My Math Forum Proof for natural logarithm limit without differentiation

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 May 18th, 2019, 09:55 AM #1 Member   Joined: Aug 2016 From: Romania Posts: 32 Thanks: 1 Proof for natural logarithm limit without differentiation I have another limit where I'm struggling with the solving.Can somone help me? https://ibb.co/5Kq58jR I used a method like this but I'm not 100% if it's correct! https://ibb.co/JQrpdL1 What should I do from that step? I know something like arctan(x)/x when x tends to 0 is 1. How is that going to help me?
 May 18th, 2019, 12:41 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra I would always use Taylor series for that, but they are hard to come by without differentiation. $\log (1+x) \ne \log x$ and $\log (1-x) \ne \log \frac1x$. Last edited by v8archie; May 18th, 2019 at 01:16 PM.
May 18th, 2019, 01:00 PM   #3
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Joined: Aug 2016
From: Romania

Posts: 32
Thanks: 1

Quote:
 Originally Posted by v8archie I would always use Taylor series for that, but they are hard to come by without differentiation. $\log (1+x) \ne \log x$ and $\log (1-x) \ne \log \frac1x$.
Thanks for the answer. Do you know how to solve this problem? I'm stuck with it.

Last edited by greg1313; May 19th, 2019 at 01:15 AM.

 Tags differentiation, limit, logarith, logarithm, natural, proof

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