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数学
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当x趋向于0时,(1+ax^2)^1/3-1与cosx-1是等价无穷小,则a等于?
人气:195 ℃ 时间:2020-03-25 15:56:10
解答
cosx-1=1-2(sinx/2)^2-1=-2(sinx/2)^2
而-sin(x/2)^2和-(x/2)^2=-x^2/4是等价无穷小
因为(1+x)^y-1和yx是等价无穷小
所以(1+ax^2)^1/3-1和1/3ax^2是等价无穷小
由题意则-1/4=1/3a a=-3/4
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