sinx-xcosx怎么化
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sinx-xcosx化简：
sinx = x - (1/3!) x^3 + (1/5!) x^5 - ...
cosx = 1 - (1/2!) x^2 + (1/4!) x^4 - ...
sinx - x * cosx = [ x - (1/3!) x^3 + (1/5!) x^5 - ... ] - x * [ 1 - (1/2!) x^2 + (1/4!) x^4 - ... ]
= [ - (1/3!) + (1/4!) ] * x^3 + [ (1/5!) - (1/4!) ] * x^5 + ....
= [ - (1/3!) + (1/4!) ] * x^3 + o(x^3)
= - (1/8) * x^3 + o(x^3)
sinx = x - (1/3!) x^3 + (1/5!) x^5 - ...
cosx = 1 - (1/2!) x^2 + (1/4!) x^4 - ...
sinx - x * cosx = [ x - (1/3!) x^3 + (1/5!) x^5 - ... ] - x * [ 1 - (1/2!) x^2 + (1/4!) x^4 - ... ]
= [ - (1/3!) + (1/4!) ] * x^3 + [ (1/5!) - (1/4!) ] * x^5 + ....
= [ - (1/3!) + (1/4!) ] * x^3 + o(x^3)
= - (1/8) * x^3 + o(x^3)
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