百度作业网已知函数极限求字母参数值
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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
如果lim(x^2+ax+b)\(x^2-x-2)=2,x趋近于2,求a.b的值
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
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