Nếu lim x → 1 f ( x ) = 3 thì giá trị của a + b bằng

A

Ta có \(\mathop {\lim }\limits_{x \to {1^ + }} f\left( x \right) = \mathop {\lim }\limits_{x \to {1^ + }} \left( {b{x^2} - 2x} \right) = b - 2\); \(\mathop {\lim }\limits_{x \to {1^ - }} f\left( x \right) = \mathop {\lim }\limits_{x \to {1^ - }} \left( {ax + 5} \right) = a + 5\).

Vì \(\mathop {\lim }\limits_{x \to 1} f\left( x \right) = 3\) nên \(\left\{ \begin{array}{l}b - 2 = 3\\a + 5 = 3\end{array} \right.\)\( \Leftrightarrow \left\{ \begin{array}{l}b = 5\\a =  - 2\end{array} \right.\). Do đó a + b = 3.