Question

求极限lim (1/1-x-3/1-x3)

求极限
lim (1/1-x-3/1-x3)
x->1
此/是分号线.
x3是x的三次方.

Answer 1

lim [1/(1-x)-3/(1-x^3)] 这样?拜托把括号加对 囧
=lim (1+x+x^2-3)/(1-x^3) 通分
=lim (x^2+x-2)/(1-x^3)
=lim (x-1)(x+2)/(1-x^3)
=-lim (x+2)/(1+x+x^2)
=-3/3
=-1

Answer 2

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