[问答题]
1. Use L'Hôpital's rule tohxau3t5 i6 w0jf8kf *z fn-4) 3jm9 pzo715dxjzg qa b iv2kb*xoind $\lim _{x \rightarrow \infty} x^{3} e^{-x} $.
2. Show that the proper integral $\int_{0}^{\infty} x^{3} e^{-x} \mathrm{~d} x$ converges, and state its value.
