Cho hàm số\(f(x) = \left\{ {\begin{array}{*{20}{c}...

C

- Hướng dẫn giải

\(\begin{array}{l}\mathop {\lim }\limits_{x \to {1^ + }} f(x) = \mathop {\lim }\limits_{x \to {1^ + }} \left( {\dfrac{{{x^2} - 3x + 2}}{{\sqrt {x - 1} }} + 2} \right)\\ = \mathop {\lim }\limits_{x \to {1^ + }} \dfrac{{{x^2} - 3x + 2}}{{\sqrt {x - 1} }} + \mathop {\lim }\limits_{x \to {1^ + }} 2\\ = \mathop {\lim }\limits_{x \to {1^ + }} \dfrac{{\left( {x - 1} \right)\left( {x - 2} \right)}}{{\sqrt {x - 1} }} + \mathop {\lim }\limits_{x \to {1^ + }} 2\\ = \mathop {\lim }\limits_{x \to {1^ + }} \sqrt {x - 1} \left( {x + 2} \right) + \mathop {\lim }\limits_{x \to {1^ + }} 2\\ = 0 + 2 = 2\end{array}\)

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

\(f(1) = {3.1^2} + 1 - 1 = 3\)

Ta có \(\mathop {\lim }\limits_{x \to {1^ + }} f(x) \ne \mathop {\lim }\limits_{x \to {1^ - }} f(x) = f(1)\)nên hàm số gián đoạn tại x=1