Tính các giới hạn :

a) \(\left\{ \begin{array}{l}\mathop {\lim }\limits_{x \to {{12}^ - }} 2024 = 2024\\\mathop {\lim }\limits_{x \to {{12}^ - }} \left( {x - 12} \right) = 0;x - 12\langle 0\end{array} \right.\)\( \Rightarrow \mathop {\lim }\limits_{x \to {{12}^ - }} \frac{1}{{x - 12}} = - \infty \)

b) \(\mathop {\lim }\limits_{x \to - \infty } \frac{{\sqrt {{x^2} - 4x} }}{{x + 1}} = \mathop {\lim }\limits_{x \to - \infty } \frac{{ - x.\sqrt {1 - \frac{4}{x}} }}{{x\left( {1 + \frac{1}{x}} \right)}}\)\( = \mathop {\lim }\limits_{x \to - \infty } - \frac{{\sqrt {1 - \frac{4}{x}} }}{{1 + \frac{1}{x}}} = - 1\)