lim(x->0)[cosx-e^(-x^2/2)]/[x^2[x+ln(1-x)]]

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/12 22:28:19

lim(x->0)[cosx-e^(-x^2/2)]/[x^2[x+ln(1-x)]]
为什么分母是四阶啊?怎么看的?
为什么ln（1-x）这一项要算到2阶啊

原式=
lim{x->0}[1-x^2/2+x^4/24+o(x^4)-(1-x^2/2+x^4/8+o(x^4))]/[x^2(x-x+x^2/2+o(x^2)]
=lim{x->0}[-x^4/12+o(x^4)]/[x^4/2+o(x^4)]
=lim{x->0}[-/12+o(1)]/[1/2+o(1)]
=-1/6
因为分子是4阶无穷小,分母是高于3阶的无穷小,所以ln(1-x)至少要展开到平方项啦.

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