3. (7p) Consider the sequence $\left(x_{n}\right)_{n \in N}$ with $x_{0} \geq 0, a \in(0,1)$ and $x_{n+1}=a x_{n} e^{-x_{n}}, n \in N$. Calculate

$$
\lim _{n \rightarrow \infty} x_{n} \ln \left(1+n^{3}\right)
$$

GM10/2015