如何解极限中参数值

(10)

(1)

lim(x->∞) [3x- √(ax^2+bx+1) ]=2

lim(x->∞) [9x^2- (ax^2+bx+1) ]/[3x+ √(ax^2+bx+1) ] =2

lim(x->∞) [(9-a)x^2- bx-1 ] /[3x+ √(ax^2+bx+1) ] =2

9-a =0

a=9

lim(x->∞) [(9-a)x^2- bx-1 ] /[3x+ √(ax^2+bx+1) ] =2

lim(x->∞) (-bx-1 ) /[3x+ √(9x^2+bx+1) ] ]=2

分子分母同时除以x

lim(x->∞) (-b-1/x ) /[3+ √(9+b/x+1/x^2) ]=2

-b/( 3+3) =2

b=-12

(a,b)=(9,-12)

(2)

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

1^2+a(1) +b=0

a+b=-1 (1)

lim(x->1) (x^2+ax+b)/(x-1) =5(0/0 分子分母分别求导)

lim(x->1) (2x+a) =5

2+a =5

a=3

from (1)

a+b=-1

3+b=-1

b=-4

(a,b)=(3,-4)