高等数学公式大全.pdf

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1、 ? ? ? ? ? 1 / 16 ? ? ? ? ? ? 222212211cos12sinududxxtguuuxuux? axxaaactgxxxtgxxxxctgxxtgxaxxln1)(logln)(csc)(cscsec)(seccsc)(sec)(22?222211)(11)(11)(arccos11)(arcsinxarcctgxxarctgxxxxx?CaxxaxdxCshxchxdxCchxshxdxCaadxaCxctgxdxxCxdxtgxxCctgxxdxxdxCtgxxdxxdxxx)ln(lncsccscsecseccscsinseccos22222222Caxx

2、adxCxaxaaxadxCaxaxaaxdxCaxarctgaxadxCctgxxxdxCtgxxxdxCxctgxdxCxtgxdx?arcsinln21ln211csclncscseclnsecsinlncosln22222222?CaxaxaxdxxaCaxxaaxxdxaxCaxxaaxxdxaxInnxdxxdxInnnnarcsin22ln22)ln(221cossin222222222222222222222020? ? 2 / 16 ? ? ? ? ? ? ? ? ? ? A sin cos tg ctg ? -sin? cos? -tg? -ctg? 90-? cos? s

3、in? ctg? tg? 90+? cos? -sin? -ctg? -tg? 180-? sin? -cos? -tg? -ctg? 180+? -sin? -cos? tg? ctg? 270-? -cos? -sin? ctg? tg? 270+? -cos? sin? -ctg? -tg? 360-? -sin? cos? -tg? -ctg? 360+? sin? cos? tg? ctg? ? ? ? ? 2sin2sin2coscos2cos2cos2coscos2sin2cos2sinsin2cos2sin2sinsin?ctgctgctgctgctgtgtgtgtgtg?1)

4、(1)(sinsincoscos)cos(sincoscossin)sin(?xxarthxxxarchxxxarshxeeeechxshxthxeechxeeshxxxxxxxxx?11ln21)1ln(1ln(:2:2:22?.590457182818284. 2)11 (lim1sinlim0?exxxxxx? ? 3 / 16 ? ? ? ? ?cos1sinsincos1cos1cos12cos1sinsincos1cos1cos122cos12cos2cos12sin?ctgtg? ?RCcBbAa2sinsinsin? ?Cabbaccos2222? ?arcctgxarctgx

5、xx?2arccos2arcsin? ?Leibniz? ?Leibniz? )()()()2()1()(0)()()(!) 1() 1(! 2) 1()(nkknnnnnkkknknnuvvukknnnvunnvnuvuvuCuv? ? ? ? ?xxFfaFbFafbfabfafbf?)(F)()()()()()()()()(? ? ? ?23333133cos3cos43cossin4sin33sintgtgtgtg?222222122212sincossin211cos22coscossin22sintgtgtgctgctgctg? ? 4 / 16 .1; 0.)1 (limMsMM

6、:.,13202aKaKyydsdsKMMsKtgydxydss? ? ? ? ?bannnbannbanyyyyyyyynabxfyyyynabxfyyynabxf)(4)(2)(3)()(21)()()(1312420110110? ? ? ?babadttfabdxxfabykrmmkFApFsFW)(1)(1,2221? ? ? ? ? 5 / 16 ?,cos)(.sin,cos,cosPrPr)(Pr,cosPr)()()(2222222212121221221221cbacccbbbaaacbacbarwvbacbbbaaakjibacbbbaaababababababababa

7、a ja jaajuABABABjzzyyxxMMdzyxzyxzyxzyxzyxzyxzyxzzyyxxzzyyxxuu? ?113,22211;,1302),(,0)()()(1222222222222222222220000002220000000000?czbyaxczbyaxqpzqypxczbyaxptzzntyymtxxpnmstpzznyymxxCBADCzByAxdczbyaxDCzByAxzyxMCBAnzzCyyBxxA? ? ? 6 / 16 ? ? zyzxyxyxyxyxFFyzFFxzzyxFdxdyFFyFFxdxydFFdxdyyxFdyyvdxxvdvdyy

8、udxxuduyxvvyxuuxvvzxuuzxzyxvyxufztvvztuuzdtdztvtufzyyxfxyxfdzzdzzudyyudxxududyyzdxxzdz?0),()()(0),(),(),(),(),()(),(),(),(22 ),(),(1),(),(1),(),(1),(),(1),(),(0),(0),(yuGFJyvvyGFJyuxuGFJxvvxGFJxuGGFFvGuGvFuFvuGFJvuyxGvuyxFvuvu? ? ? ),(),(),(30)(,()(,()(,(2),(),(),(1),(0),(,0),(0),(0)()()()()()(),()(

9、)()(000000000000000000000000000000000000000000000000000zyxFzzzyxFyyzyxFxxzzzyxFyyzyxFxxzyxFzyxFzyxFzyxFnzyxMzyxFGGFFGGFFGGFFTzyxGzyxFzztyytxxtMtzztyytxxzyxMtztytxzyxzyxzyxyxyxxzxzzyzy? ? 7 / 16 ? ?lyxflfljieeyxflfjyfixfyxfyxpyxfzlxyfxflflyxpyxfz),(gradsincos),(grad),(grad),(),(sincos),(),(? ? ?,00),

10、( , 0),( , 00),(,),(,),(0),(),(22000020000000000BACBACyxAyxABACCyxfByxfAyxfyxfyxfyyxyxxyx ? ? ?DzDyDxzyxDyDxDDyDxDDDayxxdyxfaFayxydyxfFayxxdyxfFFFFFaaMzxoydyxxIydyxyIxdyxdyxyMMydyxdyxxMMxdxdyyzxzAyxfzrdrdrrfdxdyyxf23222232222322222D22)(),()(),()(),(,)0(), 0 , 0(),(,),(),(),(,),(),(1),()sin,cos(),(?

11、? ? ? 8 / 16 ?dvyxIdvzxIdvzyIdvxMdvzMzdvyMydvxMxdrrrFddddrdrrFdxdydzzyxfddrdrdrdrrddvrzryrxzrrfzrFdzrdrdzrFdxdydzzyxfzzryrxzyxr?)()()(1,1,1sin),(sin),(),(sinsincossinsincossin),sin,cos(),(,),(),(,sincos222222200),(0222? ? ?)()()()()(),(),(),(,)()(),(22tytxdtttttfdsyxfttytxLLyxfL? ? 9 / 16 ?0),(),(),

12、(),()0 , 0(),(),(21212,)()()coscos()()(),()()(),(),(),()()(00),(),(00?yxdyyxQdxyxPyxuyxuQdyPdxyPxQyPxQGyxQyxPGydxxdydxdyADyPxQxQyPQdyPdxdxdyyPxQQdyPdxdxdyyPxQLdsQPQdyPdxdttttQtttPdyyxQdxyxPtytxLyxyxDLDLDLLLL? ? ? ?dsRQPRdxdyQdzdxPdydzdzdxzxzyxQdzdxzyxQdydzzyzyxPdydzzyxPdxdyyxzyxRdxdyzyxRdxdyzyxRdzdx

13、zyxQdydzzyxPdxdyyxzyxzyxzyxfdszyxfzxyzxyxyDDDDyx)coscoscos(),(,),(,),(),(),(,),(),(),(),(),(),(1),(,),(22? ? ? ? 10 / 16 ?dsAdvAdsRQPdsAdsnAzRyQxPdsRQPRdxdyQdzdxPdydzdvzRyQxPnn?div)coscoscos(., 0div,div)coscoscos()(? ?dstARdzQdyPdxARQPzyxAyPxQxRzPzQyRRQPzyxRQPzyxdxdydzdxdydzRdzQdyPdxdxdyyPxQdzdxxRzP

14、dydzzQyR?kjirotcoscoscos)()()(? ? ? ?nnnnqqqqqnn1312112) 1(32111112? ? ? ? ? 11 / 16 ?nnnnnnnnnnsuuusUUu?lim;3111lim2111lim1211? ?1113214321,0lim)0,(?nnnnnnnnurrusuuuuuuuuuuu? ? ? ?111) 1(1) 1 () 1 ()2() 1 ()2()2() 1 (232121pnpnnnuuuuuuuupnnnn? ? ? ? ? 12 / 16 0010) 3(lim)3(1111111221032?RRRaaaaRRxR

15、xRxRxaxaxaaxxxxxxxnnnnnnnn? ? ? ? ?nnnnnnnnnxnfxfxffxfxRxfxxnfRxxnxfxxxfxxxfxf!)0(! 2)0()0()0()(00lim)(,)()!1()()(!)()(! 2)()()()(2010)1(00)(20000? ? )()!12() 1(! 5! 3sin) 11(!) 1() 1(! 2) 1(1)1 (121532?xnxxxxxxxnnmmmxmmmxxnnnm? ? ? ?2sin2cossincosixixixixixeexeexxixe? ? ? ?0,cos,sin2cos,2sin,cos,si

16、n, 1cossin)sincos(2)sin()(001010?nxnxxxxxxtAbAaaAanxbnxaatnAAtfnnnnnnnnnnnn ? ? ? ? 13 / 16 ?nxaaxfnnxdxxfabnxbxfnxdxxfbannxdxxfbnnxdxxfanxbnxaaxfnnnnnnnnnnncos2)(2 , 1 , 0cos)(20sin)(3 , 2 , 1nsin)(201241312116413121124614121851311)3 , 2 , 1(sin)(1)2 , 1 , 0(cos)(12)sincos(2)(00022222222222222210?

17、?l 2? ? ? 14 / 16 ?llnllnnnnndxlxnxflbndxlxnxflallxnblxnaaxf)3 , 2 , 1(sin)(1)2 , 1 , 0(cos)(12)sincos(2)(10? ? ?uxyuuduxdxudxduudxduxudxdyxyuxyyxyxfdxdyCxFyGdxxfdyygdxxfdyygdyyxQdxyxPyxfy?)()(),(),()()()()()()(0),(),(),(? ? ) 1 , 0()()(2)(0)(,0)()()(1)()()(?nyxQyxPdxdyeCdxexQyxQCeyxQxQyxPdxdyndxxPd

18、xxPdxxP? ? ?CyxuyxQyuyxPxudyyxQdxyxPyxdudyyxQdxyxP?),(),(),(0),(),(),(0),(),( ? ?0)(0)()()()(22?xfxfxfyxQdxdyxPdxyd ? 2122,)(2,(*)0)(1,0(*)rryyyrrqprrqpqyypy? ? ? ? 15 / 16 ?(*),321rr ?21rr (*)? ?)04(2? qp xrxrececy2121? ?)04(2? qp xrexccy1)(21? ?)04(2? qp 242221pqpirir? )sincos(21xcxceyx? ? ?sin)(cos)()()()(,)(xxPxxPexfxPexfqpxfqyypynlxmx? ?