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Unformatted text preview: M ATH 224 P ROBLEM S ET 3 D UE : 12 F EBRUARY 2008 When you hand in this problem set, please indicate on the top of the front page how much time it took you to complete. Reading. 4.54.8. Problems from the book: 4.5.5, 4.5.8, 4.5.12, 4.5.17 4.6.2, 4.6.4, 4.6.6 4.8.1, 4.8.2 Additional problems: 1. Two cylinders, both of radius R, intersect at a right angle. That is, their axes intersect at a right angle. What is the volume of the region common to both cylinders? 2. Let A Rn. A sequence of functions fk : A R pointwise converges to a function g : A R if, for every x A, the sequence fk(x) converges, and k lim fk(x) = g(x). Prove the following statement, or find a counterexample. Let fk : [0, 1] R be a sequence of functions, each integrable. Suppose that the sequence pointwise converges to a function g : [0, 1] R. Then g is integrable. 3.1 3. Compute e- 2 dx 3 x2 to within 10-4, with proof that you are within that range. ...
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This homework help was uploaded on 02/24/2008 for the course MATH 2240 taught by Professor Taraholm during the Spring '08 term at Cornell University (Engineering School).
- Spring '08