problem with proof (e^x)' = e^x | Mathematics | Page 1

thorny current Sep 19, 2022, 2:25 AM

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one of the steps to the proof doesnt make sense

waxen kettleBOT Sep 19, 2022, 2:30 AM

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Daniel_The_Maniel

thorny current Sep 19, 2022, 2:37 AM

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at some point in the proof we get that $\lim_{n\to 0} \frac{1}{\ln{((1+n)^{\frac{1}{n}})}}=\frac{1}{\ln{(\lim_{n\to 0} (1+n)^{\frac{1}{n}}})}$

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but i thought it was only justifiable to take the function $f(x)=\frac{1}{\ln{(x)}}$ outside of the limit if f is continuous at 0, which it isnt.

waxen kettleBOT Sep 19, 2022, 2:37 AM

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Daniel_The_Maniel

#problem with proof (e^x)' = e^x