Giới hạn A = lim 1 - cos2x/ 2sin3x/2 bằng

Ta có \(\mathop {\lim }\limits_{x \to 0} \frac{{\sin ax}}{{ax}} = 1.\)

Do đó \(A = \mathop {\lim }\limits_{x \to 0} \frac{{{{\sin }^2}x}}{{\sin \frac{{3x}}{2}}} = \left[ {\mathop {\lim }\limits_{x \to 0} x.{{\left( {\frac{{\sin x}}{x}} \right)}^2}} \right]:\left[ {\frac{3}{2}\mathop {\lim }\limits_{x \to 0} \frac{{\sin \frac{{3x}}{2}}}{{\frac{{3x}}{2}}}} \right] = 0.\)

Đáp án: 0.