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《中学数学》曾经刊载了《中考也考高等数学》一文,作者对2008年杭州市一道中考数学试题作出解答及点评,令读者深受启发.笔者再提供两种解法,仅供大家参考.原题(2008年杭州)如图1,记抛物线y=-x~2+1的图象与x轴正半轴的交点为A,将线段OA分成n等份,设分点分别为P_1,P_2,…,P_(n-1).过每个分点作x轴的垂线,分别与抛物线交于点Q_1,Q_2,…,Q_(n-1),再记直角三角形OP_1Q_1,P_1P_2Q_2,…的面积分别为S_1,S_2,…,这
“High School Mathematics” has published a “high school entrance examination is also a higher mathematics,” a text, the author of Hangzhou in 2008 a senior high school entrance examination math questions to answer and comments, so readers are inspired. I then provide two solutions, for your reference. (2008 Hangzhou) As shown in Figure 1, the intersection of the image of the parabola y = -x ~ 2 + 1 and the positive semi-axis of the x-axis is A, and the line OA is divided into n equal parts. The points are P_1, P_2 , ..., P_ (n-1). Each point is taken as a perpendicular to the x-axis and is intersected with the parabola at points Q_1, Q_2, ..., Q_ (n-1). The right triangles OP_1Q_1, P_1P_2Q_2, ... The area is S_1, S_2, ..., respectively