Tính các giới hạn sau

a) Ta có \[\lim \frac{{2{n^2} - 5n + 3}}{{3{n^2} - 2n + 1}} = \lim \frac{{2 - \frac{5}{n} + \frac{3}{{{n^2}}}}}{{3 - \frac{2}{n} + \frac{1}{{{n^2}}}}}\]\[ = \frac{{2 - 0 + 0}}{{3 - 0 + 0}} = \frac{2}{3}\].

b) Ta có \[\mathop {\lim }\limits_{x \to 3} \frac{{\sqrt {x + 13} - 4}}{{x - 3}} = \mathop {\lim }\limits_{x \to 3} \frac{{x + 13 - 16}}{{(x - 3)\left( {\sqrt {x + 13} + 4} \right)}}\]=\[\mathop {\lim }\limits_{x \to 3} \frac{1}{{\left( {\sqrt {x + 13} + 4} \right)}}\]\[ = \frac{1}{8}\].