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January 27th, 2010, 06:30 PM  #1 
Member Joined: Jul 2009 Posts: 40 Thanks: 0  For the limit below, find values of ? that correspond to the
For the limit below, find values of ? that correspond to the ? values. lim_(x>0) (e^x  1)/x = 1 ? is 0.05 and 0.01. What is ? for each? Round answer to four decimal places. Anyone can show me the steps? I want to see how it's done since I will have a quiz on a similar problem tomorrow. 
January 28th, 2010, 07:13 AM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: For the limit below, find values of ? that correspond to the
Basically, you have to solve (e^x  1)/x = 1.05 and (e^x  1)/x = 0.95 for x, then choose the smaller absolute value x as your ?. Then for (b), do the same for 1.01 and 0.99. There is no procedure I can recommend; you just have to get out your calculator for guessandcheck, trying various small values of x. You could also try Newton's method I suppose. It can be solved with special functions but they won't be accessible on your calculator. For part (a) you will get 0.0968 and 0.1035, so ? = 0.0968. For part (b) you will get 0.0199 and 0.0201, so ? = 0.0199. 

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