Project #6 is due Tuesday 25 Feb 2003

Unstapled assignments will not be accepted.

The first line of the worksheet should include your name.

Plots must be rotated to a "nice" position and "look good (smooth)".
Plots must include axes and titles. Titles must include your name.

1. Find the quadratic Taylor polynomial (call it T) about (1,1) to
f=1/(3+x^2-2x+y^2-2y) and plot the two graphs together in a fashion
you can tell which is which. Make sure your title also makes it clear
which is which (for example, it could say which is on the bottom or
make one wireframe and the other another style). Use the range
0 <= x <= 2 and 0 <= y <= 2. [Hint: mtaylor]

2. Repeat #1 for f=sin(x)sin(y) about (Pi,Pi) using the range
Pi-1..Pi+1 for x and y.

3. (Roughly #10 on test2 for fall02) Plot the z=1 contour for
g(x,y)=x^2+xy+y^2 and on the same graph plot several contour lines
for f(x,y)=x+y. Be sure to pick contours which include the minimum
and maximum values of f(x,y) subject to the constraint g(x,y)=1.

4. Read maple help on `arrow' (part of plottools). Add 4 arrows
to the graph of #3, The grad of f at the max, the grad of f at the
min, the grad of g at the max and the grad of g at the min. Make
sure you can see all four arrows and that `angles are correct'.

5. (Roughly based on HH15.2#17). Plot xy+3x+z^2=9 and a sphere
centered at the origin tangent to the surface. [The radius of the
sphere is the minimal distance required by #17.] Use the range
-7..7 for all variables.