Maple #5 is due Thursday 15 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 "expand" the binomials (x+y)^10 and (x+y)^20 [hint: "expand"]
2. Find both an exact answer and an decimal approximation (scientific
notation) for both sin(pi/8) and sin(pi/12). [Hint sin^2 x = (1-cos 2x)/2
and remember to trash extra roots.]
3. Plot the functions f, -f, f*g, and g on the same graph where f is
e^-x/4pi and g is sin x, limit x to 0..4pi. Use a legend (in the plot
command) and use color, thickness or linestyle to clearly identify
which curve is which WHEN PRINTED. Made sure the f and -f plots look
less important than the sine curves.  Don't forget the title. [hint
maple will screw up e^-x/4pi for several reasons.]
4. Plot (plot3d) the surface of revolution when the area between
x^3-6x^2+10x, x=0, x=3.5 and y=0 is rotated about the x-axis. Also
have Maple compute the volume of solid.
5.Consider the polynomial p(x)=x^5+3*x^4-5*x^3-15*x^2+4*x+10.
Find decimal approximations for the all the real roots of p(x).
[Hints: fsolve/solve and explain why you know you got all the real roots.]