Homework_3 - Homework 3 - Math 139 Due Sep 22nd Instructor...

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Unformatted text preview: Homework 3 - Math 139 Due Sep 22nd Instructor Office Office hours Web page Mauro Maggioni 293 Physics Bldg. Monday 1:30pm-3:30pm. www.math.duke.edu/˜ mauro/teaching.html Reading: from Reed’s textbook: Sections 2.4,2.5 Problems: §1.3: #3(c) , 8. In both exercises, note that the sets need not be disjoint! §2.1: #2b,3b,4b,6,9b Additional Problem: Show that limn→+∞ r n does not exist if r ≤ −1, by showing that for any L ∈ R, the statement lim r n = L n→∞ is false. [Suggested steps: after carefully stating what you want to prove, take ǫ = 1 in 4 1 your statement. If |L − r n | > 4 (what is n?), you are good. If not, notice that |r n − r n+1 | ≥ 1 (why?), then use the inequality of #10, §1.1 to conclude that |L − r n+1 | > 1/4). ...
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