Cho hàm số \(f(x) = \left\{ \begin{array}{l}\frac{{{x^2} - 3x + 2}}{{x - 2}}\,\,\,\,khi\,\,\,x \ne 2\\m\,\,\,\,\,\,\,\,\,\,\,\,\,\,khi\,\,\,x = 2\end{array} \right..\) Tìm tất cả c...

* Hướng dẫn giải

Ta có:

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

Hàm số liên tục tại \({x_0} = 2\)

\(\begin{array}{l} \Leftrightarrow \mathop {\lim }\limits_{x \to 2} f\left( x \right) = f\left( 2 \right)\\ \Leftrightarrow 1 = m\end{array}\)