Exam #1 Review
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This 1 page Study Guide was uploaded by Anna Huryn on Monday February 8, 2016. The Study Guide belongs to MA 231 at North Carolina State University taught by Mr. Glen Sidle in Spring 2016. Since its upload, it has received 33 views. For similar materials see Calc Life Management B in Math at North Carolina State University.
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Date Created: 02/08/16
MA 231-002 REVIEW SHEET 2 2 2 1. Compute @f ,@f , @ f, @ f, and @ f . @x @y @y2 @x2 @x@y (a) f(x;y) = e x +xy+y 2 (b) f(x;y) = x y ln(xy) 2. Find all the critical points of the given function and use the Second Derivative Test to classify the points. 3 2 2 3 (a) f(x;y) = x + y ▯ 3x ▯ 8y + 12 (b) f(x;y) = 2x + y ▯ x ▯ 12y + 7 3. Use Langrange multipliers to maximize (a) f(x;y) = 3x + 2xy ▯ y 2 subject to the constraint 2x + y = 5. (b) 2 2 2 f(x;y;z) = 3x + 2y + z + 4x + y + 3x subject to the constraint x + y + z = 4. 4. Evaluate the double integral. Z 1 Z 3 Z 2 Z 1 (a) 2x ▯ 4y dydx (b) xex +y dydx ▯2 1 1 0 1
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