Please solve and explain the solution for question d) only:

2. Let S be the region bounded by the graph of the polar curve r (0) = 310 sin(02 ) for Oses vit in the figure to the right. (a) Find the area of S. (b) What is the average distance from the origin to a point on the polar curve r (0) = 3V0 sin (02 ) for Oses Vn (c) There is a line through the origin with positive slope m that divides the region S into two regions with equal areas. Write, but do not solve, an equation involving one or more integrals whose X O B solution gives the value of m. (d) For k > 0, let A(k) be the area of the portion of region S that is also inside the circle r = kcose . Find lim A(k) k - too