lim趋于0时 (xsinx-sinx^2)/x^4

lim(x->0)(xsinx-sinx^2)/x^4
=lim(x->0) (sinx+xcosx-2xcosx^2)/4x^3
=lim(x->0)(cosx+cosx-xsinx-2cosx^2+2x^2sinx^2)/12x^2
=lim(x->0)(-2sinx-sinx-xcosx+2xsinx^2+4xsinx^2+4x^3cosx^2)/24x
=lim(x->0)(-3cosx-cosx+xsinx+2sinx^2+2xcosx^2+4sinx^2+8x^2cosx^2+12x^2cosx^2-8x^4sinx^2)/24
=-4/24=-1/6

1

罗比达法则，-1/24

原式=lim(x->0){[x(x-x³/3+x^5/15+o(x^6))-(x²-x^6/3+o(x^6))]/x^4}
(展开成级数，o(x)表示高阶无穷小)
=lim(x->0){[(x²-x^4/3+x^6/15+o(x^6))-(x²-x^6/3+o(x^6))...