Tính √ a + b + 2018 .

\(\mathop {\lim }\limits_{x \to 3} \frac{{\sqrt {x + 1}  - 2}}{{x - 3}}\)\( = \mathop {\lim }\limits_{x \to 3} \frac{{x - 3}}{{\left( {x - 3} \right)\left( {\sqrt {x + 1}  + 2} \right)}}\)\( = \mathop {\lim }\limits_{x \to 3} \frac{1}{{\sqrt {x + 1}  + 2}}\)\( = \frac{1}{{{2^2}}}\).

Suy ra \[a = 1;\,b = 2\].

\(\sqrt a  + b + 2018 = 1 + 2 + 2018 = 2021\).

Trả lời: 2021.