Question

lim x→1 [(1/(1-x)-2/(1-x^2)]

1.lim x→1 [(1/(1-x)-2/(1-x^2)]
2.lim n→无限 n-[(n^2-2n+7)/n+1]
【详细过程】

Answer 1

1.lim x→1 [(1/(1-x)-2/(1-x^2)]
解：原式=lim x→1 [(1+x)/(1-x^2)-2/(1-x^2)]
=lim x→1[(x-1)/(1-x^2)]
= lim x→1[-1/(1+x)]
=-1/2

2.lim n→无限 n-[(n^2-2n+7)/n+1]
解：原式=lim n→无限 (n^2+n/n+1)-[(n^2-2n+7)/n+1]
=lim n→无限(3n-7)/(n+1)
=lim n→无限 (3-7/n)/(1+1/n)
=3

追问

lim x→1[-1/(1+x)]
怎麼突然變=-1/2
？？

追答

把1代进去就行了