Tìm a để hàm số \(f(x) = \left\{ {\begin{array}{*{...

D

- Hướng dẫn giải

\(\mathop {\lim }\limits_{x \to {1^ + }} f\left( x \right) = \mathop {\lim }\limits_{x \to {1^ + }} \left( {{x^2}{\rm{ + ax + 1}}} \right){\rm{ = 2 + a}}\) \(\mathop {\lim }\limits_{x \to {1^ - }} f\left( x \right) = \mathop {\lim }\limits_{x \to {1^ - }} \left( {2{x^2}{\rm{ - x + 3a}}} \right){\rm{ = 1 + 3a}}\)

Để f(x) có giới hạn khi \(x \to 1\) thì \(\mathop {\lim }\limits_{x \to {1^ + }} f\left( x \right) = \mathop {\lim }\limits_{x \to {1^ - }} f\left( x \right) \Leftrightarrow 2 + a = 1 + 3a \Leftrightarrow a = \dfrac{1}{2}\)