I know that in the very small values of x
(1+x)n≈1+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)n−1x,
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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