MATH 129 Midterm: MATH 129 University of Arizona Exam 3A S16
31 Jan 2019
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Exam # 3, sections 8. 5 & 9. 1 - 9. 5. 5: a cylindrical barrel, standing upright on its circular end, contains muddy water. The top of the barrel, which has a diameter of 1 meter, is open. The height of the barrel is 1. 8 meters and it is lled to a depth of 1. 5 meters. The density of the muddy water at a depth h meters below the surface is given by. (h) = 1 + kh (units are kg m3 ) where k is some positive constant. Set up the integral to nd the total work done to pump the muddy water to the top of the rim of the barrel. You do not need to evaluate the integral. Leave your answer in terms of , g (the gravitational constant, units are m s2 ), and k: determine if each of the following converges or diverges.
