\(\mathop {\lim }\limits_{x \to 0} \dfrac{{\ln \left( {1 + x} \right)}}{x} = 1\)

\(\mathop {\lim }\limits_{x \to 0} \dfrac{{\ln \left( {1 - x} \right)}}{x} = 1\)

\(\mathop {\lim }\limits_{x \to 0} \dfrac{{\ln x}}{x} = 1\)

\(\mathop {\lim }\limits_{x \to 0} \dfrac{{\ln \left( {1 + x} \right)}}{{1 + x}} = 1\)