Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\lim \dfrac{{\left( {n - 1} \right)\left( {n + 2} \right)}}{{2{n^2} - 1}}\\
= \lim \dfrac{{\dfrac{{n - 1}}{n}.\dfrac{{n + 2}}{n}}}{{\dfrac{{2{n^2} - 1}}{{{n^2}}}}}\\
= \lim \dfrac{{\left( {1 - \dfrac{1}{n}} \right)\left( {1 + \dfrac{2}{n}} \right)}}{{2 - \dfrac{1}{{{n^2}}}}}\\
= \dfrac{{\left( {1 - 0} \right)\left( {1 + 0} \right)}}{{2 - 0}}\\
= \dfrac{1}{2}\\
b,\\
\mathop {\lim }\limits_{x \to 2} \dfrac{{{x^2} - 4}}{{x - 2}} = \mathop {\lim }\limits_{x \to 2} \dfrac{{\left( {x - 2} \right)\left( {x + 2} \right)}}{{x - 2}} = \mathop {\lim }\limits_{x \to 2} \left( {x + 2} \right) = 2 + 2 = 4
\end{array}\)
