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师:在数学解题过程中,经常会出现这样或那样的错误,这是不可避免的.但重要的是,分析错误产生的原因,利用错误加深对基本知识、基本技能、基本思想方法的理解和使用,培养自己的思辨能力.生甲:设y_=0.4~(1/3),y_2=0.5~(1/3),y_3=0.5~(1/4),则y_1,y_2,y_3大小关系为__.我利用指数函数y=x~(1/3)和y=0.5~x的单调性,得出y~2>y_1>y_3,错在哪里?师:你将指数函数与幂函数混淆了,关键是要分清底数和指数哪个不变、哪个在变:另外函数的单调性运用错了,这说明你对基本函数的性质还没有掌握好.
Teacher: It is unavoidable that one or the other mistakes occur during the process of solving mathematical problems, but it is important to analyze the causes of mistakes and make use of mistakes to deepen the understanding of basic knowledge, basic skills and basic thought and method And use to develop their own ability to speculate .Birth A: set y_ = 0.4 ~ (1/3), y_2 = 0.5 ~ (1/3), y_3 = 0.5 ~ (1/4), y_1, y_2, y_3 size The relationship is __. I use the monotonicity of the exponential functions y = x ~ (1/3) and y = 0.5 ~ x to get y ~ 2> y_1> y_3, where is the error? The function is confused, the key is to distinguish between the base and the index which is unchanged, which is changing: the other monotonicity of the function is wrong, indicating that you have not mastered the nature of the basic functions.