高中数学知识整理(续1)

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1、F•XCHANGF•XCHANGDEDEPPwwClicktobuyNOW!ClicktobuyNOW!wmwmwowo.d.c.d.cocu•trackocu•trackᣛ᭄ߑ᭄੠ᇍ᭄ߑ᭄ᣛ᭄੠ᇍ᭄(1)ᣛ᭄⊩߭Ϣn⃵ᮍḍèn⃵ᮍⱘᛣНnӏᛣᅲ᭄a䖲㓁Ьn触ⱘ⿃⿄Ўa蠿n⃵ᮍˈ䆄Ўa.ℸᯊ,n塡㞾✊᭄ˈnㄝѢ2瀝⿄Ўᑇ23ᮍˈㄝѢ3瀝⿄Ўゟᮍ,ㄝѢ4瀝⿄Ў4⃵ᮍ,a,a,a,L㒳⿄Ўa蠿Ьᮍ.èn⃵ᮍḍnᏆⶹӏᛣᅲ᭄aˈᔧn³2蠿ᭈ᭄ᯊ,ᶤ᭄Ьҹn触塡a蠿᭄,頼⒵䎇ᮍ⿟ᓣxa=蠿x婣Ўa蠿n触ᮍḍDŽa蠿ᑇᮍḍˈゟᮍḍ,4⃵ᮍḍ,Lㄝㄝ㒳⿄Ў

2、a蠿n⃵ᮍḍ.nᅲ᭄a蠿n⃵ᮍḍЁЎᅲ᭄ⱘ⿄Ўᮍ⿟xa=蠿ᅲḍˈབϟ㸼᠔⼎.a>0a=0a<0n塡ي᭄na,-na0᮴ᅲḍn塡༛᭄na0naèn⃵ᮍḍⱘᗻ䋼a>0,b>0觟m³2,n³2ⱘᭈ᭄ˈ߭nnɂ1()aa=nnnɂ2ab=abnmnmɂ3()aa=naaɂ4=nnbbmnnmnmɂ5aaa==npmpmnɂ6aa=(݊Ёp塡ℷᭈ᭄)èᣛ᭄⊩߭(a,b塡ᅲ᭄,m,n塡ℷᭈ᭄)mnmn+ɂ1aaa=mnmnɂ2()aa=nnnɂ3()ab=abnnæöaaɂ4ç÷=nèøbbF•XCHANGF•XCHANGDEDEPPwwClicktob

3、uyNOW!ClicktobuyNOW!wmwmwowo.d.c.d.cocu•trackocu•trackìïmn-a()mn>nïɂaam¸=í()mn=(݊Ёa¹0)51ï1()mn<ïnm-îanè(1)-蠿Ьᮍnn塡㞾✊᭄ᯊ,局(1)-蛞nn塡ي᭄ᯊ(1-=)1nn塡༛᭄ᯊ(-1)1=-(2)ᣛ᭄ⱘᠽሩèᣛ᭄ⱘᠽሩᇚᣛ᭄⊩߭Ёⱘ㞾✊᭄ᣛ᭄ᠽሩࠄᭈ᭄ˈ᳝⧚᭄ˈЎℸܜᅮНᣛ᭄Ў0,䋳᭄,ߚ᭄ᰃⱘᚙᔶ.ɂ1ᣛ᭄Ў0贍Ў䋳ᭈ᭄ᯊa¹0觟n萙ℷᭈ᭄ᯊ,0-n1a=1,a=naɂ2ᣛ᭄Ў᳝⧚᭄ᯊa>0觟m,n(2)³蠿ᭈ᭄ᯊ,m1m-11aan

4、=nm,aan=n,an==mnmnaaèᠽሩৢⱘᣛ᭄⊩߭a>0,b>0觟m,n塡᳝⧚᭄ᯊ,mnmn+ɂ1aaa=mnmn-ɂ2aaa¸=mnmnɂ3()aa=nnnɂ4()ab=abnnæöaaɂ5ç÷=n(݊Ёb¹0)èøbbèࣙ৿ᣛ᭄ⱘ᭄ⱘ໻ᇣ݇㋏1)蠟Ⳍৠⱘᚙᔶɂ1a>1瀝mnaa>Û>mnɂ201<Û>1瀝mnɂ1ab=

5、>Û<1mnmnɂ2ab=<Û>1mn(3)ᇍ᭄èᇍ᭄ⱘᅮНxa>0,a¹1瀝,映ӏᛣⱘℷ᭄bˈ⒵䎇ab=蠿x⿄Ўҹa塡ᑩb蠿ᇍ᭄,䆄԰xb=log.ℸᯊ萗b塡logb蠿ⳳ᭄.aaèᇍ᭄ⱘᑩ੠ⳳ᭄ⱘᴵӊì⹧:0aa>¹,1ïlogb߾۰í㰚㑮0:b>aïî⪲⁎Ṩ:㔺㑮èᇍ᭄ⱘᗻ䋼a>0,a¹1,M>0,N>0觟n塡ӏᛣᅲ᭄ᯊɂ1log1aa=,log10a=ɂ2logaMNMN=+logaalogMɂ3logaaa=-logMNlogNnɂ4logaaMnM=log1ɂ5logab=(bb¹>1,0)logablogbcɂ6logab=(cc

6、¹>1,0)logacèᇍ᭄ⱘ৘⾡݀ᓣa>0,b>0,c>0觟,a¹1,b¹1,c¹1瀝nn1ɂ1logambb=loga,logambb=loga(݊Ё,m¹0蠿ᅲ᭄,n塡ᅲ᭄)mmɂ2logabba×=log1ɂ3logabcbca××=loglog1aclogbbca=log,ablogab=ɂ4(4)ᐌ⫼ᇍ᭄F•XCHANGF•XCHANGDEDEPPwwClicktobuyNOW!ClicktobuyNOW!wmwmwowo.d.c.d.cocu•trackocu•trackèᐌ⫼ᇍ᭄ⱘᅮНᔶབlogN(N>0)蠿ҹ10塡ᑩⱘᇍ᭄⿄

7、Ўᐌ⫼ᇍ᭄,䆄԰logN10èᐌ⫼ᇍ᭄ⱘᭈ᭄䚼ߚঞᇣ᭄䚼ߚᐌ⫼ᇍ᭄logN蠿ؐЎn+a(n塡ᭈ᭄ˈ0£a<1)瀝,萗ᭈ᭄n塡logN蠿ᭈ᭄䚼ߚ,ᇣ᭄a塡logN蠿ᇣ᭄䚼ߚ.ᭈ᭄䚼ߚϢᇣ᭄䚼ߚ᳝ϟ߫ᗻ䋼.ɂ1ᐌ⫼ᇍ᭄ᭈ᭄䚼ߚⱘᗻ䋼(1)logN蠿ⳳ᭄N蠿ᭈ᭄䚼ߚⱘԡ᭄Ўn局ˈ݊ᇍ᭄ⱘᭈ᭄䚼ߚЎn-1.(2)logN蠿ⳳ᭄Nⱘᇣ᭄䚼ߚⱘ㄀ϔϾ䴲0᭄೼㄀n蚳瀝ˈ߭݊ᇍ᭄ⱘᭈ᭄䚼ߚЎ-n.(-n᳝ᯊгㅔऩ䆄Ўn.)ɂ2ᐌ⫼ᇍ᭄ᇣ᭄䚼ߚⱘᗻ䋼᭄ᄫᥦ߫Ⳍৠˈাᇣ᭄⚍ⱘԡ㕂ϡৠⱘ᭄ˈ݊ᐌ⫼ᇍ᭄ⱘᇣ᭄䚼ߚ䛑Ⳍৠ.è↨՟⊩ব䞣೼ᇣ㣗ೈݙব࣪ᯊˈेՓϡᰃᔶབߑ᭄

8、y=ax蠿ᔶᓣˈг⫼ℷ↨՟ߑ᭄䖥Ԑⱘএ᳓ҷॳߑ᭄∖ߎ䖥Ԑؐˈ䖭⾡ᮍ⊩⿄Ў↨՟⊩.(5)ᣛ᭄੠ᇍ᭄ⱘ݇㋏èᣛ᭄੠ᇍ᭄ⱘ݇㋏axlogab=ɂ1蠿ϸ䖍পҹa塡ᑩⱘᇍ᭄l