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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 guess-and-check, 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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