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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 $\log (1x) \ne \log \frac1x$. Last edited by v8archie; May 18th, 2019 at 01:16 PM. 
May 18th, 2019, 01:00 PM  #3 
Member Joined: Aug 2016 From: Romania Posts: 32 Thanks: 1  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. 

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differentiation, limit, logarith, logarithm, natural, proof 
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