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Use Maple for this Problem! Look at the graphs of the function for -2<x <2, -2<y< 2 and
and at MORE values of your own choice.
Do you have any conjectures on how the graph depends on the parameters a,b,
and c? Try to cover some special cases: e.g. suppose a >0 and c >0;
what happens as b varies ?
- a=1, b=0, c= 1,
- a=1, b=2, c= 1,
- a=1, b=4, c= 1,
- a=1, b=6, c= 1
- a=1, b=0 ,c= 4
- a=1, b=0, c = 6,
Find functions whose graphs fit the descriptions below. Use Maple to print
graphs verifying your solution. Include axes in the graphs.
- A bowl which opens upward and has its vertex at 5 on the z axis.
- A parabolic cylinder opening upward from along the line y=x in the
xy plane. (A parabolic cylinder is the shape formed by extruding a parabola
perpendicular to the plane in which it lies.)
- A cone with circular cross section having a vertex in the plane z=5
and passing through the origin.
Problem 3* (Extra Credit)
Explain why level curves of
for function values either
in absolute value are generally predictable. Sketch what these should look like
- small (e.g. c = .1), or
- large (e.g. c = 10)
HINT: implicitplot(, color=red);