$$\color{rgb(0,127,0)}u_{1}$$

$$\color{rgb(255,0,0)}u_{2}$$

$$\color{rgb(255,0,0)}u_{2} ≃ 1.609437912434$$

$$\color{rgb(255,0,0)}u_{2} = f(u_{1})$$

$$\color{rgb(0,0,0)}u_0$$

$$\color{rgb(0,0,255)}y=x$$

$$\color{rgb(127,0,0)}\left\{ \begin{array}{l} f(x)=\ln \left( 2e^x - 1 \right) \\ \text{avec }x \ge 0 \end{array}\right.$$

$$\color{rgb(127,0,0)}C_f$$