limx→-1.x^2-1/x^3-1

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limx→-1.x^2-1/x^3-1limx→-1.x^2-1/x^3-1limx→-1.x^2-1/x^3-1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→

limx→-1.x^2-1/x^3-1
limx→-1.x^2-1/x^3-1

limx→-1.x^2-1/x^3-1
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

lim (x^2-1/x^3-1)=lim2x/3x (罗比达法则)
=2/3

查百度

=limX(x→-1)(X-1)(X+1)/(X-1)(X^2+X+1)
=limX(x→-1)X+1/X^2+X+1
=0