Giới hạn \(\mathop {\lim }\limits_{x \to 0} \frac{{\cos 2018x - \cos 2019x}}{x}\) bằng

* Hướng dẫn giải

Ta có \(\mathop {\lim }\limits_{x \to 0} \frac{{\cos 2018x - \cos 2019x}}{x}\)

\( = \mathop {\lim }\limits_{x \to 0} \frac{{ - 2\sin \frac{{4037x}}{2}.\sin \left( { - \frac{x}{2}} \right)}}{x}\)  

\( = \mathop {\lim }\limits_{x \to 0} \left( {\sin \frac{{4037x}}{2}} \right).\mathop {\lim }\limits_{x \to 0} \frac{{\sin \frac{x}{2}}}{{\frac{x}{2}}}\)

\( = 0.1 = 0\)