函数极限的教学实践研究

Study on Teaching Practice of Function Limit

高职院校数学教学中函数极限的教学有一定难度,主要表现在技巧性较高或过程复杂等方面。本文考虑第二个重要极限及其应用的问题,通过教学实践探索,找到了一种不需要多大技巧且十分方面的求解方法;无穷小替换定理只适合两个无穷小的积与商,对两个无穷小的代数和不能直接利用等价无穷小进行替换,在附加一个条件的情况下,将等价无穷小的替换推广到适用于分子或分母是几个无穷小的代数和的情形。

Teaching of function limit in mathematics teaching in higher vocational colleges is difficult, such as higher skill and complex process. The article considers the second important limit and its application. Through the exploration on teaching practice, we found a kind of convenient solution without high skill. Infinitesimal substitution theorem is only suitable for the product and quotient of two infinitesimals, which can not be used to replace two infinitesimal algebra and equivalent infinitesimal; under the additional condition, extend equivalent infinitesimal substitution to algebraic whose numerator or denominator is infinitesimal.