📝 题目
例 1 求极限 $\displaystyle{\mathop{\lim }\limits_{{x \rightarrow 0}}\frac{x - \sin x}{{x}^{3}}}$ .
💡 答案与解析
解 $\displaystyle{\mathop{\lim }\limits_{{x \rightarrow 0}}\frac{x - \sin x}{{x}^{3}} = \mathop{\lim }\limits_{{x \rightarrow 0}}\frac{1 - \cos x}{3{x}^{2}} = \mathop{\lim }\limits_{{x \rightarrow 0}}\frac{\sin x}{6x} = \mathop{\lim }\limits_{{x \rightarrow 0}}\frac{\cos x}{6} = \frac{1}{6}}$ .