limx→-1.x^2-1/x^3-1

题目

limx→-1.x^2-1/x^3-1

答案

如果分母是x^3-1,直接代入x=-1,极限=0
猜测分母是x^3+1
因式分解
limx→-1.x^2-1/x^3+1
=limx→-1 (x-1)(x+1)/(x+1)(x^2-x+1)
=limx→-1 (x-1)/(x^2-x+1)
=-2/3