作业帮关于函数无穷大无穷小的阶的问题Interpret and prove3 the following relations as x → x0 ∈ R:O(f(x)) + O(g(x)) = O(|f(x)| + |g(x)|),O(f(x))o(g(x)) = o(f(x))o(g(x)) = o(f(x)g(x)),o(O(f(x)) = O(o(f(x)) = o(o(f(x))) = o(f(x))如何证明
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/30 09:13:05
关于函数无穷大无穷小的阶的问题Interpret and prove3 the following relations as x → x0 ∈ R:O(f(x)) + O(g(x)) = O(|f(x)| + |g(x)|),O(f(x))o(g(x)) = o(f(x))o(g(x)) = o(f(x)g(x)),o(O(f(x)) = O(o(f(x)) = o(o(f(x))) = o(f(x))如何证明
关于函数无穷大无穷小的阶的问题
Interpret and prove3 the following relations as x → x0 ∈ R:
O(f(x)) + O(g(x)) = O(|f(x)| + |g(x)|),
O(f(x))o(g(x)) = o(f(x))o(g(x)) = o(f(x)g(x)),
o(O(f(x)) = O(o(f(x)) = o(o(f(x))) = o(f(x))
如何证明这三个式子?
关于函数无穷大无穷小的阶的问题Interpret and prove3 the following relations as x → x0 ∈ R:O(f(x)) + O(g(x)) = O(|f(x)| + |g(x)|),O(f(x))o(g(x)) = o(f(x))o(g(x)) = o(f(x)g(x)),o(O(f(x)) = O(o(f(x)) = o(o(f(x))) = o(f(x))如何证明
这些式子里的等于号你应该理解为一个“属于”号,然后搞明白它们的意思就很简单了.我举一例,希望你能举一反三,你看第一个式子,它实际上是说,如果我们记φ(x)=O(f(x)),ω(x)=O(g(x)),那么原式翻译一下就是：若φ(x)/f(x)和ω(x)/g(x)是x趋于x0时的有界变量,则[φ(x)+ω(x)]/[|f(x)|+|g(x)|]也是x趋于x0时的有界变量,而这结论只需要你把分母部分适当放缩下就立刻证得了.都是很简单的题目,关键是对里面“＝”的理解和对“等式”正确的解读.相信你没问题的!