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Unformatted text preview: (b) (3 pts) Evaluate f (3 , 11). (c) (5 pts) On the axes below, sketch the level curves of f for c = 1 3 , 1 2 , and 1. a45 a27 a54 a63 x y Exam 2, Page 4 of 8 March 25, 2010 3. (5 pts) If you want to create a perpetuity that pays out $4000/month, and the money is in an account earning interest at a rate of 3%, how much money do you need to start with? 4. Let s ( x, y, z ) = cos( x ) ln( y ) z 2 . Evaluate the following partial derivatives. (a) (6 pts) s yx = ∂ 2 s ∂x∂y (b) (6 pts) s zy = ∂ 2 s ∂y∂z (c) (6 pts) s zz = ∂ 2 s ∂z 2 Exam 2, Page 5 of 8 March 25, 2010 5. (12 pts) Let h ( x, y ) = xy 2 + x + 5 x + 2 y . Find and classify the relative extrema of h . Exam 2, Page 6 of 8 March 25, 2010 6. (12 pts) Let f ( x, y ) = x 3 + 3 y 2 + 6 and let g ( x, y ) = 1 2 x 2 y 1. Under the constraint g ( x, y ) = 0, the function f has an absolute minimum and two other relative extrema. Use the method of Lagrange multipliers to find these extrema, and state which one is the absolute minimum. Exam 2, Page 7 of 8 March 25, 2010 7. (12 pts) Let R be the region { ( x, y )  4 √ ln x ≤ y ≤ √ x, e ≤ x ≤ e 4 } . Evaluate integraldisplayintegraldisplay R √ ln x y 3 dA . Exam 2, Page 8 of 8 March 25, 2010 8. (12 pts) Find the average value of the function f ( x, y ) = 2 y sin( x + y 2 ) on the region where 11 π 4 ≤ x ≤ π 4 and √ π 2 ≤ y ≤ √ π ....
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 Spring '12
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 Math, Derivative, Optimization, Following, 1971, 1969

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