复合函数求极限之定则
definition
设\(y=f[\phi (x)]\)由 \(y=f(u), u=(x)\) 复合组成.
\(f[\phi (x)]在点x_{0}\)的某一去心邻域内有定义.
假若:
\[\lim_{x \to x_{0}} \phi (x)=u_{0}
\\ \\
\lim_{u \to u_{0}} f(u)=A
\]
并且符合以下条件:
- \(\delta_{0} >0\)
- 当\(x \in \mathring{U}(x_{0},\delta_{0})\)时, $ \quad \phi(x) \ne u_{0}(即 u \ne u_{0})$
如若满足以上条件,则: $$ \lim_{x \to x_{0}} f[\phi (x)]=\lim_{u \to u_{0}} f(u)=A $$
