Tính các giới hạn sau

a) \(\mathop {\lim }\limits_{n \to + \infty } \left( {\sqrt {{n^2} + 3n + 1} - n} \right) = \mathop {\lim }\limits_{n \to + \infty } \frac{{{n^2} + 3n + 1 - {n^2}}}{{\sqrt {{n^2} + 3n + 1} + n}} = \mathop {\lim }\limits_{n \to + \infty } \frac{{3n + 1}}{{\sqrt {{n^2} + 3n + 1} + n}}\)

\( = \mathop {\lim }\limits_{n \to + \infty } \frac{{3 + \frac{1}{n}}}{{\sqrt {1 + \frac{3}{n} + \frac{1}{{{n^2}}}} + 1}} = \frac{3}{2}\)

b)\(\mathop {\lim }\limits_{x \to 2} \frac{{{x^2} - 3x + 2}}{{4 - {x^2}}} = \mathop {\lim }\limits_{x \to 2} \frac{{\left( {x - 1} \right)\left( {x - 2} \right)}}{{\left( {2 - x} \right)\left( {2 + x} \right)}}\)

\( = \mathop {\lim }\limits_{x \to 2} \frac{{\left( {x - 1} \right)}}{{ - \left( {x + 2} \right)}} = - \frac{1}{4}\)