\(\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {x + 1} - \sqrt {{x^2} + x + 1} }}{x}\) có giá trị là bao nhiêu?

* Hướng dẫn giải

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