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Math 246 Final Exam Fall 2006 M.Jakobson
Solve each of the following eight problems on a separate auswer sheet, using
the back of the sheet if necessary. Put your name, section number, the name
of your recitation instructor, and the number of the problem on each sheet.
Carefully show all your steps and explain your arguments. Cross out any
material that is not to be graded. You may NOT use calculators, notes or
texts.
1. Solve the initial value problem. Find the maximal interval in which
the solution is valid.
, x
y = 2yvx2 _ 16 y(5) = 2
2. (a) A tank contains 10 kg of salt dissolved in 100 liters of water. A
solution of salt water containing 1 kg/liter flows into the tank at
a rate of 5 liters/minute, and well rnixed solution flows out of the
tank a.t the same rate.
I. Write down an initial value problem satisfied by the amount
of salt Q(t) in the tank at time t.
11. Solve the initial value problem.
m. Determine the limiting amount of salt in th...

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