Biết lim x → − ∞ g ( x ) = 1 . Tính lim x → − ∞ ( x^2 − 1 ) g ( x ) .

Ta có \(\mathop {\lim }\limits_{x \to - \infty } \left( {{x^2} - 1} \right)g(x) = \mathop {\lim }\limits_{x \to - \infty } {x^2}\left[ {\left( {1 - \frac{1}{{{x^2}}}} \right)g(x)} \right] = + \infty \)

(do \(\mathop {\lim }\limits_{x \to - \infty } {x^2} = + \infty \) và \(\mathop {\lim }\limits_{x \to - \infty } \left[ {\left( {1 - \frac{1}{{{x^2}}}} \right)g(x)} \right] = 1 > 0\) ).