设当x->0,lim((ln(1+f(x)/x))/(a^x-1))=A,(a>0,a不等于1),求当x->0,lim(f(x)/_数学解答

设当x->0,lim((ln(1+f(x)/x))/(a^x-1))=A,(a>0,a不等于1),求当x->0,lim(f(x)/x^2)

人气：480 ℃　时间：2020-04-16 20:14:08

解答

lim((ln(1+f(x)/x))/(a^x-1))=A
=lim [f(x)/x]/(xlna) [ln(1+f(x)/x)的等价无穷小为f(x)/x,a^x-1的等价无穷小为xlna]
=lim f(x)/x^2lna=A
所以lim[f(x)/x^2]=Alna