数学分析数学分析数学分析 (4).pdf

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1、?yx?1?yx?x?2?yx24?()1yx24 1?()?yx?yxx?sin2x?0?x?yx?eyx?ex?1?yx?|ln|y?0 x?01.?x?10?xttyttt?2202223,?xatyatt?cos,sin,3302?(8)?ra?8,88?02,?(9)?ra?e,888?02,?(10)?rab?cos8?ba?.?0 (11)?rr?3cos8?1cos8 (33?8?)?(12)?82cos22ar?(13)?ra?cos28?(14)Descartes?xyax333y?(15)xyaxy44222?().?1?2ln23)ln21()1(12221?Fxxdx

2、xxA?2?316)22(2)14()41(22022022?()$%&?FFdyydyyyA?3?2)2cos1(21sin002?FFdxxxdxA?231?4?21)(10?F?eedxeeAxx?5?1.0111011.0101101.0)1(ln)1(lnlnlnln?FFFxxxxxdxxdxdxxA108110ln1099?6?158)32(2)22)(2(204322032?FFdttttdttttA?7?FF?2?206422023)cos(cos12cossin3cos4?dtttatdttataA2283961516312aa?()$%&?8?2320223421adaA

3、?88?F?9?F?88202221deaA41?241ae?10?FF?8888820222202)cos2cos(21)cos(21dbabadbaA?F?88?220222cos12bda2221ba?11?FF?333322)cos22cos43(21)cos1()cos3(21?888888ddA?12?24022cos214adaA?2?F?88?13?2402402221)4cos1(22cos218adadaA?8888?2?FF?14?txy?313tatx?3213taty?0:t?AF?()$%&?03321313dttattat=F?033232)1()21(9dttt

4、ta?3tu?232?A2032203223)1(3)1(23)1()21(3aduuuaduuua?()$%&?FF?88sin,cosryrx?xyax333y?888833cossincossin3?ar?2,0?8?FF?20232220233222tan)1(tantan29)cos(sincossin29?88888888dadaA20232231tan123aa?2?8?15?88sin,cosryrx?xyaxy44222?()?884422cossin?ar?FF?2?2042220442tan1tan1tan2cossin214?888888dadaA?8tan?t?FF?

5、0211204222)()(2112ttttdadtttaA201222arctan2atta?ya24?x?,?)0,(ax88sin,cosryarx?ya24 x?8cos12?ar?F?88?daA22)cos1(421)(?233?42222sincos8)cos1(1)cos1(12)(aaA?()$%&?0)(?A?2?2?0)(?A?2?0)(?A?)(?A?2?)2(?A?)2(?A2232222322223102cot)2cot1()cos1(12adada?FF?8888?04yx?3 2/?x?xyy?242ln?1?ye?yx?lncos02?xa?xatyatt?c

6、os,sin,3302?xatttyatttt?(cossin),(sincos),02?ra?(cos18)02?8?ra?8,02?8?3sin38ar?830?1?F40491dxxL2781080?2?21 2111111()()42eeeLyydyyydy?14?FF?3?2001tansecln(tansec)aaLxdxxdxa?FFa?4?2043 sin cos6Lattdx?Fa?5?()cos,()sinx tatt y tat?t?2342202Latdt?a?F?6?2222002 sin82Lrr dada?888?FF?7?22222001Lrr dad?888?

7、FF?22412ln241?aa?8?33222003sin32Lrr dada?888?FF?1?3?)2cos1(4sin)cos1(022221?FadttataL?)2cos1(4sin)cos1(222222?FadttataL?123LL?212cos?32?)23,)2332(aa?abA?B?Aa Bb?,h?xaybzc2222221?xya22?2xza222?xyza222?2xxya22?1?0()()(226hAaBbhVax bx dxABabAbahh)B?F?2?abcdzczabVcc?34)1(22?F?3?yz03022316)(8adxxaVa?F?4?

8、yz0 235F?222222)(xaxxaxdyyxaxAxaxxaaxaxax?arcsin)(222222?)31(arcsinarcsin)(320022xxadxaxdxxaxxaaa?FFF?aadxxaxaxxaxaxxxa032032)(2)31(arcsin)31(3)45323(a?30022154)(adxxaxadxaxaxaxaa?FF?3)9832(aV?f x().0)(0,0 xfybxa?yF?badxxxfV)(2?00?8?8,rr()?F?888?drVsin)(323?1?,babxxxxaPn?210:,?)(0,),(1xfyxxxyxii?y?)

9、()(212iiiixfxxV?9:?iiixxfx:9)(2?)(max1inix:?4?0?4?F?badxxxfV)(2?236(2)?88cos)(rx?,88sin)(ry?,?cos)(ra?,?cos)(rb?,?F?abdxyV2?22sin)(31ar?22sin)(31br?F?abdxy2?F?baxyd)(312?F?8888?drrr)sincos(sin22?F?888888?drrrr332322sincossin2cossin331F?888?drsin)(323?ar?0,0?8?3cos2222)cos1(32)(cossin3adxxaaaVaa?F?,?

10、8888?n?210?)(0,18888rrii?33122()(1 cos)()(1 cos)33iiiiiVrr?888?:9?8iiir888?:29sin)(323?:9niiiirV13sin)(32888?0)(max1?:?ini84?Vr?F233?88?()sin d8?1?xayb22221?x?2?yx?siny?00?x?x?y 237?3?xatyatt?cos,sin,330?x?xa ttyatt?(sin),(cos),10 2?y?0?yya?2?5?xyba222?()0?ab?x?6?ra?(cos18)?7?ra?e,80?8?8?()(xyaxy222

11、222?)x?1?2222234)(abdxxaabVaa?F?2?20221sin?FxdxV?202sin2?FxdxxV?3?FF?02732cossin3tdttadxyVaa32097310532)sin(sin6adttta?F?4?3220236)cos1)(sin(2)(2adttttadxxxfVba?FF?3220237)cos1()cos1(2)2(adttataaaV?F?5?badxxabdxxabxabVaaaa222222222224)()(?FF?6?303338sin)cos1(32adaV?888?F?7?33033)1(15sin32aedeaV?F?8?

12、88?8?F?40233sin)2(cos34?888?daV?8cos?t?238F?1212323)12(34dttaV?F?121232)12(dttF?12121221232)12(6)12(21dttttt31?F?121232)12(dttF?121212)12(3dtt?F?121232)12(dtt41?F?121212)12(43dtt81)21ln(1623122ln1222834121122?()$%&?tttt?F?1212323)12(34dttaV?332)12ln(24a!#+,-?yx xa?(),0ax?xa c?,?x?c?a?FF?caadxaxxdxax

13、x22022)()(?061510254325?caccaa?V?()5yxx?12?x?,0 5?x?a?V aV()lim()?1255?239)1(2)1()(22022aadxxxaVa?F?2)(lim?55?V?21122?aa?1?a?xayb22221?x?x?r?rb?r?xayb22221?x?202221342abdxxaabVa?()$%&?F?()$%&?2?F?232222222222)(34)1(2222rbbaabdxaxbrbbarVarbba?212VV?2213?br?x?ay?10?a2xy?1S1?x2S?1?a21SS?2?x?1?312131)()

14、(3120221?FFaadxaxxdxxaxSSaa?312131)(3?aaaf?aafaaf2)(,21)(2?0)(?af21?a?02)21(?f?21SS?21?a?12111min()(1)322SSf?2?)5131154()()(25124042?FFaadxaxxdxxaxVaa?21?a?240V2130?12.?)(xf 1,0)1,0(223)()(xaxfxf x?a?)(xfy?1?x?0?y?2?S?1?)(xf?2?aSx?1?223)()(xaxfxf x?23)(axxf?()$%&?cxaxxf?23)(?cxxaxf?223)(?223)()(xaxf

15、xf x?x2)()(1010adxxfxxdf?FF?24)1(af?ac?4?xaxaxf)4(23)(2?2?V1220()(10160)30fx dxaa?F?0?V5?a?015?V?5?a?pxy22?0?xa?x?yx?sin0?x?x?xayb22221?x?xatyatt?cos,sin,330?x?ra?(cos1)8?82cos22ar?(i)?(ii)?8?2?241?1?FF?aadxpxpdxxppxA00222122?=!#+,-?2323)2(32ppap?2?F?02cos1sin2dxxxA?022cos1ln(coscos1cos?xxxx?=)12ln(

16、222?3?FF?2?aaadxxbaaabdxxaxabxaabA02224222222)(4)(12?=?baababababbaabbaaabbabbab222222222222arcsin224ln22?4?22042203512sinsin12cossin3sin4attdatdttataA?2?FF?5?FF?8888?88?020222sinsin)cos1(4sin2dadrrrA20425322cos2sin16ada?888?F?6?i?24024022)224(sin4sin4adadrrrA?88?88?FF?ii?F?4022cos4?88?drrrA240222co

17、s4ada?88?F?14?1?xy?xx?121?xy?1?xy?),00yx?)(21000 xxyyy?1,200?yx?xy21?242?FF?2120)14111241122dxxxdxxA（?)1511(634252120?FF?dxxxdx?xx tyy tzz ttT T?(),(),(),12?Oxy?S?Fz tx ty tdtTT()()()2212?x t()?y t()z t()?,21TT0)(.tz?,21TT22101TttttTn?,1iitt?Oxy?is:?12222()()()()iitiitsx ty tdtxy55?:?:Fiit?,1iiitt?5

18、?Oxy?22()()()()iiiiiiSzszxyt5555:9:?:i?1max()ii nt4?:?2201lim()()()niiiit:iSzxy4555?2122()()()TTz tx ty tdt?F?4?xy)2,2(?)cos1(),sin(tayttax?0?a2/?t?328,4xyxy?24322,42)(1 232?RyyK?242sin1cot,csc(1 cos)242dyattd ytdxatdxa?aRayyK22,42)(1 232?pxy22?0?p?12222?byax?323232ayx?0?a?)cos(sin),sin(costttayttta

19、x?0?a?221,dxyd xdypdyp?2323222232)2()()(1 1xppypppypK?pxpR23)2(?tbytaxtan,sec?tabttttabdxydtabtttabdxdy322222cotsectancsccot,cscsectansec?2?234222423222323232)()csc(cot)csc1 cotaxbabatbatabtabtabK?（?baaxbaR4234222)(?taytax33sin,cos?244?22223 sincos11tan,3 cossin3sin cosdyattd ytdxattdxatt?2?4?433221

20、11113sin cos3sin cos3(1tan)attKattaxyt?33Raxy?2223(coscossin)sec1tan,(sinsincos)coscosdyattttd yttdxattttdxattatt?atttatK1)tan1(cos12323?atR?xyln?)0,1(?21,1xyxy?)0,1(,42)11(12322?xxK?22?R?xyln?)0,1(1?y?1?xy?),(ba1?ab?8)0()1(22?ba2,3?ba?8)2()3(22?yx?)(8rr?)2,0(,?8?)(8r?),(8r?2/32222)(2rrr rrrK?.?)()(tyytxx 2452322)()()()()()(tytxtxtytxtyK?()cos,()sinxryr888?8?cossin,sincosxrryrr888?8?cos2sincos,sin2cossinxrrryrrr88888?8?2222)()(rryx?r rrrxyxy?222?2/32222)(2rrr rrrK?246