MATH 230 Midterm: Math 230 Spr2014Exam2c
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Will be deducted if the majority of your answers are not. 2 (1) (5 pts) decide whether or not the limit below exists. Do not compute the value of f (x, y) at the critical points. Each critical point should be classi ed as either a local max, a local min, or a saddle point. 6 (5) (10pts) find the absolute maximum and minimum values of the function f (x, y) = px2 + y2, over the region d bounded by the ellipse x2. + y2 = 1. (6) (10pts) use lagrange multipliers to nd the point on the plane x + 3z 6 = 0 closest to the point (0, 0, 3). D over the region d bounded by the y-axis, the line y = 1, and the curve y = x. y. 1 + 2y4 da (8) (10 pts) find the volume of the solid bounded by plane z = 0 and surface z = 2 2x2 2y2.
