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

$$calculate{lim}_{x\to 0}\frac{ln(1+ln(1+x))}{x}$$

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

$$ln(1+x)\sim x$$$$\Rightarrow ln(1+ln(1+x))\sim ln(1+x)$$$$\frac{ln(1+x)}{x}\to 1$$$$\Rightarrow \underset{x\to 0}{\lim }\frac{ln(1+ln(1+x))}{x}\to 1$$

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