, prove that I like this limit, 'cause most of people the first thing they do is apply L'Hôpital's Rule.
Last edited by Krizalid; Dec 1st 2007 at 05:24 AM. Reason: Removing title
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Originally Posted by Krizalid , prove that I like this limit, 'cause most of people the first thing they do is apply L'Hôpital's Rule. I (almost) never used L'Hopital's Rule. Thus, . Since power series are uniformly convergent we can pass the limit through to get, . --- Solution #2. This is just the derivative of at .
Then
Originally Posted by red_dog Then nice solution! i believe this is the first time i've seen someone bring a limit inside a log. i didn't know you could do that
Originally Posted by Jhevon i believe this is the first time i've seen someone bring a limit inside a log. i didn't know you could do that The reason you can do it is that the log function is continuous. That means that if then .
Okay Here's another solution similar to red_dog's one Let's set a change of variables according to , this yields Which finally yields
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