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Unformatted text preview: 2.33 By Exercise 2.31 and Example 2.53, each is strictly increasing on + . That is 1 < 2 = ( 1 ) < ( 2 ) for every (2.32) and therefore lim ( 1 ) lim ( 2 ) This suces to show that ( ) = lim ( ) is increasing (not strictly increasing). However, 1 + is strictly increasing, and therefore by Exercise 2.31 = 1 + + ( ) is strictly increasing on + . While it is the case that = lim is strictly increasing on + , (2.32) does not suce to show this. 2.34 For every > 0, log is strictly increasing (Exercise 2.32) and therefore log is strictly increasing (Exercise 2.28). For every < 0, log is strictly increasing and therefore (Exercise 2.30 log is strictly decreasing. Therefore log is strictly decreasing (Exercise 2.28).decreasing (Exercise 2....
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This note was uploaded on 01/16/2012 for the course ECO 2024 taught by Professor Dr.dumond during the Fall '10 term at FSU.
- Fall '10