Question

已知a,b为常数，lim x趋近于1 (ax+b)/(x+1)=2 则a=? b=?

求详细步骤，不胜感激！
分母应该是x-1

Answer 1

是a = 2，b = - 2

(ax + b)/(x - 1)
= [a(x - 1) + (a + b)]/(x - 1)
= a + (a + b)/(x - 1)
极限存在，且等于2，对应系数就可以了
常数a = 2
令后面那项消失，必有a + b = 0 得到b = - 2