ThmDex – An index of mathematical definitions, results, and conjectures.
Result R2658 on D865: Standard natural real logarithm function
Standard natural real logarithm function grows linearly near 1
Formulation 0
Let $x \mapsto \log x$ be the D865: Standard natural real logarithm function.
Then \begin{equation} \lim_{x \searrow 0, \, x \neq 0} \frac{\log(1 + x)}{x} = 1 \end{equation}