x趋近于0时,(1-cosx/2)是x的高阶无穷小怎么算?
问题描述：
x趋近于0时,(1-cosx/2)是x的高阶无穷小怎么算?
答
(1-cosx)/2 = (1-(1-2sin^2 (x/2)))/2
=sin^2 (x/2)
~= (x/2)^2
x趋近于0时,(1-cosx/2)是x的高阶无穷小请问您是不是看错题了？do you mean 1 - cos (x/2) ?是的almost the same:1-cos(x/2) = 1- (1-2sin^2 (x/4)))= 2 sin^2 (x/4)~= 2(x/4)^2 是x的2阶无穷小