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Unformatted text preview: PRACTICE for EXAM # 3 December 6, 2007 – MA 225 B1 – Emma Previato IMPORTANT! EXAM TIMES AND LOCATIONS Exam 3 December 6 12:301:50 Room CAS 224 • Final Exam December 18 9:0011:00 Room SCI 107 Exam 3 will be returned graded at the end of lecture December 11. Grades will be posted in CourseInfo as they become available. The actual test will be shorter, there may be 2 questions of a given Type, or none. Sketch all regions for full credit. Calculus techniques must be used for credit (even when an answer can be found by elementary geometry, e.g., in 6.a ). Hint for integrating: cos 2 θ = 1+cos2 θ 2 . This formula will be printed on the exam if necessary for solution. TYPE I 1. (a) Evaluate the following double integral by sketching the region and reversing the order of integration: Z e 2 e Z ln x dy dx. (b) What is the best iteration strategy for integrating x cos( xy ) over a rectangle, and why? Find the integral over { ≤ x ≤ π 2 , ≤ y ≤ 1 } . (c) Evaluate the following double integral by sketching the region and reversing the order of integration: Z 1 Z x 2 +1 x +1 dy dx. TYPE II 2. Find the area of the polar region which is both inside the curve r 2 = 4 and outside the curve r = 1 + sin θ. TYPE III 3a. Set up a triple integral and calculate the volume of the tetrahedron bounded by the plane x +2 y + z = 1 and the three coordinate planes....
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This note was uploaded on 04/07/2008 for the course MA 225 taught by Professor Previato during the Fall '07 term at BU.
 Fall '07
 Previato
 Calculus

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