Question

根据极限值确定参数a，b求过程

根据极限值确定参数a，b求过程

Answer 1

1. 2-a+b=0 => a=2+b
lim(x->-1) (2x+b)(x+1)/(x+1) = 3 => -2+b=3
=> b=5, a=7
2. a-2+b=0 => b=2-a
lim(x->1) (ax+a-2)(x-1)/[(x-1)(x+2)]
= lim(x->1) (ax+a-2)/(x+2) = (2a-2)/3 = 3
=> a = 11/2, b = - 7/2
3. a=1
原式= lim(x->-∞) [x - x√(1+b/x -2/x²)]
= lim(x->-∞) [1 - √(1+b/x -2/x²)] /(1/x) 令 t = 1/x, 则 t ->0-
= lim(t->0-) (-b/2) * t / t
= - b/2 = 1
=> a =1, b = -2