Tính các giới hạn sau: \(\mathop {\lim }\limits_{x \to 1} \dfrac{{{x^3} - 3{x^2} + 2}}{{{x^2} - 4{\rm{x}} + 3}}\)

* Hướng dẫn giải

\(\mathop {\lim }\limits_{x \to 1} \dfrac{{{x^3} - 3{x^2} + 2}}{{{x^2} - 4{\rm{x}} + 3}}\)

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