Tính lim x → + ∞ ( √ x ^2 + 1 − x − 1 ) .

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