Nếu \(\mathop {\lim }\limits_{x \to a} f\left( x \right) = + \infty \) thì \(\mathop {\lim }\limits_{x \to a} \left[ { - f\left( x \right)} \right]\) bằng:

A. +∞.

B. –∞.

C. a.

D. – a.

Đáp án đúng là: B

Ta có: \(\mathop {\lim }\limits_{x \to a} \left[ { - f\left( x \right)} \right] = \mathop {\lim }\limits_{x \to a} \left[ {\left( { - 1} \right).f\left( x \right)} \right] = \mathop {\lim }\limits_{x \to a} \left( { - 1} \right).\mathop {\lim }\limits_{x \to a} f\left( x \right)\).

Mà \(\mathop {\lim }\limits_{x \to a} \left( { - 1} \right) = - 1 < 0\) và \(\mathop {\lim }\limits_{x \to a} f\left( x \right) = + \infty \).

Do vậy, \(\mathop {\lim }\limits_{x \to a} \left( { - 1} \right).\mathop {\lim }\limits_{x \to a} f\left( x \right) = - \infty \). Vậy \(\mathop {\lim }\limits_{x \to a} \left[ { - f\left( x \right)} \right] = - \infty \).