$\lim_{x\to0} \frac{(1+x)^a-1}{x} $

Question

$\lim_{x\to0} \frac{(1+x)^a-1}{x} $ I really stuck, because $a$ is not an integer. If it is, I can solve it, but here I totally stuck

Or this: https://math.stackexchange.com/questions/1789815/how-to-solve-lim-x-rightarrow-0-frac1xa-1x — Martin R, Jan 30 '18 at 15:51

score 0 · Answer 1 · answered Jan 30 '18 at 15:52

0

Using L'hopital you could easily find that: $lim_{x->\infty} \frac{(1+x)^a -1}{x} = lim_{x->\infty} a(1+x)^{a-1}$. Do you think you can answer it from here?

answered Jan 30 '18 at 15:52

Fibonacci

291

score 0 · Answer 2 · answered Jan 30 '18 at 15:53

0

This is the limit of the rate of variation of the function $(1+x)^a$ when $x$ tends to $0$. The limit is the derivative of the function at $x=0$.

answered Jan 30 '18 at 15:53

Bernard

175,478

$\lim_{x\to0} \frac{(1+x)^a-1}{x} $

2 Answers2