test1_(in_class) - a n +1 = 1 + 1 1 + a n , n N , where a 1...

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Test 1 (In class part), MAA4226 Fall 2010 Student Name: 60 minutes. Closed book. This part weighs 40% of the total weight of Test 1. 1: State and prove the extreme value theorem. 2: Let { a n } be a sequence such that lim n →∞ a 2 n = lim n →∞ a 2 n +1 = l . Show that lim n →∞ a n = l . 3: Let { a n } be the sequence defined by the recurrence relation
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Unformatted text preview: a n +1 = 1 + 1 1 + a n , n N , where a 1 = 1. Use problem 2 above to show that { a n } is convergent and nd its limit. 3: Let f : [0 , 1] R be continuous and one-to-one. Show that f is strictly monotone. 1...
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This note was uploaded on 11/18/2011 for the course MAP 4426 taught by Professor Tamasan during the Fall '10 term at University of Central Florida.

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