calculate-lim-x-0-ln-1-ln-1-x-x-

Question Number 82920 by abdomathmax last updated on 25/Feb/20

c a l c u l a t e {l i m}_{x \to 0} \frac{l n (1 + l n (1 + x))}{x}

Answered by mind is power last updated on 25/Feb/20

l n (1 + x) \sim x

\Rightarrow l n (1 + l n (1 + x)) \sim l n (1 + x)

\frac{l n (1 + x)}{x} \to 1

\Rightarrow \lim_{x \to 0} \frac{l n (1 + l n (1 + x))}{x} \to 1