Question

已知函数极限求字母参数值如果lim(x^2+ax+b)\(x^2-x-2)=2,x趋近于2,求a.b的值

Answer 1

lim (x^2+ax+b) / (x^2-x-2) = 2

分母 (x^2-x-2) = (x+1)(x-2) |x=2 = 0

分子 (x^2+ax+b) |x=2 = 0 => 4+2a+b=0 => a = - 2 - b/2

(x^2+ax+b) = (x-2) * (x-b/2)

原式 = limit 【(x-b/2)/(x+1),x->2】= (2- b/2)/3 = 2

=> b = - 8,a = 2