这个极限怎么泰勒展开

cosx = 1 - (1/2) * x^2 + o(^2)
[ cos(2x) ]^(1/2) = [ 1 - (1/2) *(2x)^2 ]^(1/2) + o(^2) = 1 - (1/2) *(1/2) *(2x)^2 + o(^2)
= 1 - x^2 + o(^2)
[ cos(3x) ]^(1/2) = [ 1 - (1/2) *(3x)^2 ]^(1/2) + o(^2)
= 1 - (1/2) *(1/2) *(3x)^2 + o(^2) = 1 - (9/4) * x^2+ o(^2)
分子 = 1 - { [ 1 - (1/2) * x^2+ o(^2) ] * [ 1 - x^2 + o(^2) ] * [ 1 - (9/4) * x^2+ o(^2)]
= - [ (1/2) + 1 + (9/4) ] * x^2 + o(^2) = (15/4 ) * x^2 + o(x^2)
故 [ (15/4 ) * x^2 + o(x^2) ] / x^2
= - 15/4 + o(1)
原式 = - 15/4
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