Wednesday, July 6, 2016

How to calculate this limit without L'Hopital's rule

I know that in the very small values of x
(1+x)n1+nx


and I can prove it using Taylor series.
But I wanted to prove it without any smell of derivative.



So... In order to calculate the following limit



limx 0(1+x)n1x,



I know that the result must be equal to n.




But is there any method without using l'Hospital's rule?



Note : n can be any real value not just for integers, so I didn't want to use binomial theorem.

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