limx→1(3/1-x^3)-(1/1-x)

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/03 03:35:37
limx→1(3/1-x^3)-(1/1-x)
xM 1 F"RBt`Q T/E4¬ 3n {Mm8 1oMuX)JgR_uu]hbX&c 95[5J逅6!BA@+0t(;m +#Q4LZѪ`P*]%sW _ؐF~ٹS

limx→1(3/1-x^3)-(1/1-x)
limx→1(3/1-x^3)-(1/1-x)

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

原式=lim(x->1) 3/(1-x^3)-(1+x+x^2)/(1-x^3)
=lim(x->1) (3-1-x-x^2)/(1-x^3)
=lim(x->1) (x^2+x-2)/(x^3-1)
=lim(x->1) (x+2)/(x^2+x+1)
=3/3
=1