3. (a) Plot the vectors r'(0), HQ), r'(1r) and 1'93\") in the diagram below. In each case, base the vector at the point ['(t). Example 3.42 in lectures illustrates this. (1)) The curve C has vertical tangent lines at i 2 i- 2 _i 2 _i_ 2 (w slim Bl'lw slim 3)- Using this information and the vectors you plotted in (a) to sketch P = C in the diagram below. Indicate the vertical tangent points clearly. 2. In Questions 2 and 3 we consider the the path P of the parametric curve r : R - R2 defined by r(t) = 2 cos(t) sin?(t)i + sin(t)j so P = range(r) and the set C = {(x, y) ER2 | 22 + 4y6 = 4y4}. In Assignment 1, you proved that P C C. Here we use the approach of Question 2 of Practice class 9 (which you should review) to prove that C C P, completing the proof that P = C.Assignment 1 Written Part - Due: 11:59PM, Monday 15 August. Upload a scan of your solutions to "Assignment 1 Written Part" in Gradescope (accessed in the Canvas Assignment). We strongly recommend using a document scanning app on your phone to scan your work. 1. Define sets P, C C R2 by: C = {(x, y) ER2 | 202 + 4y6 = 4y4} P = {(2 cos(t) sin?(t), sin(t)) | te R}. Note that P is expressed using "abbreviated" descriptive notation. Prove that P C C. Reviewing Question 5 of Workshop 2 should get you started