设x趋近于零时,tanx-sinx与ax^k是等价无穷小,求常数a与k的值
问题描述：
设x趋近于零时,tanx-sinx与ax^k是等价无穷小,求常数a与k的值
答
用泰勒展开
tanx = x + x^3/3 + o(x^3)
sinx = x -x^3/6+ o(x^3)
tanx -sinx = x^3/2 + o(x^3)
a = 1/2
k = 3