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Unformatted text preview: 2. By induction, the distance between g n ( x ) and 2 is less than 1 2 n of the distance between x and 2. Thus, in this case as well, g n ( x ) 2 as n . The last case to consider is x < 2. In this case for any c between x and 2 we must have g ( c ) < 0. Using the Mean Value Theorem again, this implies that g ( x ) would be greater than 2. Thus, all the elements of the sequence { g n ( x ) } n =1 are greater than 2 and the previous case applies to show that g n ( x ) 2 as n . A similar argument shows that for any x < 0, g n ( x )  2 as n . 2...
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This note was uploaded on 11/12/2011 for the course STA 3032 taught by Professor Kyung during the Summer '08 term at University of Florida.
 Summer '08
 Kyung
 Statistics

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