《无穷小的比较》PPT课件.ppt

无穷小的比较 一、无穷小的比较 例如, 观察各极限 不可比. 极限不同, 反映了趋向于零的“快慢”程度不同. 定义: 例1 解 例2 解 常用等价无穷小: 注1. 上述10个等价无穷小（包括反、对、幂、 指、三）必须熟练掌握 用等价无穷小可给出函数的近似表达式: 一般地有 即与等价 与互为主要部分 例如, 补充 高阶无穷小的运算规律 二、等价无穷小替换 定理(等价无穷小替换定理) 证 意义 求两个无穷小之比的极限时，可将其中的分子 或分母或乘积因子中的无穷小用与其等价的较简单 的无穷小代替，以简化计算。具体代换时，可只代 换分子，也可只代换分母，或者分子分母同时代换 。 例3 解 注意 不能滥用等价无穷小代换. 对于代数和中各无穷小不能分别替换. 等价关系具有：自反性，对称性，传递性 例4 解错 解 例5 解 例6 求 解一 解二 解三 例7 求 解 关于1型极限的求法 三、小结 1.无穷小的比较: 反映了同一过程中, 两无穷小趋于零的速度 快慢, 但并不是所有的无穷小都可进行比较. 高(低)阶无穷小; 等价无穷小; 无穷小的阶. 2.等价无穷小的替换: 求极限的又一种方法, 注意适用条件. 思考题 任何两个无穷小量都可以比较吗？ 思考题解答 不能例当 时 都是无穷小量 但不存在且不为无穷大 故当 时 I7F4C0z)w&s!pXmUjRfOcL9H6E2B+y(u%r#oWlThQeNbJ8G5D1A-w*t$qYnVkSgPdMaI7F3C0z)v&s!pXmUiRfOcK9H6E2B+x(u%rZoWlThQeMbJ8G4D1A-w*t!qYnVjSgPdLaI6F3C0y)v&s#pXlUiRfNcK9H5E2A+x(u$rZoWkThQeMbJ7G4D1z-w*t!qYmVjSgOdLaI6F3B0y)v%s#pXlUiQfNcK8H5E2A+x*u$rZnWkThPeMaJ7G4C1z-w&t!pYmVjRgOdL9I6F3B0y(v%s#oXlUiQJ7G4D1z-w*t!qYmVjSgOdLaI6F3B0y)v%s#pXlUiQfNcK8H5E2A+x*u$rZnWkThPeMbJ7G4C1z- 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