√(1-cosx)/1-cosx的极限 x趋近于无穷 极限0

(1-cosxcos2xcos3x)/(1-cosx)当x趋近于0时的极限_百度知道当X的右极限趋向于0时,求lim(1-根号cosx)/[x(1-cos根号x)的极限
天下雨了81
∵x→0时,1-cosx~x²/2∴1-cos√x x/2lim [1- √(cosx) ] / [x(1- cos√x )]= lim [1- √(cosx)] / (x²/2)= lim [1-√(cosx)][1+√cosx] / (x²/2)[1+√cosx]= lim (1- cosx) / (x²/2)(1+√cosx)= lim (x²/2) / (x²/2)(1+√cosx)= 1/2
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分子分母同乘以(1+根号cosx).后分子1-cosx~1/2x^2
分母为x(1/2x)(1+根号cosx).答案为1/2
分母怎么变形啊? 消不去啊
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/etc/nginx/nginx.conf.x趋近于0,lim(1-根号下cosx)/x(1-cos根号下x)
cc晨晨°ISHD
=lim (1-cosx)/[x(1-cos根号下x)·(1+根号下cosx)]=(1/2)·lim (x²/2)/[x(1-cos根号下x)]=(1/4)·lim x/(1-cos根号下x)=(1/4)·lim x/((根号下x)²/2)=1/2
看不明白第一步怎么到第二部的,就是分母为什么变成[x(1-cos根号下x)]?
1+根号下cosx的极限是2,直接提到lim的外面去了。没看见最前面有个(1/2)吗?
当x趋近于0时,1-cosx与x²/2是等价无穷小
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