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