(完整版)高中数学选修不等式选讲

技术官员村位于位于亚运城东部，主干道二以东石楼涌以西的地块，占地面积、m2，总建筑面积、m2，共包括地下室南区、地下室北区、地上部分1栋～12栋、服务中心、室外工程等多个单体工程。其中住宅面积m2，共12栋，1～7栋建筑层数为11层，8～12栋11层（局部复式顶层），首层局部架空，布置公建配套设施。integratedenergy,chemicalsandtextileYibincity,arethethreecorepillarsoftheindustry.In2014,thewuliangyebrandvalueto73.58billionyuan,thecity'sliquorindustrysliptostabilise.Promotingdeepdevelopmentofintegratedenergy,advancedequipmentmanufacturingindustry,changningdistrict,shalegasproductioncapacityreached277millioncubicmetres,builtthecountry'sfirstindependenthigh-yieldwellsandpipelinesinthefirstsection,theleadinfactoryproductionandsupplytothepopulation.2.1-3GDPgrowthfigure2.1-4Yibin,Yibincity,Yibincity,fiscalrevenuegrowth2.1.4topographyterrainoverallisSouthwest,North-EasternState.Lowmountainsandhillsinthecitylandscapeasthemainridge-and-Valley,pingbasmallfragmentednaturepictureforwaterandthesecondlandofthesevenhills.236metersto2000metersabovesealevelinthecity,lowmountain,46.6%hills45.3%,pingbaonly8.1%.2.1.5developmentofYibinlandscapesanddistinctivefeatureinthecenterofthecity,withlimitations,andspatialstructureoftypicalzonalgroup,2012-citiesinbuildingwithanareaofabout76.2km2.Fromcity-buildingsituation,oldtown-theSouthBankCenterconstructionislaggingbehind,disintegrationoftheoldcityisslow,optimizationandupgrading,qualitypublicserviceresourcesarestillheavilyconcentratedintheoldtowntogether.SouthbankCentrehasnotbeenformed,functionsoftheserviceareaspaceismissing.Meanwhile,peripheralgroupcentresservicewasweakandinadequateaccountingforcitydevelopment,suspiciouspatterncouldnotbeformed.Asregardstransport,withtheoutwardexpansionofcities,citieshavebeenexpanding,centripetalcitytrafficorganizationhasnotchanged,integratedenergy,chemicalsandtextileYibincity,arethethreecorepillarsoftheindustry.In2014,thewuliangyebrandvalueto73.58billionyuan,thecity'sliquorindustrysliptostabilise.Promotingdeepdevelopmentofintegratedenergy,advancedequipmentmanufacturingindustry,changningdistrict,shalegasproductioncapacityreached277millioncubicmetres,builtthecountry'sfirstindependenthigh-yieldwellsandpipelinesinthefirstsection,theleadinfactoryproductionandsupplytothepopulation.2.1-3GDPgrowthfigure2.1-4Yibin,Yibincity,Yibincity,fiscalrevenuegrowth2.1.4topographyterrainoverallisSouthwest,North-EasternState.Lowmountainsandhillsinthecitylandscapeasthemainridge-and-Valley,pingbasmallfragmentednaturepictureforwaterandthesecondlandofthesevenhills.236metersto2000metersabovesealevelinthecity,lowmountain,46.6%hills45.3%,pingbaonly8.1%.2.1.5developmentofYibinlandscapesanddistinctivefeatureinthecenterofthecity,withlimitations,andspatialstructureoftypicalzonalgroup,2012-citiesinbuildingwithanareaofabout76.2km2.Fromcity-buildingsituation,oldtown-theSouthBankCenterconstructionislaggingbehind,disintegrationoftheoldcityisslow,optimizationandupgrading,qualitypublicserviceresourcesarestillheavilyconcentratedintheoldtowntogether.SouthbankCentrehasnotbeenformed,functionsoftheserviceareaspaceismissing.Meanwhile,peripheralgroupcentresservicewasweakandinadequateaccountingforcitydevelopment,suspiciouspatterncouldnotbeformed.Asregardstransport,withtheoutwardexpansionofcities,citieshavebeenexpanding,centripetalcitytrafficorganizationhasnotchanged,不等式选讲（高考试题汇编）一、知识点整合：1．含有绝对值的不等式的解法(1)|f(x)|a(a0)⇔f(x)a或f(x)－a；(2)|f(x)|a(a0)⇔－af(x)a.(3)对形如|x－a|＋|x－b|≤c，|x－a|＋|x－b|≥c的不等式，可利用绝对值的几何意义求解．2．含有绝对值的不等式的性质|a|－|b|≤|a±b|≤|a|＋|b|.3．柯西不等式(1)设a，b，c，d均为实数，则(a2＋b2)(c2＋d2)≥(ac＋bd)2，当且仅当ad＝bc时等号成立．(2)若ai，bi(i∈N*)为实数，则(∑ni＝1a2i)(∑ni＝1b2i)≥(∑ni＝1aibi)2，当且仅当a1b1＝a2b2＝…＝anbn(当某bj＝0时，认为aj＝0，j＝1,2，…，n)时等号成立．(3)柯西不等式的向量形式：设α，β为平面上的两个向量，则|α|·|β|≥|α·β|，当且仅当这两个向量共线时等号成立．4．不等式的证明方法证明不等式常用的方法有比较法、综合法、分析法、反证法、放缩法、数学归纳法等．二、典型题型题型一含绝对值的不等式的解法例1(2013·课标全国Ⅰ)已知函数f(x)＝|2x－1|＋|2x＋a|，g(x)＝x＋3.(1)当a＝－2时，求不等式f(x)g(x)的解集；(2)设a－1，且当x∈－a2，12时，f(x)≤g(x)，求a的取值范围．审题破题(1)可以通过分段讨论去绝对值；(2)在x∈－a2，12时去绝对值，利用函数最值求a的范围．解(1)当a＝－2时，不等式f(x)g(x)化为|2x－1|＋|2x－2|－x－30.设函数y＝|2x－1|＋|2x－2|－x－3，则y＝－5x，x12，－x－2，12≤x≤1，3x－6，x1，其图象如图所示，由图象可知，当且仅当x∈(0,2)时，y0，所以原不等式的解集是{x|0x2}．(2)∵a－1，则－a212，∴f(x)＝|2x－1|＋|2x＋a|技术官员村位于位于亚运城东部，主干道二以东石楼涌以西的地块，占地面积、m2，总建筑面积、m2，共包括地下室南区、地下室北区、地上部分1栋～12栋、服务中心、室外工程等多个单体工程。其中住宅面积m2，共12栋，1～7栋建筑层数为11层，8～12栋11层（局部复式顶层），首层局部架空，布置公建配套设施。integratedenergy,chemicalsandtextileYibincity,arethethreecorepillarsoftheindustry.In2014,thewuliangyebrandvalueto73.58billionyuan,thecity'sliquorindustrysliptostabilise.Promotingdeepdevelopmentofintegratedenergy,advancedequipmentmanufacturingindustry,changningdistrict,shalegasproductioncapacityreached277millioncubicmetres,builtthecountry'sfirstindependenthigh-yieldwellsandpipelinesinthefirstsection,theleadinfactoryproductionandsupplytothepopulation.2.1-3GDPgrowthfigure2.1-4Yibin,Yibincity,Yibincity,fiscalrevenuegrowth2.1.4topographyterrainoverallisSouthwest,North-EasternState.Lowmountainsandhillsinthecitylandscapeasthemainridge-and-Valley,pingbasmallfragmentednaturepictureforwaterandthesecondlandofthesevenhills.236metersto2000metersabovesealevelinthecity,lowmountain,46.6%hills45.3%,pingbaonly8.1%.2.1.5development