Math 215 Written Homework Set 5 Bonus Part Problem 1. (from Stewart's "Calculus; Early Transcedentals" book) (max. 24 points) Below you are given some (partial) parametrications of certain (smooth, or piecewise smooth) surfaces in R3 (note that the domain of the parametrization is not given to you in most cases, as it is can be inferred from the graphs on the next page more or less, and knowing it accurately is not especially needed for this problem). On the next page you will also find graphs labelled I-VI, corresponding to these parametric sations. Match each parametrication to the corresponding graph. Give some justification for your answers. [Hint. You may want to consider different grid curves that the parametrizations give you in other words, curves that you will get once you fix one of the input variables to be equal to a specific value, and just allow the other variable to vary), and then look for those curves on the given graphs, fining the 'best candidate' to contain the specific grid curve you are considering each time.] . al(u, v) = (u cos(v), usin(v), v). . 02(u, v) = (ucos(v), usin(v), sin(u)), -T SuST. . a3(u, v) = (sin(v), cos(u) sin(2v), sin(u) sin(2v)). . a4(u, v) = (14(u, v), y4(u, v), Z4(u, v)) with TA(u, v) = (1 - u)(3 + cos(v)) cos(4Tu), y4(u, v) = (1 - u)(3 + cos(v)) sin(4Tu), and z4(u, v) = 3u + (1 - u) sin(v). . 05(u, v) = (15(u, v), 95(u, v), 25(u, v)) with x5 (u, v) = cos (u) cos3 (v), y5(u, v) = sin3(u) cos3(v), zs(u, v) = sin' (v). . 06(u, v) = (1 - [ul) cos(v), (1 - lul) sin(v), u).Z II X X III 2 4 IV V Z VI Z X 2