Cho hàm số f(x) xác định trên R và thỏa mãn lim x->2

* Hướng dẫn giải

$\begin{array}{l}=\underset{x\to 2}{\lim }\frac{\left(\sqrt[3]{5f\left(x\right)-16}-4\right)\left({\sqrt[3]{5f\left(x\right)-16}}^2+4\sqrt[3]{5f\left(x\right)-16}+16\right)}{\left(x+4\right)\left(x-2\right)\left({\sqrt[3]{5f\left(x\right)-16}}^2+4\sqrt[3]{5f\left(x\right)-16}+16\right)}\\ =\underset{x\to 2}{\lim }\frac{5f\left(x\right)-16-64}{\left(x+4\right)\left(x-2\right)\left({\sqrt[3]{5f\left(x\right)-16}}^2+4\sqrt[3]{5f\left(x\right)-16}+16\right)}\\ =\underset{x\to 2}{\lim }\frac{5\left[f\left(x\right)-16\right]}{\left(x+4\right)\left(x-2\right)\left({\sqrt[3]{5f\left(x\right)-16}}^2+4\sqrt[3]{5f\left(x\right)-16}+16\right)}\\ =\underset{x\to 2}{\lim }\frac{f\left(x\right)-16}{x-2}.\frac{5}{\left({\sqrt[3]{5f\left(x\right)-16}}^2+4\sqrt[3]{5f\left(x\right)-16}+16\right)}\end{array}$