122(s08)reviewchapter7

122(s08)reviewchapter7 - minimize the cost of fencing if...

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REVIEW: Chapter 7 1.) Given: 2 2 2 2 ) , ( x y xy y x f + - = Compute: ) 2 , 3 ( ) 5 , 3 ( - - x f f 2.) Given: x y y x f - = 2 ) , ( find and sketch the level curve for the given function when C=0. 3.) Given: 4 2 2 2 ) 3 2 ( ) , ( 2 ) , ( ) 5 2 ln( ) , ( 3 y x y x f y x e y x f y x y x f xy - = - + = - = Compute all first and second order partials (including the mixed partials) 4.) Given: 1 3 ) , ( 3 4 3 ) , ( 3 3 2 2 - - + = - - - + - = xy y x y x f y x y xy x y x f Find and classify all extreme points 5.) Using Lagrange Multipliers, minimize 2 2 5 ) , ( y xy x y x f - - - = subject to the constraint 0 3 2 = - + y x 6.) (using Lagrange Multipliers) Find two positive numbers whose sum is 36 and whose product is as large as possible. 7.) (using Lagrange Multipliers) What are the dimensions of the rectangular field of 20,000 cubic feet that will
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Unformatted text preview: minimize the cost of fencing if one side cost three times as much as the other three? 8.) Given: (0,4),(1,2),(2,2),(3,1),(4,1) Using partial derivatives compute the formula for the best least square line (or the regression line). Also, compute the least square error. 9.) Compute: ∫ ∫ 1 2 ) 48 ( x x dx xydy 10.) Compute 1 2 ) 6 ( 2 ≤ ≤ ≤ ≤ ∫ ∫ y x where dxdy xy R...
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This note was uploaded on 04/07/2008 for the course MATH 122 taught by Professor Rommero during the Spring '08 term at SUNY Buffalo.

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