当x→0时,x-sinxcos2x~cxk,则c=________,k________.

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问题 当x→0时,x-sinxcos2x~cxk,则c=________,k________.

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答案[*]

解析 因为x→0时,sinx=x-x3/3!+o(x3),
cos2x=1-(2x)2/2!+o(x2)=1-2x2+o(x2),
sinxcos2x=x-13/6x2+o(x3),
所以x-sinxcos2x=13/6x3+o(x3)~13/6x3,故c=13/6,k=3.
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