lim(1/(x-1)-2/(x平方-1) x趋近于1

问题描述:

lim(1/(x-1)-2/(x平方-1) x趋近于1

lim(1/(x-1)-2/(x平方-1) x趋近于1
=lim(x-1)/(x平方-1) x趋近于1
=lim1/2x,x趋近于1
=1/2

答案是1/2
将括号中的后一项裂项
2/(x^2-1)=1/(x-1)-1/(x+1)
所以原极限=lim(1/(x-1)-1/(x-1)+1/(x+1))=lim(1/(x+1) )=1/2 x趋于1