lim [(sinX+X²cos1/X)] / [(1+cosX)ln(1+X)]
=(1/2)lim [(sinX+X²cos1/X)] / x
=(1/2)lim [(sinX)/x+Xcos1/X)]
=1/2
是同阶但不是等价无穷小
是sinx +x²cos(1/x)么?sinx +x²cos(1/x) ~ x +x²cos(1/x) = x(1+xcos(1/x) )
|cos(1/x)| <1,所以xcos(1/x) ->0, 1+xcos(1/x) ~1
所以sinx +x²cos(1/x) ~ x
而(1+cosx)ln(1+x) ~ 2x,所以他们是等阶无穷小