Cho hàm số \(f(x) = \left\{ \begin{array}{l}\dfrac{{x - 8}}{{\sqrt[3]{x} - 2}}\,\,\,\,\,khi\,\,\,x > 8\\ax + 4\,\,\,\,\,\,\,\,\,khi\,\,x \le 8\end{array} \right.\) . Để hàm số liên...

* Hướng dẫn giải

\(\eqalign{
& \mathop {\lim }\limits_{x \to {8^ + }} f(x) = \mathop {\lim }\limits_{x \to {8^ + }} {{x - 8} \over {\root 3 \of x - 2}} \cr
& = \mathop {\lim }\limits_{x \to {8^ + }} {{\left( {\root 3 \of x - 2} \right)\left( {\root 3 \of {{x^2}} + 2\root 3 \of x + 4} \right)} \over {\root 3 \of x - 2}} \cr
& = \mathop {\lim }\limits_{x \to {8^ + }} \left( {\root 3 \of {{x^2}} + 2\root 3 \of x + 4} \right) = 12 \cr} \)