How do you solve 4c ? Thank you.

Math 1910, Final Exam December 6, 2012, 2:00 PM to 4:30 PM You are NOT allowed calculators, the text or any other book or notes. SHOW ALL WORK! Writing clearly and legibly will improve your chances of receiving the marimum credit that your solution deserves. Please label the questions in your answer booklet clearly. There are 7 questions. Write your name and section number on each booklet you use. You may leave when you have finished, but if you have not handed in your cram booklet and left the room by 4:15pm, please remain in your seal so as not to disturb others who are still working. 1. (5 points) The decay constant of cobalt-60 is 0.13/year. Find its half-life. 2. (12 points) Let R be the region below y = e- above the r-axis, and to the right of the y-axis. (a) Evaluate the volume of the solid obtained by rotating R about the r-axis. (b) Evaluate the volume of the solid obtained by rotating R about the y-axis. 3. (10 points) Find the power series about I = 0 of the solution to the differential equation 1/' = ry, where y = 1, when z = 0. 4. (24 points) Calculate the following integrals or show that they do not exist: (a) ( sin' zoos rda () fide () | wehadr (d) frieds, where soch z = 2/(e" + e") is the hyperbolic secant function. (Reduction formulas are not needed for Part (a)). 5. (18 points) Explain with reasons which of the following infinite series converge and which diverge: (a) ( b ) ( 0) 1 (NEXT PAGE)