Comments on Lesson 1.09

• G.6.b.ii I am not sure whether the hint for G.6.b.ii, the "Trick Shots" part of the projectile plotting problem, is useful. It seems that many students have been unable to decode what this humonguous solve command does, and there seems little learning in doing so. Perhaps better would be to cut the hint and make it extra credit. (Provided "ordinary" techniques work to solve it--check.)

• I think emphasizing the plotting tubes, etc. is useful for later on in the 3-D part, when students are apt to misunderstand that 3-D tubes can be of several forms (for example, they can be drawn by circles parallel to the xy-plane, or they can be drawn by circles in a plane perpendicular to the curve).

• It is worth noting that after doing the whole lesson, most people could not parametrically plot a tube of radius 1.5 around the curve {t,t^2,0} for t in [-2,2]. They also could not give the parametric form for the surface made by a function y = f(x) rotated around the x-axis.