Midterm 2-2009 (Pink Version)

Midterm 2-2009 (Pink Version) - Calculus II Midterm 2...

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Calculus II Midterm 2 March, 2009 2 1. (3 marks each; total 9 marks) Answer each question in the space provided. You MUST show your work. a) Mad scientists colonize an empty island with 10 gremlins. The rate of growth of the population can be modeled by the differential equation P dt dP 7 = . Find the population of gremlins as a function of time. b) If t e x = and 3 ln t t y = , find dx dy when 5 = t . c) Use Euler’s Method to approximate ) 4 . 1 ( y with step size 2 . 0 = h for the following initial value problem: , ' xy x y = 0 ) 1 ( = y
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Calculus II Midterm 2 March, 2009 3 2. (5 marks) Let = elsewhere x x kx x f 0 1 0 ) 1 ( ) ( 2 a) For what value of k is f a probability density function? b) Find the mean.
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March, 2009 4 3. (9 marks) A tank contains 1000 L of pure water. Brine that contains 0.10 kg of salt per liter of water enters the tank at a rate of 7 L/min. Brine that contains 0.06 kg of salt per liter of water enters the tank at a rate of 14 L/min. The solution is kept thoroughly
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Midterm 2-2009 (Pink Version) - Calculus II Midterm 2...

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