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Unformatted text preview: MAC 2313, Fall 2010 — Midterm 3 Review Problems 1 We will discuss these problems in class on Monday 10/25. Solutions will be posted on the course webpage over the weekend. 1 Use the method of Lagrange multipliers to find the maximum and minimum values of f ( x, y ) = 3 x 4 + 5 y 4 subject to the constraint x 2 + y 2 = 1. 2 Using the method of Lagrange multipliers, find the point on the surface x 2 y + zy = 2 which is closest to the origin. 3 Evaluate the integral integraldisplay 3 integraldisplay 9 y 2 y cos( x 2 ) dx dy by first changing the order of integration. 4 Sketch the region of integration of the iterated integral integraldisplay 2 1 integraldisplay ln x f ( x, y ) dy dx and change the order of integration. 5 Let R denote the region in the xy-plane bounded by the lines x =- 1, x = 1, y =- 1, and y = 1 which is outside the square given by | x | + | y | = 1. Express the double integral integraldisplayintegraldisplay R f ( x, y ) dA as a sum of iterated integrals....
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- Fall '08
- Calculus, dy dx, Multiple integral, dx dy, 3-space