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
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![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](/uploads/image/z/1646079-15-9.jpg?t=lim%28x-%3E0%29%5Bcosx-e%5E%28-x%5E2%2F2%29%5D%2F%5Bx%5E2%5Bx%2Bln%281-x%29%5D%5D%E4%B8%BA%E4%BB%80%E4%B9%88%E5%88%86%E6%AF%8D%E6%98%AF%E5%9B%9B%E9%98%B6%E5%95%8A%3F%E6%80%8E%E4%B9%88%E7%9C%8B%E7%9A%84%3F%E4%B8%BA%E4%BB%80%E4%B9%88ln%EF%BC%881-x%EF%BC%89%E8%BF%99%E4%B8%80%E9%A1%B9%E8%A6%81%E7%AE%97%E5%88%B02%E9%98%B6%E5%95%8A)
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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
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
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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