当前位置:首页 >> >>www.hm8089.com

www.33012.com:高中数学 3.4基本不等式ab≤a+b2(一)导学案新人教版必修5

WWW.1188118.COM bokebuyuhedantou www.179aa.com www.67727.com longma www60455com www.128336.com

zunyi360.com www.2623.com www.6374.com www323ch.con 3344sv yangzai1188 www.413sunbet.com

3.4

基本不等式 ab≤

a+b (一) 2

学习目标 理解基本不等式及证明; 熟练运用基本不等式来比较大小; 能运用基本不等式证明简单的不等式. 预习篇 1.如果 a,b∈R,那么 a2+b2 2ab(当且仅当 时取“=”). 2.若 a,b 都为 数,那么 a+b 2 ab(当且仅当 a b 时,等号成立),称上述不等式为 不

等式,其中 称为 a,b 的算术平均数, 3.基本不等式的常用推论 (1)ab≤? a+b? a2+b2 (a, b∈R); ? 2 ?2≤ 2

称为 a,b 的几何平均数. 1 1 (2)当 x>0 时, x+ ≥ ; 当 x<0 时, x+ ≤ x x .(4)a2+b2+c2 ab+bc+ca,(a,b,c∈R).

.

b a b a (3)当 ab>0 时, + ≥ ;当 ab<0 时, + ≤ a b a b 4 . 当 a>0 , b>0 且 a≠b 时 ,

a+b 2 , ab , , 2 1 1 + a b

a2+b2 按从小到大的顺序排列 2

为 . 课堂篇 探究点一 基本不等式的证明 问题 1 利用作差法证明:a∈R,b∈R,a2+b2≥2ab. 问题 2 当 a>0,b>0 时,a=( a)2,b=( b)2.据此证明:a>0,b>0 时,a+b≥2 ab.

a+b 探究 下面是基本不等式 ab≤ 的一种几何解释,请你补充完整. 2 如图所示,AB 为⊙O 的直径,AC=a,CB=b,过点 C 作 CD⊥AB 交⊙O 上 半圆于点 D,连接 AD,BD.由射影定理可知,CD= ,而 OD= ,因为 OD CD,所以 a+b 2 ab,当且仅当 C 与 O ,即 时,等号成立. a2+b2 这是一条重要的基本不等式链,请证明. 2

a+b 2 探究点二 当 a>0,b>0 时, ≤ ab≤ ≤ 1 1 2 + a b

典型例题 例 1 已知正数 0<a<1,0<b<1,且 a≠b,则 a+b,2 ab,2ab,a2+b2,其中最大的一个是( A.a2+b2 B.2 ab C.2ab D.a+b )

b+c c+a a+b 例 2 设 a,b,c 都是正数,求证: + + ≥6. a b c

例 3 a>b>c,n∈M 且

1 1 n + ≥ ,求 n 的最大值 a-b b-c a-c

巩固篇 1.若 0<a<b,则下列不等式一定成立的是 a+b A.a> > ab>b 2 a+b B.b> ab> >a 2 a+b C.b> > ab>a 2 )

( a+b D.b>a> > ab 2

)

2.设 a、b 是实数,且 a+b=3,则 2a+2b 的最小值是(

A.6 B .4 2 C .2 6 D.8 3.若不等式 x2-ax+1≥0 对一切 x∈(0,1]恒成立,则 a 的取值范围是________. 4.a,b,c∈R,求证:a2+b2+c2≥ab+bc+ca.


以下是今天幸运会员获奖名单

789kkk.com,www.jinbo881.con,www.gjdc0.com,www.aobo1.com,www.894938.com,3435bet,wwwii9068com,h3032jkl,www.j8159.com,ks5582.vip,zhu123123,wan0342.com

wwwsun9981com,zhongdongnvyou,yabet9976com,cchang15971,www.69388.net,www.yabox15.com/?i_code=29823,www.222353.com,www.aassy7. com,x561449,miyingxx,琪琪色原网站20岁以下,www.ttt258.com,874111com,wuzangping,wu008,www.521by.com,984931com,www.jing2019.com,WWW.CQGXDMR.COM,www.312876.com,139kk779,www88730com,www.5616y.com,www.mu444.com,wangzhannidongwoyisiba2019mianfei,免费国产av在线观看,wwwpj424com,xzghhj,www.eee276.com,bet1955com,www.74447.org,WWW.M886.COM,www.5511hu.com,www.9522.com,www.39551239.com,5272f.com,yj4433,ctyhh,www.603646.com,www.5087033.com,www.hs056. con,奇米第四,ag1183.win,www.xpj55552.com,WWW469987COM,66300.co,tcp745.com,xpj8857com,longaiiot登录,WWW.AK6996.COM,www.s6605.com,wwwhg9100com,qq290976993,c6217,ag.444bygj.com,www.se8088.net.,868061com,www.111564.com,www.2538116.com,kb8836.com,hg6731com,wwwesjyscom,www.ben333.com,821505com,www.hl.cm,676290.com,www.t6131.com,WWW123456CCCOM_WWW.123456CC,COM,www.q81316.com,www.935222.com,wwwhg3762com,www.jsdc7.com,www.5908.com,www7613com,wb5337com,js31398.com,www.1876789.com,www.yl7722.org,www.5858178.com,xujinlong,www.hg4113.com,lc188,99rr6网址最新获取,22933acom,liuzhen,15777.com,www.568899.com,m.vips895.com,www.122841.com,www.h6t4.com,xiaowei521,56833.com,WWW.NH557.COM,www59964scom,www.23msc.com,www.052567.com,5817aaa,www.666hhh,www.sx167.com,wwwmeijuttcom,wwwceo3377com,ww851212com,c2399831990,ag2649vip,361dy.cc,www.hg99950.com,wwwbet365com,jihaohao,1c11c111111111a1111v1x11zz1rt4wf7cn/?p=484',www.44t88.com,qq3399,yabovip7425com,www.10000.ttrr.com,m.xxdm.com,767kj.com,san18138212858,46874317,www.mg2672.com,www.8444777.com,www.20349.com,ss2d3,5fhcpcom,hg28-77.com,425com,www.x9f.com,www140suncitycom,78800e.com,www68228com,g14.com,www222365ccom,k0677.com,www.97022.com,wb9362com,www.v8qq4.com,yb4955.com,hg9174.com,www.fj002.xyz/?tg=816,tyc1570.com,848665com,wwwfc407com,yh4398com,ks668.com,www.5083.com,huangguanxin2xianjin,amyh1288.com,yuanjiang555,wwwhycb8888com,wwwc4558com,huangwenxiaoshuo,80032277,zzxx111,wan8850.com,3318888.com,1273lb.com,hg4400.com,www.699896.com,ning9998,www.94533.com,yabet1072com,www.6394.com,1232365com,www.n4444.net,ly19920321,yb4396.com,www.8987v.com,boletongyule,ww444kkk在线 视频播放,hg2807com|

baozi140035,www434ppcom,44kkmm,www.3704588.com,lifaguojiguanfangwang,qy6576vip,8565.com,www.sb88803.com,www.28vnsvns.com,wwwimhuicomcn,www.swty9922.com,www.7777bx.com,wwwrenren.com,www.js38111.com,www.806099.com,547987.com,agks6554com,www.111230.com,www.854365.com,www.xx1101.com,lovebetlove276.com,www.vip9685.com,84499vcom,www.xingqiba0008.com,sunyanjing0817@163.com,hyhy90.com,004949.com,www.bet99599.com,www.985se.com,25882588,wuyanrui,cdy369258,xuai,www789comcn,www.567365v.com,qy4677vip,www.18299.com,bcbm24com,mlipeng,www.8d56sc.com,seqiyi,yabo3161.vip,www.582143.com,40299.com,sun518,a1314920,happyld,www.390084.com,ag5091com,www.424000.com,www.4433p.com,www.485587.com,wwwshenbo191com,www.un2288.com,39695p,8439com,www.256737.com,baizhaoteng,50996.com,21795057@qq.com,111577.com,www.jxf50.com,97bbee新域名,luhongx1,www.aoao1.com,www309898com,mg8385.com,www. h 3285.com,www.mn399.com,www.866js.cc,www.hm577.com,438877com,www88yulecom,www.pj7038.com,pj88z,www.37008.com,www.wc998.net,www.hc8688.com,fun144,474w6,www.whdykj.com,baishiyulewang,ww1234,060588com,www.tonghejs.com,www.1177558.com,kunkun1255,2213BB,52888ppp,95099.com,www.92188.com,qqcgood新站点,www.uuu51,cqwerty132,0517bocai.com,www.167888.com,ssni233在线,dongjunyan,www.95099qq.com,www.81031.com,oubao606.com,wwwxpj2620com,www3651002com,798500.com,wwweee6678com,ks8899com,www.54579.com,zhangjunli,https://www.byjj222jzdou077fulc,ghhffhfhd,ok50000com,lh2412.com,luoqun,www.496855.com,6632777.com,ag5111vip,811830.com,wan8710.com,www666675com,mengtaisuolishutxtxiazai,bk188.net,www.o448.cc,www.910211.com,ljm88,www.xpj000007.com,www.mbaex.com,wwwjzt7777com,www7439com,www.bet6259.com,zhengyuhao,www.135598.com,wwwbm1085com,meng5521,www.www.2987js.com,www.dasm-nj.com,xpj1479.com,v07888.com,www.2lll.com,838796com,cp2720com,www.088ee.com,b9y8com,www.2200.com,www.820654.com,m.kb883.cc,www.6365668.com,www.un7722.com,www.11160011.com,www344772com,bk8866com,www.502mk.com,vip58.pw,www6xxpw,03034,www.ms3388.com,wwww.76755.com,www.20008.com,www.bm666.com,www.jing8844.com,www.149123.com,wwwccc881com,72239,a.mimiai.net,zuqiu18.com,ldh753,最新6666kp网址,www.8003588.com,xkxkxk|

wwwtyc50com,www.vn66hd.com,z88nncom,www.xpj7194.com,www.hgw877.com,www.9922927.com,772773com,ab254829320,WWW.5454.COM,501819054@qq.com,www.ttt.ppp.com,hgamecn,WWW.9896739.COM,yb9432com,fdgsdfsas,WWW.D28666.COM,www.799ut.c0m,xxcc889,www.yl12322.cc,jxt520,bj1005.com,mgm222.com,78899t,www.123191.com,zhanghe,www.w668f.com,www.5213.com,www49198com,www.r9899.com,HG7334COM,shiduruming,www.5467333.com,978lulu03xyz,ping2243,nahongfu,www.vns6456.com,www.66533,taoge888,897801com,1040376288@qq.com,mao33212@126.com,www.353290.com,www.b3650001.com,www.647848.com,jr0011.com,www.161570.com,www.vwnfja45.top,www.ytgj555.com,www.88fh.net,www689994com,822974com,huangfei,www.7800011.com,582ks.net,46999.co65kk.co.cc,xin496.com,wwwra883com,www.hg3060.com,842878.com,www.400xx.com,72707com,bbdnsdn8999,yqy315,www.2004yx.com,yabo2719.com,www.637777.com,long884.com,wwwbet8688com,lehu2301com,2229.com,www.333dhy.com,www.hg7926.com,https://www.c8.cn/,xpj3043com,WWW.BET80365.COM,www.995nn.com,www0727ocom,www.5206b.com,wwwmmtx44com,844623com,selao123在线观看,nn459136310,www516666com,wwwypt668net,www.98msc.com,60007x.com,www4444kkkavcom,wwwvip5599tkcom,wwwhj5599com,www.805zz,www.01bbb.com,229bx.com,sss1111,wer6869erer,739936674,77412323@qq.com,www.789777d.com,www.16933.com,831780com,www.6617h.com www.1717ss.com,wwwhg7081com,www.698698.com,www.108741.com,wwwggg34com,www.88622.com,wwwhg1117tw,dq008,www.899uuu.com,www.kk168318.com,www.9m138.com,WWWHAODIAOMACOM_WWW.HAODIAOMA,COM,www.679654.com,songtangguozenmebiaoda,www6666ycom,6860.ag,yyy49.com,WWW.6038TTT.COM,a2013,www.hg1835.com,www.0040eee.com,www.51558.com,50588c.com,永久野鸡2018的网址,2222dz.com,www.38iii.com,www.444987.com,ifcf.letong1688.com,www.yhw6.cc,www.751584.com,358pw,8666lb.com,www.5547666.com,ttyyttw,yabox46.com,www.91881.cc,jjtxl,9219pcom,www.796334.com,www.pj99924.com,国产AV在线一区日本无码二区,861356.com,www.795566.com,www610123com,www.h518cn.com,www.1346m.com,8333.com,yl2520com,www.567998.com,www.v2209.com,vns6940com,www.dzstdzy.com,nuvid,bet5423com,qy1507.com,WWWDD444COM_WWW.DD444,COM,www.g2220.com,mhkyt,www.hwx26.com,wwwpj7556com,www.hg2566.net,w8693.com,7065.bet,www488765com,www.pj0201.com,wwwxg6699com,www.160652.com,114查询,www.13220009.com|

www1118ylcom,yh538.com,www.4444168.com,847962com,www.yao.com,huangzebo,https://www.121zh.com/ https://,5495.com,vbct55988,wwwjxcp23com,bet6887com,99xiaoshuowang,www.7246k.com,l61654com,www.47ac.com,www.90148.com,826115com,dz689.com,wwwyhjt1com,j27com,mo06162,www.673920.com,zyd328,yabo9874com,wwwgpk666com,www23268com,0245cc.com,kanzhelu21 cc,www.01314ok.com,jintaoge,wwwhjcp06com,jjja68668,www.557331.com,bai01811.com,wuge777888,wwwra888com,www.1342n.com,486eencom,www.ccc833.com,www39039com,www.3229667.com,877582com,www.190678.com,334749610@qq.com,www.367381.com,caca025.com,www.81455.com,www.67890ff.com,wwwg5131com,shicaizuwangzhi,41960.com,ccm16688,www.xpj2779.com,zhiqinbao,k8679,youfa5601com,www.602755.com,tianyu2000,tcp415.cc,www.downg.com,www84577com,lloo88,s1381.com,www.suncity99.com,www.nitipaisalkul.pichaya,www.xpj9032.com,www.78bbbb.com,lh7689.com,meimeidy,wwwbyj03com,wwwjsh738com,www.758058.com,www33005004com,www9898netcom,www.554400.com,cxnn1991,www.213373.com,WWW.C288.COM,wwwyh1080com,www.7eee.com,zcw36.cc,cp3015com,4518s.com,WWW.5084.COM,www274123com,v43n.com,chen888,www. 457zh. com,2279h.con,www56766com,www.8490262.com,www.78378027.com,www.015677.com,www.qibiwu.com,www800749com,penggp,www.135fc.com,www.dd239.com,maohaiqiang,1943785812,www.ccc177.com,guazha8bushipinzaixianguankan,lh7215.com,wan3268.com,seba111.com,5078.bet,1904.win,wwwh88802com,124082150,www.da11111.com,www.hg5226.com,www.35442777.com,nvrfvxc8,js888400.com,39832017.com,9606icom,agent.js550101.com,www.41iii.com,349988956@qq.com,77885309.com,ag3679vip,www.v52666.com,zssumu,www.808288.com,www.337319.com,pxccbccb,www.bojue78.com,aomenweinisirenwangzhi,js2403com,www.151ff.com.cn,国产欧美国日产,www6227ycom,88882.com,a855.vip,www. gay55999.com,wysltxcom,lai1978.com,16888b.com,820519com,863775com,ribo,爱情岛讨坛论,gh23weu,wwwmaomimp225com,563571945,208hk com,hg8234.com,www.659745.com,yzozishan,www.52taose.com,wwwbmw8014com,crowncasinobz,www3534ocom,suyan001,WWW.330088.COM,002900.com,123321aa,long7494com,25888,318msccom,6500t.cc,WWW.6892.COM,hedong,414660583@qq.com,baijiechuanxiaoshuo,www.ry222.com,luhu001.com,www.partieswedding.com|

以上会员名单排名不分前后