Texts: MA 261 Homework - Due Thursday, October 25 Worth 10 Points
For Problems 1 and 2, you are to choose values for constants and graph the resulting functions using Maple in one of the open labs. (If you wish to use other software than Maple, you may do that. Don't choose values you know someone else is using.) What you turn in should include printouts of graphs that give a good view and answers to the questions below.
1. Consider xy + xz + yz = c. For any value of the constant c, the graph of this equation will be one of the cylinders or quadric surfaces discussed in Section 10.6. The question is what kind.
A. Choose a c value, c > 6, and use implicitplot3d to graph the resulting equation. (You may need to change the ranges of values for x, y, and z or change your viewpoint to get a picture you can recognize. You can use the option grid - [] of implicitplot3d to increase the number of points plotted.) Give the name of the kind of quadric surface that you got.
B. Do the same for a value of c, c < -6.
C. As c changes gradually from your part A value down to your part B value, what kinds of cylinders or quadric surfaces do you get? At what value of c does the kind of surface change?
2. Consider rt = 3t + 4cos(mt) + 4sin(mt).
A. Choose a value of m in the range 10 ≤ m ≤ 20 and use spacecurve (or tubeplot with a small radius) to graph the resulting curve. It is best to use a range for t that includes negative and positive values. (You will probably need to use the option numpoints = n to increase the number of points that Maple plots - the default is 50.)
B. Looking at your graph (and maybe trying some larger m-values), guess what quadric surface your curve lies on and what its equation is. (It will help to include axes in your graph, and you may want to use the 1-1 button.) Then (without Maple), show your guess is correct by doing the algebra to show that each point on the curve satisfies the equation of that quadric surface.
