Cho dãy số \[\left( {{u_n}} \right),\] biết \[\mathop {\lim }\limits_{n \to + \infty } \left( {{u_n} - a} \right) = 0.\] Tìm khẳng định đúng.

Ta có: \[\mathop {\lim }\limits_{x \to 2} \frac{{\sqrt {x + 7} - 3}}{{x - 2}} = \mathop {\lim }\limits_{x \to 2} \frac{{\left( {\sqrt {x + 7} - 3} \right)\left( {\sqrt {x + 7} + 3} \right)}}{{\left( {x - 2} \right)\left( {\sqrt {x + 7} + 3} \right)}}\]

                                 \[{\rm{ = }}\mathop {\lim }\limits_{x \to 2} \frac{{x - 2}}{{\left( {x - 2} \right)\left( {\sqrt {x + 7} + 3} \right)}}\]

                                \[{\rm{ = }}\mathop {\lim }\limits_{x \to 2} \frac{1}{{\left( {\sqrt {x + 7} + 3} \right)}} = \frac{1}{6}\].