Cho L = lim x → − ∞ ( √ x ^2 + a x + 5 + x ) . Khi đó: a) L = 5 khi a = − 10 b) L > 0 khi a > 0

\(\mathop {\lim }\limits_{x \to - \infty } \left( {\sqrt {{x^2} + ax + 5} + x} \right)\)\( = \mathop {\lim }\limits_{x \to - \infty } \frac{{ax + 5}}{{\sqrt {{x^2} + ax + 5} - x}}\)\( = \mathop {\lim }\limits_{x \to - \infty } \frac{{x\left( {a + \frac{5}{x}} \right)}}{{\left| x \right|\sqrt {1 + \frac{a}{x} + \frac{5}{{{x^2}}}} - x}}\)

\( = \mathop {\lim }\limits_{x \to - \infty } \frac{{a + \frac{5}{x}}}{{ - \sqrt {1 + \frac{a}{x} + \frac{5}{{{x^2}}}} - 1}} = - \frac{a}{2}\).