w07final - Math 42: Calculus Final Exam March 19, 2007 Name...

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Math 42: Calculus Final Exam — March 19, 2007 Name : Section Leader (Circle one) : Buyukboduk Chang Lee Segerman Zhang Section Time (Circle one): 11:00 1:15 This is a closed-book, closed-notes exam. No calculators or other electronic aids will be permitted. In order to receive full credit, please show all of your work and justify your answer. You do not need to simplify your answers unless specifically instructed to do so. If you need extra room, use the back sides of each page. If you must use extra paper, make sure to write your name on it and attach it to this exam. Do not unstaple or detach pages from this exam. Please sign the following: “On my honor, I have neither given nor received any aid on this examination. I have furthermore abided by all other aspects of the honor code with respect to this examination.” Signature: The following boxes are strictly for grading purposes. Please do not mark. 1 9 7 12 2 10 8 16 3 12 9 13 4 15 10 12 5 21 11 6 6 11 12 13 Total 150 GOOD LUCK ON THE REST OF YOUR EXAMS, AND HAVE A GREAT SPRING BREAK!
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1. (9 points) Let R be the region bounded by the curves y = f ( x ) and y = g ( x ) shown in the graph below. - 4 - 2 2 4 x 4 - 2 2 4 y f H x L H - 3, 2 L H 2, - 3 L g L (a) Set up a definite integral that will give the area of the region R . (b) Set up a definite integral that will give the volume of the solid generated when the region R is revolved about the line y = 4. (c) If the base of a solid V is the region R , and if all cross-sections of V that are perpendicular to the x -axis are squares, set up a definite integral that will give the volume of V .
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2. (10 points) According to Newton’s Law of Gravity, an object near the earth at a distance of r meters from the center of the earth feels a gravitational force of F = k/r 2 Newtons, where k is a positive constant that depends on the mass of the object.
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w07final - Math 42: Calculus Final Exam March 19, 2007 Name...

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