MATH 226 Study Guide - Final Guide: Surface Integral, Lagrange Multiplier, Tangent Space

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Mancera (11am 1pm) mikulevicius (10am 11am) russell (9am 12pm) You must show your work to obtain full credit. Points may be deducted if you do not justify your nal answer. Please indicate clearly whenever you continue your work on the back of the page. The exam is worth a total of 8 25 = 200 points. 1: given f (x, y) = xp3 x2 y2, (a) find and sketch the domain of f . (b) find the linearization of f at (1,1). Write an equation of the tangent plane to z = xp3 x2 y2 at (1, 1, 1). 3: use lagrange multipliers to nd the absolute maximum and minimum values of the function f (x, y) = x2y subject to the constraint 2x2 + y2 = 3. 4. (a) evaluate r r re(xpx2 + y2 + z2 + zy)dv , where.

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