233review-ex3-sp2013 - Solutions to old Exam 3 problems Hi...

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Solutions to old Exam 3 problemsHi students!I am putting this version of my review for the Final examreview (place and time TBA) here on the website.DO NOTPRINT!!; it is very long!!Enjoy!!Best,Bill MeeksPS. There are probably errors in some of the solutionspresented here and for a few problems you will need tocomplete the the solutions or simplify the answers; somequestions are left to you the student to complete. Also youmight need to add more detailed explanations or justificationson the actual similar problems on your exam. I have put theproblems that involve Lagrange multipliers at the beginning ofthe review because there will be a problem on this material onyour exam!
Problem 11 - Spring 2008Find the absolutemaximumand absoluteminimumvalues off(x,y) =x2+ 2y2-2yin the setD={(x,y) :x2+y24}.
Problem 11 - Spring 2008Find the absolutemaximumand absoluteminimumvalues off(x,y) =x2+ 2y2-2yin the setD={(x,y) :x2+y24}.Solution:Find critical points off(x,y):
Problem 11 - Spring 2008Find the absolutemaximumand absoluteminimumvalues off(x,y) =x2+ 2y2-2yin the setD={(x,y) :x2+y24}.
Problem 11 - Spring 2008Find the absolutemaximumand absoluteminimumvalues off(x,y) =x2+ 2y2-2yin the setD={(x,y) :x2+y24}.
Problem 11 - Spring 2008Find the absolutemaximumand absoluteminimumvalues off(x,y) =x2+ 2y2-2yin the setD={(x,y) :x2+y24}.
Problem 11 - Spring 2008Find the absolutemaximumand absoluteminimumvalues off(x,y) =x2+ 2y2-2yin the setD={(x,y) :x2+y24}.
Problem 11 - Spring 2008Find the absolutemaximumand absoluteminimumvalues off(x,y) =x2+ 2y2-2yin the setD={(x,y) :x2+y24}.

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