Tìm giới hạn \(A = \mathop {\lim }\limits_{x \to 0} \frac{{1 - \cos \;2x}}{{2\sin \;\frac{{3x}}{2}}}\)

* Hướng dẫn giải

\(A = \mathop {\lim }\limits_{x \to 0} \frac{{1 - \cos \;2x}}{{2\sin \;\frac{{3x}}{2}}} = \mathop {\lim }\limits_{x \to 0} x{\left( {\frac{{\sin x}}{x}} \right)^2}.\frac{3}{2}\frac{{\sin \frac{{3x}}{2}}}{{\frac{{3x}}{2}}} = 0\)