《高中數(shù)學 第二章 柯西不等式與排序不等式及其應(yīng)用 2.1.1 平面上的柯西不等式的代數(shù)和向量形式課件 新人教B版選修45》由會員分享，可在線閱讀，更多相關(guān)《高中數(shù)學 第二章 柯西不等式與排序不等式及其應(yīng)用 2.1.1 平面上的柯西不等式的代數(shù)和向量形式課件 新人教B版選修45（21頁珍藏版）》請在裝配圖網(wǎng)上搜索。

1、第二章 柯西不等式與排序不等式及其應(yīng)用2 2.1 1柯西不等式柯西不等式2 2.1 1.1 1平面上的柯西不等式的代數(shù)和向量形式目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIA

2、NXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航1.認識二維形式的柯西不等式.2.理解二維形式的柯西不等式的幾何意義.3.會利用二維形式的柯西不等式進行簡單問題的證明.目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISH

3、ULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航1.二維形式的柯西不等式定理1(柯西不等式的代數(shù)形式)設(shè)a1,a2,b1,b2均為實數(shù),則定理2(柯西不等式的向量形式)設(shè),為平面上的兩個向量,則|.當及為非零向量時,上式

4、中等號成立向量與共線(平行)存在實數(shù)0,使得=.當或為零向量時,規(guī)定零向量和任何向量平行,如,中至少有一個是零向量,則規(guī)定=0,上面的結(jié)果仍然正確.目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析

5、SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航【做一做1-1】 若a,bR,且a2+b2=10,則a-b的取值范圍是()解析:(a2+b2)12+(-1)2(a-b)2,a2+b2=10,(a-b)220.答案:A 目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGL

6、IANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航【做一做1-2】 已知p,q(0,+),且p3+q3=2,則p+q的最大值為()答案:A 目標導航DI

7、ANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂

8、演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航2.定理4(平面三角不等式) 3.定理5(平面三角不等式的向量形式)設(shè),為平面向量,則|-|+|-|-|.當-,-為非零向量時,上面不等式中等號成立存在非負常數(shù),使得-=(-)向量-與-同向,即夾角為零.名師點撥定理4與定理5是同一定理的不同表示形式,它們都可以看作是定理3的變式.目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重

9、難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航【做一做2】 已知,為空間向量,求證:|-|+|-|-|.分析:參照平面三角不等式的向量形式的證明方法進行證明即可.證明:設(shè)=(a1,a2,a3),=

10、(b1,b2,b3),=(c1,c2,c3),則-=(a1-b1,a2-b2,a3-b3),-=(b1-c1,b2-c2,b3-c3),-=(c1-a1,c2-a2,c3-a3),|-|+|-|-|,且等號成立存在非負常數(shù),使得-=(-).目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGN

11、ANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航如何理解柯西不等式?剖析:柯西不等式的幾種形式都需要對其結(jié)構(gòu)進行理解與記憶,因此,柯西不等式可以理解為有四個順序的數(shù)來對應(yīng)的一種不等關(guān)系或構(gòu)造成一個不等式,如基本不等式是由兩個數(shù)來構(gòu)造,但怎樣構(gòu)造要仔細體會.例如:結(jié)合具體問題靈活地應(yīng)用柯西不等式. 目標導航DIANLI

12、TOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZH

13、ONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航題型一題型二題型三題型四利用柯西不等式的代數(shù)形式證明不等式【例1】 設(shè)a,b(0,+),且a+b=2.目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIA

14、NLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航題型一題型二題型三題型四反思利用柯西不等式證明某些不等式時,有時需要將數(shù)學表達式適當?shù)刈冃?這種變形往往要求具有很高的技巧,必須善于分析題目的特征,根據(jù)題設(shè)條件,綜合地利用添、拆、分解、組合、配方、變量代換、數(shù)形結(jié)合等方法才能發(fā)現(xiàn)問題的本質(zhì),找到突破口.目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGN

15、ANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目

16、標導航題型一題型二題型四題型三利用柯西不等式的向量形式證明不等式【例2】 已知a,b(0,+),且a+b=1.求證:(ax+by)2ax2+by2.分析:利用柯西不等式的向量形式.當且僅當存在實數(shù)0,使得m=n時等號成立.故(ax+by)2ax2+by2.目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂

17、演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航題型一題型二題型三題型四利用柯西不等式解決實際問題【例3】 在半徑為R的圓內(nèi),求周長最大的內(nèi)接長方形.分析:首先表示出長方形的周長,得出目標函數(shù),再利用柯西不等式求解.目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNA

18、NJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標

19、導航題型一題型二題型三題型四反思當函數(shù)的解析式中含有根號時常利用柯西不等式求解. 目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難

20、聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航題型一題型二題型三題型四易錯辨析易錯點:應(yīng)用柯西不等式時,因不注重等號是否成立,從而導致結(jié)果錯誤.目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGL

21、IANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航1 2 3 4 5A.a2+b2B.2abC.(a+b)2D.4ab答案:C 目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITO

22、UXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航1 2 3 4 52已知a+b=1,則a2+b2的最小值為() 答案:C

23、 目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGL

24、IANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航1 2 3 4 53若3x+4y=2,則x2+y2的最小值為() 答案:D 目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANL

25、ITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航1 2 3 4 5目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理DIANLITOUXI典例透析SUITANGLIANXI隨堂演練ZHONGNANJUJIAO重難聚焦ZHISHISHULI知識梳理目標導航1 2 3 4 55設(shè)實數(shù)x,y滿足3x2+2y26,則p=2x+y的最大值是.