question 2. (b). Do it using integration

solutions on scrap paper. Do f only pen/ pencil. No calculator or computer or phone. (1) Let C be the curve x = sin (y) between the points where y = - - and y = - 5 75 3 (a) (10 points) Draw the curve C on a labeled graph, and label the endpoints of the curve. (b) (20 points) Find the surface area produced by revolving C around the line r = -2. You may leave the answer as an unsimplified integral. (2) A container in the shape of an upside down cone (with the apex at the ground) has a height of 20.00 feet, and the top has diameter 10.00 feet. It is filled with water, . which has a density of 62.424 pounds per cubic foot. A pump is used to pump the water to a pipe that is at a height of 31.00 feet. The pump runs for a while until the water level in the container is down to a height of 5.00 feet. (a) (10 points) Draw a picture of the situation. (b) (20 points) How much work does the pump do? You may leave the answer as an unsimplified integral. (3) (10 points each) Find the limit of each sequence defined below, with brief justification. k + 35 + cos (TK) (a) For k 2 2, bk = 7 (3k) + 400k (b) c1 = -1, Cm+1 = V5 + 3cm for m > 1. 2 (4) (10 points each) Find the sum of each series, or determine that the series diverges, with justification. 20063 (a) E 20062 + 300 + 63