求极限lim(x→∞) ((x²+1）/（x-1）-ax-b)=0求a,b

题目

求极限lim(x→∞) ((x²+1）/（x-1）-ax-b)=0求a,b
求极限lim(x→∞) ((x²+1）/（x-1）-ax-b)=0求a,b

答案

lim [(x² +1) / (x-1) - ax -b]
=lim [(x²+1) - (x-1)(ax+b)] / (x-1)
=lim [(1-a)x² +(a-b)x +b] / (x-1)
= 0
故只需 1-a =0 ,a-b=0
解得 a=b=1