131 practice test 2 - Practice for Test II Math 131 Show...

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Practice for Test IIMarch 27, 2014Math 131Show enough work that we can follow your thinking. You must show all appro-priate algebraic work in order to receive full credit for an answer.1.(20 points)(a) Assume that the population of adult owls and juvenile owlschanges from year to year according to the Leslie matrixA=0.20.70.70.2Assuming that the initial population distribution is30001000, describe the popula-tion distribution afternyears. Use the fact that30001000=20002000+1000-1000Hint: ApplyAto each of the vectors on the right hand side.(b) Find the eigenvalues and eigenvectors of this matrix:57-2-4
2Math 1302.(25 points)For each of the following, find all the second order partial derivatives.(a)f(x, y) = 5xy-7x2-y2+ 3x-6y-4(b)f(x, y) = 5x3+ 2y2-60xy-3(c)f(x, y) =x2+ey3.(25 points)For each of the following, find all points where there might be arelative maximum or minimum or saddle point, and identify each one as one of

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