高等数学第三章-要求与练习(含答案)

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,第三章微分中值定理与导数的应用一、要求：1、罗尔定理，拉格朗日定理应用；2、洛必达法则；3、函数单调性、极值、最值、凹凸性、拐点的判断，函数图形的描绘；4、简单不等式证明；5、最值在实际问题中的应用。二、练习1.在区间[1,1]上满足罗尔定理条件的函数是(C).A.21()fxxB.()||fxxC.2()1fxxD.2()21fxxx.2.函数xxfarctan)(在]1,0[上满足拉格郎日中值定理的值是(A).A.41B.41C.14D.41.3.设函数)3)(2)(1()(xxxxf，则方程()0fx有2个零点，这些零点所在的范围是（1，2），（2，3）.4.函数()ln2xfxxe在(0,)内的零点的个数为2.解：00lim()limln20xxxfxxe；又21121()10,(1)0()20efffeeee，2()220fee，32()50fee；11()0,fxxe，xe，,()0;,()0xefxxefx.所以，函数()ln2xfxxe在(0,)内有2个的零点.5.曲线xyxe的拐点22,2e，凹区间2,，凸区间,2.解：,1,2xxxyxeyxeyxe，6.函数2ln1yxx的单调递增区间,.7.曲线()1xefxx的渐近线为x=-1,y=0.8.（1）154lim1xxxx（2）011lim()1xxxe（3）220(1cos)limtanxxx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-cit