Please answer the following questions by showing all work and providing explanation when needed- thank you.

- Please include BRIEF explanations for 13 below.

12. (10 pts.) Find the area of the region enclosed by one loop of the curve. Hint: consider r = sin(20) 13. (2 pts. each) Mark as True or False: (a) [T] [F] If lim,-+co an = 0, then the series En, an converges. (b) [T] [F] If the series _ne, b, diverges, and 0 0. (c) [T] [F] A series of the form En, a (x -3)" converges whenever |r - 3| $ 1. (d) [T] [F] There exist power series _ne, on (x -2)" which converge on the interval (1, 5]. (e) [T] [F] If a point is represented by (r, y) in Cartesian coordinates, where y