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Unformatted text preview: n N . Hence x n = n is both frequently even and odd. This does not conict with 3.2.4 as the rst case says via 3.2.4 that it is not true that x n = n is ultimately odd, while the second case says that it is not true that x n = n is ultimately even. Page 36 Problem 2. a. Note x n = 1 for n = 4 k + 1 with k Z . Hence given N take n = 4 N + 1 to get n N with x n = 1. b. Note rst that sin x x for all x 0 (this is used in Calculus 1 to show that (sin x ) = cos x ). Now 2 n < 1 for all n 7, so also sin( 2 n ) < 1 for all n 7. 1...
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This note was uploaded on 02/05/2012 for the course MATH 554 taught by Professor Girardi during the Fall '10 term at South Carolina.
- Fall '10