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May 18th, 2019, 09:55 AM   #1
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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?
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May 18th, 2019, 12:41 PM   #2
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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.
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May 18th, 2019, 01:00 PM   #3
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Quote:
Originally Posted by v8archie View Post
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.
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