Cho hàm số y = f(x) xác định trên R thỏa mãn

Theo giả thiết ta có: \(\mathop {\lim }\limits_{x \to 2} f\left( x \right) = 2.\)

Ta có \(\mathop {\lim }\limits_{x \to 2} \frac{{\sqrt[{}]{{f\left( x \right) + 2}} - 2}}{{{x^2} + 2x - 8}} = \mathop {\lim }\limits_{x \to 2} \frac{{f\left( x \right) - 2}}{{\left( {x - 2} \right)\left( {x + 4} \right)\left( {\sqrt[{}]{{f\left( x \right) + 2}} + 2} \right)}}\)

\( = \left( {\mathop {\lim }\limits_{x \to 2} \frac{{f\left( x \right) - 2}}{{\left( {x - 2} \right)}}} \right).\left( {\mathop {\lim }\limits_{x \to 2} \frac{1}{{\left( {x + 4} \right)\left( {\sqrt[{}]{{f\left( x \right) + 2}} + 2} \right)}}} \right) = \frac{{2023}}{{24}}.\)