Two part of question.

Math 250 Writing Assignment 3 1. A region R in the plane is simply connected if every closed simple curve (a loop that doesn't cross itself) can be deformed and contracted to a point, continu- ously in R. (See the diagram; it's from our textbook, p. 1115.) In this problem we will pay attention to this denition and where the term appears in the hypotheses to some of our theorems. Let F 2 L 2 . lrlz x3 +y2 (https : //ww . desmos . com/calculator/lsvhcfuen2t This curve cannot be contracted to a point and remain in R. Connected. _ simply connected : R I \\Q R\\ Not connected. _ simply connected Conneclcd. not simply connected Not connected. not simply connected (a) (3 points] Let P be the natural domain I" (the set of points in R2 where F is dened). Describe P and explain why P is NOT simply connected. (By the way, P is both open and connected; this might be good to know later.) (b) (5 points] Using the Test for Conservative Vector Fields in R2 (Theorem 1?.3, p. 11 15 of the text), show that F is conservative over any simply connected region contained in P. (This is similar to a problem on quiz || 1)