求x趋向于(1+kx^3)^1/2-1与sinx-x是等价无穷小,则k等于? 各位大神,求...
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(1+kx^3)^(1/2)-1~k/2·x^3
lim(sinx-x)/x^3
=lim(cosx-1)/(3x^2)
=lim(-1/2·x^2)/(3x^2)
=-1/6
∴k/2=-1/6
∴k=-1/3
