Giới hạn \(\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {x + 1} - 1}}{x}\) bằng

* Hướng dẫn giải

\(\begin{array}{l}\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {x + 1}  - 1}}{x}\\ = \mathop {\lim }\limits_{x \to 0} \frac{{\left( {\sqrt {x + 1}  - 1} \right)\left( {\sqrt {x + 1}  + 1} \right)}}{{x\left( {\sqrt {x + 1}  + 1} \right)}}\\ = \mathop {\lim }\limits_{x \to 0} \frac{{x + 1 - 1}}{{x\left( {\sqrt {x + 1}  + 1} \right)}}\\ = \mathop {\lim }\limits_{x \to 0} \frac{x}{{x\left( {\sqrt {x + 1}  + 1} \right)}}\\ = \mathop {\lim }\limits_{x \to 0} \frac{1}{{\sqrt {x + 1}  + 1}}\\ = \frac{1}{{\sqrt {0 + 1}  + 1}} = \frac{1}{2}\end{array}\)