Đáp án:
\[\mathop {\lim }\limits_{x \to 2} \frac{{\left( {\sqrt[3]{{8x + 11}} - \sqrt {x + 7} } \right)}}{{{x^2} - 2x + 2}} = 0\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\mathop {\lim }\limits_{x \to 2} \left( {\sqrt[3]{{8x + 11}} - \sqrt {x + 7} } \right) = \sqrt[3]{{8.2 + 11}} - \sqrt {2.7} = 3 - 3 = 0\\
\mathop {\lim }\limits_{x \to 2} \left( {{x^2} - 2x + 2} \right) = {2^2} - 2.2 + 2 = 2\\
\Rightarrow \mathop {\lim }\limits_{x \to 2} \frac{{\left( {\sqrt[3]{{8x + 11}} - \sqrt {x + 7} } \right)}}{{{x^2} - 2x + 2}} = \frac{0}{2} = 0
\end{array}\)
