Maple #7 is due Thursday 24 Feb 2000 

For FULL credit STAPLE your sheets together.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Each plot must be rotated to a "nice" position and "look good (smooth)".
Each plot must have include axes and the title must include your name
and what was plotted. Note that the expressions below are not
necessarily in a form that Maple likes. Be sure to answer the questions
in 3.

1. Use Maple and Lagrange multipliers to find the maximum and minimum
values to f = x^2 + y^2 subject to g = x^4+y^4 - 1 = 0.
2. Combine a plot of g with several level curves of f. Make sure that
both contours for the min value and max value of f subject to g = 0
are in the contour plot. Make sure your plot is constrained.
3. Use Maple and Lagrange multipliers to find the extrema
values to f = x^2+2y^2+z^2+t^2 subject to x+3y-z+t-2=0 and 2x-y+z+2-4=0.
Why is there only one value, is it a minimum, a maximum or neither.
4. Use Maple to do #27 on page 770. Reverse the order of integration
and use Maple again. Use evalf to show the answers are the same.
5. Use Maple to do #28 and use implicitplot to show the region of
integration.