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Math 1910, Final Exam SolutionsDecember 6, 2012, 2:00 PM to 4:30 PM1. (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.