Đáp án:
\[\mathop {\lim }\limits_{x \to 2} \frac{{2 - \sqrt {x + 3} }}{{2{x^2} - 5x + 2}} = \infty \]
Giải thích các bước giải:
\(\begin{array}{l}
\mathop {\lim }\limits_{x \to 2} \frac{{2 - \sqrt {x + 3} }}{{2{x^2} - 5x + 2}}\\
\mathop {\lim }\limits_{x \to 2} \left( {2 - \sqrt {x + 3} } \right) = 2 - \sqrt {2 + 3} = 2 - \sqrt 5 \ne 0\\
\mathop {\lim }\limits_{x \to 2} \left( {2{x^2} - 5x + 2} \right) = {2.2^2} - 5.2 + 2 = 0\\
\Rightarrow \mathop {\lim }\limits_{x \to 2} \frac{{2 - \sqrt {x + 3} }}{{2{x^2} - 5x + 2}} = \infty
\end{array}\)
