Question

若lim(x趋于1)x²+ax+b/1–x=5，求a,b的值

若lim(x趋于1)x²+ax+b/1–x=5，求a,b的值求步骤

Answer 1

令x²+ax+b=(1-x)(m-x)
x=1,
1+a+b=0
m-1=5,m=6
x²+ax+b=(1-x)(6-x)=x²-7x+6
所以
a=-7
b=6

Answer 2

lim(x->1)(x^2+ax+b)/(1–x)=5 (0/0)
=>
1+a+b =0
a+b=-1 (1)

lim(x->1)(x^2+ax+b)/(1–x)=5 (0/0)
lim(x->1) -(2x+a)=5
-(2+a)= 5
a= -7

from (1)
-7+b=-1
b=6