Question

求x趋向1时[1/(x^2-1)-1/(x-1)]的极限

Answer 1

x趋向1时[1/(x^2-1)-1/(x-1)]的极限
=lim(1-(x+1))/(x^2-1)
=-limx/(x^2-1)
=无穷大

Answer 2

1/(x²-1)-1/(x-1)
=(1-1-x)/(x+1)(x-1)
=-x/(x+1)(x-1)
分母趋于0，分子不是趋于0
一分式趋于无穷
所以极限不存在

Answer 3

通分后＝-x/(x^2-1)
分子趋于-1而分母趋于0所以答案是负的无穷大，绝对正确求采纳

Answer 4

lim[2/（x²-1）-1/（x-1)]
x—›1
=lim（2-x-1）/（x+1）（x-1)
x—›1
=lim（1-x）/（x-1)（x+1)
x—›1
=-1/2.