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X” ' 'W (ff; w ‘..,.,_,LILQJJLLWQWWWWWW—w .V 12. Problem: Consider the function f (x, y) = x2 + y2 subject to the constraint: g(x, y) : x2 — y2 =1 . a. Sketch the graph of the level curves of g(x, y) = 1, and f (x, y) = k, k = i, 1, 4, 9.
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part a. d. Find the minimum value of the function f constrained to g and the point at which this occurs. 13. Consider the following problem: Find the volume of the largest rectangular solid inscribed in a
sphere, that is, maximize V(x, y, z) = (2x)(2 y)(22) given that x2 + y2 + 22 = a2. a. Set up the problem using the method discussed in section 15.7. b. Set up the problem using Lagrange Multipliers. That is write down all the equations needed to
solve the problem using Lagrange Multipliers. c. Solve the problem using the method of your preference. 14. Find the tangent plane and the normal line to the surface x2 + y2 — 22 =18, at P0 = (3,5,—4). V1.3; _ . ., , .., ,. .: __ M. _, k .. A W _. _, . ‘ _, . 7, Ag” ,mangn V = “#2 _ , Z++£f2_;:a/+ V, > v . __ W _V E“, Y Z = M76177. v 7 y, ‘ _, _._,,_,,«_;sz aixgm 41;»). 4 _ , _ M
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 Spring '10
 RiosAdams
 Constraint, Level set, lagrange multipliers, Joseph Louis Lagrange, C NV

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