limx→1(3/1-x^3)-(1/1-x)

问题描述:

limx→1(3/1-x^3)-(1/1-x)

原式=lim3/(1-x)(1+x+x²)-1/(1-x)
=lim-(x²+x-2)/(1-x)(1+x+x²)
=lim(x+2)(x-1)/(x-1)(1+x+x²)
=lim(x+2)/(1+x+x²)
=1