第14章§6 - 10

$$\begin{array}{rl}\underset{x\to 0}{lim}\frac{\log (1+2x)}{x}& =\underset{x\to 0}{lim}\frac{1}{x}\{2x-\frac{(2x{)}^2}{2}+\cdots \}\\ & =\underset{x\to 0}{lim}(2-2x+\cdots )\\ & =2\end{array}$$