test1 - Math 072 Test 1, Spring 2008 Name: Solution $ 1....

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Math 072 Test 1 , Spring 2008 Name: Solution 1. Let 5 0ÐBÑ œ B  B-9=B%Þ $ (5 pts) a. Show that has an inverse on the real line You need to give an analytic argument, not just rely on graphs (graphs are hard to be accurate). . Since for all , is increasing, and hence, is one- Ans 0ÐBÑœ$B &=38B! B 0 w# to-one. (5 pts) b. Compute for the given above. You must show your steps for credit. Ð0 Ñ Ð  &Ñ 0 " w Ans . By Theorem 7, §7.1, , where Since 0 , Ð0 Ñ Ð+Ñ œ 0Ð,Ñ œ +Þ 0Ð Ñ œ  & Ð0 Ñ Ð&Ñ " w " w " 0Ð,Ñ w œœ œ Þ """ 0 Ð Ñ $Ð!Ñ&=38 ! & w 0 (5 pts) 2a. Describe briefly how the number was defined? Note that a decimal expansion is just an approximation, / not a definition. . is the number the curve has a slope exactly equals to 1 at or equivalently, is the Ans /C œ / B œ ! ß / B number such that lim 2Ä! /" 2 2 œ"Þ (5 pts) b. Use your definition of Part a to show if 0 ÐBÑ œ / 0 ÐBÑ œ / Þ wB B 0ÐBÑœ œ œ œ œ/ œ/ †"œ/ Þ w BB B 2Ä! 2Ä! 2Ä! 2Ä! 2Ä!
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test1 - Math 072 Test 1, Spring 2008 Name: Solution $ 1....

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