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数学语言指的是普通(文学)语言、符号语言和图象语言,普通语言刻画数学对象的意义(内涵);符号语言是数学对象的主要表达形式;图象语言是数学对象的形象表示,遇到问题,若能将数学语言的三种形式有机结合,形成对问题多角度、全方位的审视,不仅能够迅速找到解决问题的突破口,而且还能从中发现解决问题的简捷方法,兹举一例供大家参考.例:(日本高考题)设θ∈[0,π/2],且cos~2θ+2msinθ-2m-2<0恒成立,求m的取值范围.分析1:设x=sinθ,则x∈[0,1],原不等式可化为x~2-2mx+2m+1>0.将原题用函数语言表示,即为“若函数f(x)=x~2-2mx+2m+1在[0,1]上的值恒大于零,求m的取值范围”。
Mathematical language refers to ordinary (literary) language, symbolic language, and image language. Common language describes the meaning (connotation) of mathematical objects; symbolic language is the main expression of mathematical objects; image language is the image representation of mathematical objects. To the problem, if we can organically combine the three forms of mathematical language to form a multi-angle, all-round examination of the problem, we can not only quickly find a solution to the problem, but we can also find a simple solution to the problem. Everybody’s reference. Example: (Japan’s college entrance examination question) Let θ∈[0,π/2], and cos~2θ+2msinθ-2m-2<0 is constant, find the range of values of m. Analysis 1: Let x=sinθ , then x ∈ [0,1], the original inequality can be changed to x~2-2mx+2m+1>0. The original question is expressed in a function language, that is, “if the function f (x) = x ~ 2-2mx The value of +2m+1 on [0,1] is always greater than zero and the range of values for m is found.”