Tính các giới hạn sau

a) \(\mathop {\lim }\limits_{x \to 2} \left( {{x^3} - 2x + 1} \right);\)                           b)\(\mathop {\lim }\limits_{x \to + \infty } \frac{{2023x + 5}}{{2x - 3}}\).

a) \(\mathop {\lim }\limits_{x \to 2} \left( {{x^3} - 2x + 1} \right) = \mathop {\lim }\limits_{x \to 2} {x^3} - \mathop {\lim }\limits_{x \to 2} \left( {2x} \right) + \mathop {\lim }\limits_{x \to 2} 1 = 8 - 4 + 1 = 5.\)                         

 b) \(\mathop {\lim }\limits_{x \to + \infty } \frac{{2023x + 5}}{{2x - 3}} = \mathop {\lim }\limits_{x \to + \infty } \frac{{2023 + \frac{5}{x}}}{{2 - \frac{3}{x}}} = \frac{{2023 + 0}}{{2 - 0}} = \frac{{2023}}{2}.\).