“以学为中心”探讨一元函数 ∞-∞ 型极限求解方法

Research On Solving Method For∞-∞Type Limit Based on“Learning-Centered”Teaching Philosophy

基于“以学为中心”的教学理念,对一元函数∞-∞型极限求解方法进行了探讨,指出其求解思想就是“转化”.提出可以通过通分、有理化、倒代换以及先提出变量的最高次幂再利用倒代换等四种方法将∞-∞型极限转化成0/0型或∞/∞型极限进行求解.对每种方法的注意事项、使用技巧及适用范围进行了分析和说明.

Based on“learning-centered”teaching philosophy,several common methods for solving the limit of∞-∞are researched in this paper,the idea of solving the limit is“transformation”and four approaches are discussed.These include using reduction of fractions to a common denominator,rationalization,reciprocal substitution and firstly put forward the highest power of variables and then using reciprocal substitution to transform the∞-∞to 0/0 or∞/∞type limit.Furthermore,the notice,techniques and application range for each method are analyzed and illustrated.