📝 题目
例 2 求极限 $\mathop{\lim }\limits_{{x \rightarrow + \infty }}\frac{{x}^{k}}{{\mathrm{e}}^{x}},k \in {\mathbb{N}}^{\left( 1\right) }$ .
💡 答案与解析
解 $\displaystyle{\mathop{\lim }\limits_{{x \rightarrow + \infty }}\frac{{x}^{k}}{{\mathrm{e}}^{x}} = \mathop{\lim }\limits_{{x \rightarrow + \infty }}\frac{k{x}^{k - 1}}{{\mathrm{e}}^{x}} = \cdots = \mathop{\lim }\limits_{{x \rightarrow + \infty }}\frac{k!}{{\mathrm{e}}^{x}} = 0}$ .