Tìm \(m\) để \(C=2\). Với \(C = \mathop {\lim }\limits_{x \to 1} \frac{{{x^2} - mx + m - 1}}{{{x^2} - 1}}\).

* Hướng dẫn giải

\(C = \mathop {\lim }\limits_{x \to 1} \frac{{{x^2} - mx + m - 1}}{{{x^2} - 1}} = \mathop {\lim }\limits_{x \to 1} \frac{{\left( {x - 1} \right)\left( {x - m + 1} \right)}}{{\left( {x - 1} \right)\left( {x + 1} \right)}} = \mathop {\lim }\limits_{x \to 1} \frac{{\left( {x - m + 1} \right)}}{{\left( {x + 1} \right)}} = \frac{{2 - m}}{2}\)

\(C = 2 \Leftrightarrow \frac{{2 - m}}{2} = 2 \Leftrightarrow m =  - 2\)