Maple #5 is due Thursday 12 Oct 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.

1. Plot the plane P with equation, 3x+2y+5z = 30 and an normal to P
on the same plot. Have the normal plotted as an arrow with its base
at the point on the plane nearest the origin.
2. Using the function f:=x^2-y^2, draw the graph together with 
the two curves we get when we hold x = the constant 1/5 and when we
hold y = the constant 3/2. [This time define F to be the "Maple"
function F:=(x,y)->ugly expression. (NOTE not F(x,y):= ugly expression.)
and do spacecurves [1/5,y,F(1/5,y)],y=-3..3 and [x,3/2,F(x,3/2)],x=-3..3
with large thickness.]
3. For f(x,y) = x^2 -y^2 combine a gradplot and a contourplot on
the same graph.
4. Repeat #3 for the matlab demo function
f(x,y)= 3(1-x)^2 e^(-x^2-(y+1)^2)
    - 10(x/5-x^3-y^5)e^(-x^2-y^2) -(1/3)e^(-(x+1)^2-y^2).
[Remember, either define e:=exp(1) or replace e^x with exp(x). A common
error is to replace e^x with exp^x, and unfortunately Maple doesn't
notice the error, and does something dumb.]
5. Use Maple's dotprod and grad commands to find the directional
derivative of f(x,y) = x^2y^3+sin(x)cos(y) at (pi, pi/2) in the direction of
<5, 12>. [Hint subs(x=Pi,y=Pi/2, dotprod(....));.] (Give both a
symbolic and numerical answer [Hint evalf].)