Stolz定理的推广及其应用

利用简单的数学工具,证明了斯铎兹(Stolz)定理的推广定理,给出了进一步研究极限问题的新途径;对计算数列的极限、函数的极限有着重要的作用;作为一种应用,再利用斯铎兹(Stolz)定理的推广定理给出了罗比达法则的新证明,避免了传统证明中的繁杂过程。容易看出:斯铎兹(Stolz)定理的推广定理是联系斯铎兹(Stolz)定理和罗比达法则的桥梁。

The Promotion and Application of Stolz Theorem

By using simple mathematical tools to prove the generalized theorem of the Stolz Theorem,a new way is given to further research the issue of limitation,which constitutes a very important role in calculating the limitation of sequences and functions.On this basis and as an new application,a new proof is given for L ’Hopital Rule by using the generalized theorem of the Stolz Theorem,so that the complexity in the traditional proving process is avoided.It is easy to know that the generalized theorem of Stolz Theorem is the bridge between Stolz Theorem and L′Hopital Rule.