Tìm các giới hạn sau:

a)\[\mathop {\lim }\limits_{n \to + \infty } \frac{{2{n^2} - 3n + 1}}{{5{n^2} + n - 2}} = \mathop {\lim }\limits_{n \to + \infty } \frac{{2 - \frac{3}{n} + \frac{1}{{{n^2}}}}}{{5 + \frac{1}{n} - \frac{2}{{{n^2}}}}} = \frac{2}{5}\].

b) \[\mathop {\lim }\limits_{x \to 1} \frac{{{x^3} - 1}}{{x - 1}} = \mathop {\lim }\limits_{x \to 1} \frac{{\left( {x - 1} \right)\left( {{x^2} + x + 1} \right)}}{{x - 1}} = \mathop {\lim }\limits_{x \to 1} \left( {{x^2} + x + 1} \right) = 3\].