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2016-11-22 · 知道合伙人教育行家
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通分,注意到
1-x³=(1-x)(1+2x+x²)
原式=lim(x→1)[(1+x+x²)/(1-x³)-3/(1-x³)]
=lim(x→1)(x²+x-2)/(-x³)
=lim(x→2)(x-1)(x+2)/[(1-x)(1+x+x²)]
= -lim(x→1)(x+2)/(1+x+x²)
= -(1+2)/(1+1+1)
= -1
1-x³=(1-x)(1+2x+x²)
原式=lim(x→1)[(1+x+x²)/(1-x³)-3/(1-x³)]
=lim(x→1)(x²+x-2)/(-x³)
=lim(x→2)(x-1)(x+2)/[(1-x)(1+x+x²)]
= -lim(x→1)(x+2)/(1+x+x²)
= -(1+2)/(1+1+1)
= -1
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