Cho đa thức f(x) thỏa mãn lim x đến 4 f( x ) - 2018/x - 4 = 2019

* Hướng dẫn giải

Đáp án: \(2018\)

Phương pháp giải:

Giải chi tiết:

Đặt \[\frac{{f\left( x \right) - 2018}}{{x - 4}} = g\left( x \right) \Rightarrow f\left( x \right) = \left( {x - 4} \right)g\left( x \right) + 2018 \Rightarrow \mathop {lim}\limits_{x \to 4} f\left( x \right) = 2018.\]

$\begin{array}{c}L=\underset{x\to 4}{lim}\frac{1009[f\left(x\right)-2018]}{(\sqrt{x}\mathrm{ }-2)[\sqrt{2019f\left(x\right)+2019}\mathrm{ }+2019]}=\underset{x\to 4}{lim}\frac{1009[f\left(x\right)-2018](\sqrt{x}\mathrm{ }+2)}{(x-4)[\sqrt{2019f\left(x\right)+2019}\mathrm{ }+2019]}\\ =1009.\underset{x\to 4}{lim}\frac{f\left(x\right)-2018}{x-4}.\frac{\sqrt{x}\mathrm{ }+2}{\sqrt{2019f\left(x\right)+2019}\mathrm{ }+2019}=1009.2019.\frac{\sqrt{2018}\mathrm{ }+2}{\sqrt{2019.2018+2019}\mathrm{ }+2019}\\ =1009.1009.2019.\frac{\sqrt{4}\mathrm{ }+2}{2019+2019}=2018\end{array}$