Question

当x趋于0时 f(x)=x-sinx与f（x)=xln(1-ax²）为等价无穷小,则a=

Answer 1

lim(x->0)(x-sinx)/[xln(1-ax²）]
=lim(x->0)(x-sinx)/[x·(-ax²）]
=-1/a lim(x->0)(x-sinx)/[x³]
=-1/alim(x->0)(1-cosx)/[3x²]
=-1/alim(x->0)(x²/2)/[3x²]
=-1/a·1/6
=1
6a=-1
a=-1/6