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January 27th, 2010, 06:30 PM   #1
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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.
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January 28th, 2010, 07:13 AM   #2
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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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