已知limx→2（ x^2+ax+b）/（2-x）=3,求a,b的值

题目

已知limx→2（ x^2+ax+b）/（2-x）=3,求a,b的值

答案

lim(x->2)( x^2+ax+b)/(2-x) (0/0)
=lim(x->2) -(2x+a)
= -4-a = 3
a= -7
lim(x->2)(x^2+ax+b)/(2-x) =3
lim(x->2)(x^2-7x+b)/(2-x) =3
lim(x->2)[ (-x+5) + (b-10)/(2-x) ] =3
b-10 =0
b= 10