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

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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
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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
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

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
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

-1/2