Tính giới hạn: \(\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {x + 4}  - 2}}{{2x}}\).

* Hướng dẫn giải

Ta có: \(\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {x + 4}  - 2}}{{2x}} = \mathop {\lim }\limits_{x \to 0} \frac{x}{{2x\left( {\sqrt {x + 4}  + 2} \right)}} = \mathop {\lim }\limits_{x \to 0} \frac{1}{{2\left( {2 + \sqrt {x + 4} } \right)}} = \frac{1}{8}\)