2013年高中數(shù)學《3.3.1基本不等式》隨堂自測(含解析)北師大版必修5

#[A口DDDD]4 , 、1D(2012DDDDD)若x>0叫 x□一的最小皿 ( )xBD3CD2也> … 4c44/DDDDD.口x>0叫x口是口2、；'x口^(DDDDDD4x口2DDDDD);□「4……xD-Q4D0D

xD.C.2ab--tddddddaDb2口口口 a,b口(0DDD)DD \'abDa^-bD乙A.B./a2口b2a□b(-- 2ab7k丁M口二a口b2ab /a2口b2{—丁a^\丁加c aDbt—DDDDC.口口\；abD乙口aDbD2\，ab口aDbD2\，ab口口\''abD2abE口2abCDDD3D(2012DDDDD)若a>0Db>0，口 aDb口4DDDDDDDDDDDD3D(2012DDDDDA.5>，B.~D，口1ab2abC.\,''abD2DDa?Db?18TOC\o"1-5"\h\z_ a2D b2 ,aDb、 a?D b2 , 4、 a?D b2DDDDD.Q^―□(^—)2，口——D(-)2,0 D4DDa2Db2Q8DDDD.乙 乙 乙 乙 乙4口口 xyO1DDDDDDDDDDD D口 xD yD2DD xD y□□ 2口口 2xD 8yD8 1 2xD 8y□□ 8口□ |xD y|D2DDx2D 丫212.DDDD xyO 1>0，口 x、yDDDDD x、y口(0DD口)時, xD yD2 x.'xyDD xD yD2DDx、yDDODD xD yO口 [(口x)D(口 y)]DOD (口 x)D (口 y)D2 \：xyD0口 (xD y)D2DD2xD8yD8|xDy|D2DDDDDDDxDyDD2DDDD 2xD8yD8|xDy|D2DDDDDDD口2xD8y□口8DDDDDDD |xDy|O|x|D|y|D2\jxy|,DDx2D丫2口2xyD口x?Dy2Q2DODODDDDDDDD「 、?、 1 ; ； a口c5口□口 a>b>cD口-..;Da口bDDb口cDD-^—DDDDDD2DDDDa>b>cDDDDa>b>cD口 a口b>0Db口c>0D口、：口a口bDD b口cDD口a口blD口2b口cD O1DDDDD a口bOb口cD? aDc0bO-T—DDDDDD乙DDD,JDa口bDD__b口cDD6口已知a>0,b>0,c>0DD a口b口cD1DDOD111c一口出-D9.abcODD111aObOcaObOcaObOc一O二O-D O O Oabcab力a、(9b)D119,ac日/市,3口bcab一口-cc7口若 a>b>1,A口R<P<QCDQ<P<R[BDDDDDPD\'1gaD1gb,QD|(1gaDIgb),

乙BDDDRDP<Q<RP<R<QDDDDB.口a>b>11口8D(2012DDDDD）已知AD10g2a>0一?ba1CD2一口<ab21gaD1gb<|(1gaO1gb)D1g\l'ab<1ga02^0<a<b,且 aObD1DDDDDDDDDDDDc 1BD2aob<-2..口P<Q<R.DDDDD.口0<a<b,且DD10g2a□10g2b<□Ir…1 1aObD1,口0<a<2<b<1,口10g2a〈hg/,口10g2a<□1,口ADDD[0<a<b<1,且a口bD11口aOb 1「—2->Rab,口abq.□口10g2aO10g2bD10g2ab，口10g2a口Jr「10g2b10g24,即 10g2a10g2bQ2DDDD.9DDDDDDDDDDDDDDa,b口(0,O口)，口DDx,y口(0,O口)，口c. 4DDaOR,aD0DD一0aDDx,yOR,xy<0,口DDDDDDDDDDba? ,'ba?一O022；一口力2；abab1gxO1gy02 1gxD1g4,

a02 .,aDaD4；xy 「/x、 /y、[yO不口口 [(0y)O(0Q]n22"0 xDDO yDD0■-.； y x2.DDDDDDDDDDDDDDDDDDDabO(0,OD)D口b,和(0,OD)DDDDDDDDDDDDDDDDDDDDD；DDD x,yO(0,O口)，口口xO(0,1)叫1gx是□數(shù)，口yO(0,1)叫1gyDDD,DDDDDDDDDDD；c 4DDaOR,DDDDDDDDDDD,D -OaxyDD xy<0得一,-DDDD,DDDDDDDDDyxD,DDDDDDDDDDDDDDDDDDDDD10D已知 a,b,cDDDD,且a,b,cDDD,ODDD a,b,cDOOOCO abcD1,a02-\jaaD4DDDD；xy-O-DDDDD,yx且abcD1,ODDxy(07(0”為口|obO|>\''aO\.'bOqc.11，1嗎沿鳴bc口ac口ababcabc口一口交口丫>q赤2口va^i，J心.2 2 2口口abc口1,1\,；abc21\：'a2bc口\：'ab2c口 cD\'aDqb,33D111口(ODD)DDDDD \一111d33D111口(ODD)DDDDD \一1(X2口y2口Z2)口xy口2yz口2zx.DODDA>0,則Ay2D—^^2yz,Ax?D—^^2zx.AA2yzD2zx,□口Jx2D1y2口 xy01 (Ay?D；z2)D (A x?D；z2)D J(x2Dy22yzD2zx,TOC\o"1-5"\h\z22 A A 2r 1 1、r21 (A D 7)x2D (A D 7；)