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Math 1910, Final ExamDecember 6, 2012, 2:00 PM to 4:30 PMYou 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 maximum credit thatyour solution deserves. Please label the questions in your answer booklet clearly. There are7 questions.Write your name and section numberon each booklet you use. You may leave when you havefinished, but if you have not handed in your exam booklet and left the room by 4:15pm, pleaseremain in your seat 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) LetRbe the region belowy=e-xabove thex-axis, and to the right ofthey-axis.(a) Evaluate the volume of the solid obtained by rotatingRabout thex-axis.(b) Evaluate the volume of the solid obtained by rotatingRabout they-axis.3. (10 points) Find the power series aboutx= 0 of the solution to the differential equationy0=xy, wherey= 1, whenx= 0.4. (24 points) Calculate the following integrals or show that they do not exist: