作业帮lim趋于0时 (xsinx-sinx^2)/x^4
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/15 07:39:08
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
=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
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