limx->0 (sinx-xcosx)/x^3 极限 0.
问题描述：
limx->0 (sinx-xcosx)/x^3 极限 0.
答
罗比达法则解法.原式=lim(x->0)[(sinx-xcosx)/(sinx)^3]=lim(x->0)[(cosx-cosx+xsinx)/(3sin²x)] (0/0型极限,应用罗比达法则)=lim(x->0)[x/(3sinx)] (化简)=(1/3)lim(x->0)(x/sinx)=(1/3)*1 (应用重要极限lim(x...