MAT230 Study Guide - Final Guide: Talking Lifestyle 1278, Tangent Space, Lagrange Multiplier
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Instructions: you have the entire class session to complete the exam. Only scienti c non- calculus enabled calculators will be allowed. Do not approximate your answers unless explicitly told to do so. I. e- answer 2 not 1. 41 you must show all work to receive credit. Exam ii: (10 pts) find the absolute maximum and minimum of the function h(x, y) = ex2+y2+y on the region d = {(x, y)|x2 + y2 1, 1 x 1, y 0}. Exam ii: (10 pts) use the method of lagrange multipliers to nd the absolute maximum of f (x, y, z) = xy + z subject to the constraint: x2 + y2 + z2/4 = 1. T: (4 pts) using x(s, t), y(t), and z(s, t) as well as your dependence tree, compute your nal answer in terms of s and t only. If it does exist, then give the value. lim (x,y) (0,0) ex2+y2.
