: convert(f,parfrac,x)]
4. Clear all variables with the restart command. Then solve the problem
below by entering the equations, and then the known values and finally
solve for the unknowns. The point (x,y) is a distance R from the origin
and is on the line y=m*x. Suppose R is 5 and m 3/4, find x and y.
Suppose R is 13 and m is 1/2 find x and y. (eliminate RootOfs via
allvalues).
5. Use the student package to numerical approximations to integral
of e^(x^2) from 0 to 5 using each of the leftsum, rightsum, middlesum,
trapezoid (all with n=100) and maple's builtin numerical integrator.
[Hints evalf(value(middlesum(f,x=0..5,100))) and evalf(int(f,x=0..5))]