Consider the vectorvalued function Ht) 2 (at sin(t), at cos(t), 6'), t 2 0, which is tracing out a curve in space. We are going to do a multipart exercise on this curve: Exercise Lecture(s) 1. Describe qualitatively the shape of this curve. What is NO)? What happens as t increases? Unit 2: _i, L 3 2. Compute the velocity vector and the speed of this curve. Is the speed constant with respect to time? Unit 2: _4 . . _ t s, _ _ . _ . Unit2: _7 Set up an Integral for the arclength function: s(t) 2 H1- (u)|| du. Then evaluate this Integral to get an explICIt function of the 0 form 3(t) 2. . . 4. Invert your function in #3 to find t with respect to .9 (Le, isolate t). Unit 2: _-8 5. Use your expression in #4 to "reparametrize this curve with respect to arclength." Call this new parametrization F1(s). Reminder: Unit 2: _8 emu) : a. 6. Show that ||F'1(s)|| : 1. Is this always the case for a curve which has been re-parametrized with respect to arclength? Unit 2: :6, L