工程数学教案

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-WUHANCOLLEGEOFINDUSTRIALTECHNOLOGY
ᦟᫀ201L2012


ᦪᦟᦟᐳ201109ᨴ28

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10113.W/(X-O)=/(x+0),Ü/(x-0)^/(x),`f(x+0)5/(⚗))5ᑣ\X஺z#oo000ᦪ/(x)Ḅ±é9:,஺áᦟᩞ஺5.BC9D&'#ᦪḄឋ>1)ஹ(ᨵFឋLᳮ)᝞#ᦪ/ᙠBC9ra,“D&'5ᑣᙠDᨵF஺2).(ᨬᜧஹᨬKJLᳮ)µ#ᦪy=/(x),xe஺ᙠDᨵF5ÞᙠíᙠJ£={y|y=/(x),xeD}zᔲᨵpÖᨬᜧḄðᦪñ᝞ᙠ5ò᝞ózÕÖ,3£DḄ#ᦪJ%=/(x),0ᑣõö=max{/(x)÷øù#ᦪᙠDDḄᨬᜧJ஺xeD;ûᙢ5᝞0fᨵpÖᨬKðᦪ5ò᝞ózÕÖ,/eOfḄ#ᦪJ%=/(%2)5ᑣõÒ=mjn{/(x)}\Ò#ᦪᙠDḄᨬKJ஺xeDfþ,LVWXoÿ/(x0)=0,ᑣX஺ᦪḄ3).(ᳮ)᝞ᦪ/ᙠa,“!"#$/ᙠḄ%&'()/(a)*/(b)<0ᑣ-.ᨵ0&(a,b),1/(J)=04).(45ᳮ)᝞ᦪ/ᙠ6“!"#ᑣ/ᙠ7,789ᑮ;Ḅᨬᜧ5>ᨬ?5@ḄAB0&45஺CDEFGᔜI⁚KL஺

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1213ÜX-%ݶzÞ00,ᦑà*Ḩ©7ᑏᡂlimᒹᡈ1²/àஹ஺+&á7%஺?TO%æTOAXᵫ7ᑁç#ᡃéêÃᦪḄTᦪᭆV஺^yᦪy=஻xáᙠx஺Ḅq&ìíᑁᨵ^#¶ÕWÖxᙠ/ᜐ9ê×ÖAràx°+Arïᙠìíᑁár#ݵḄᦪ9ê×ÖAy=/àð+&á-/à/á᝞Ay>Ax@§¶AxfOrḄ᩽▲»ᙠ#ᑣᦪá#=/àxáᙠ/ᜐ©T#ò&᩽▲ᦪy=/àxáᙠ/ᜐḄTᦪ#óôàõá,ᓽö%á=1²ᒹ=1²¶@ᒹ^^,-0Ar-0Ax¨©óC/!…úûᡈüû஺ýà1á©TḄeþᭆVᦪ/àXáᙠX஺ᜐ©TQᦪ/Xᙠ/ᐹᨵᦪᡈᦪᙠ஺2ᦪḄḄ/Vo=lim"*஺+"—"/ᡈ/Vo=lim"■$”"஺஺20hoX-XQ3᝞(᩽▲ᙠ+,-ᦪᦪ/*ᙠx0ᜐ1஺2.ᵫ4ᦪḄ567149:Ay=/x+Ax-/x;002?@Aᒹ=//+&Tx஺MAxব4᩽▲y-lim—.AioAXD⚪74$FᦪḄᦪ஺1ஹ/a=ccJᦪ2ஹ4ᦪ/x=x"஻cN*ᙠx=aᜐḄᦪ஺(3)ஹ/(x)=sin(x)

13143.ᦪḄQᓄ᳛T⚪UQ:9:VWQ:9:X@”YUQ:yᙠZ%\x0+ArJ^Ḅ_`AraḄbᙳQᓄ᳛+dᦪ/'(X஺)ᑣYUQ:ᙠX஺ᜐḄQᓄ᳛+ghijUQ:kWQ:ḄQᓄdQᓄḄl᠒no஺4.ᦪḄᭆq᝞(ᦪy=/(rᙠs_`/ᑁḄu$ᜐv1+,wᦪ“X)ᙠs_`/ᑁ1஺yz+{|}$XG/,v{iḼ/(X)Ḅ$ḄᦪA+y᪵,᪀ᡂj$Ḅᦪ+yᦪᩭᦪy=/(x)Ḅ஺ᦪḄy+=+—)ߟ/(x)ᡈ(x)=+(X)AT஺Arjioh1VḄᐵ7ᦪ/(x)ᙠX஺ᜐ1+ᑣᦪ/(X)ᙠX஺ᜐ+hXᯠ+ᦪ/(X)ᙠa$1஺5.ᦪḄᦪ7পஹ/(x)=C(CJᦪ)(2)ஹ4ᦪ/(x)-x"(neN*)ᙠx=aᜐḄᦪ஺(3)ஹ/(x)=sin(x)(4)ஹy=a'(a>0aW1)

1415⚪7ᦪḄᑣ?+ᔠᦪஹhᦪ4¢ᑣ£z72ᦟ¥Ḅஹ⌕47§¨©ªᦪḄᑣ?¢ᑣ\ᔠᦪḄ4¢ᑣ+j«ᦪḄᑣ?¢ᑣ\$▤j«▤ᦪḄᭆq+®4¯F°ᓫᦪḄn▤ᦪ+®4hᦪḄᦪ஺ᦟ¥²³7²7ᵨᦪḄᑣ?¢ᑣµ?ᦪḄᦪ³7ᔠᦪḄᦪ+hᦪḄᦪᑁ¶71.ᦪḄᑣ?¢ᑣ7\Ḅ4¢ᑣ7·ᦪ"(x),v(x)ᙠxᜐv1+ᑣᦪy=஻(x)+v(x)ᙠxᜐ1+ᦪJyr-"(x)'+v(x)'ᡈ(M(X)+v(x))z=஻(x)'+v(x)z஺»Ḅ4¢ᑣ7·ᦪ஻(x),v(x)ᙠxᜐv1+ᑣᦪy=“(x)n(x)ᙠxᜐ1+ᦪJy'="(x)'n(x)+v(x)'஻(x)oᖪḄ4¢ᑣ7·ᦪ“(x),v(x)ᙠxᜐv1+v(x)H0ᑣᦪ¾=ᔩᙠÀ)/Xᜐ1+ᦪJj=(3]="(x)$(x)%“(x)y(x)’஺•lv(x)JV2(x)2.hᦪḄ4¢ᑣ7·ᦪy=/(x)ᙠxḄ¯ÂÃᑁÄÅᓫÆ9Ç(ÈÉ),/'(Ê)ᙠ+/”(I)஺0,ᑣᦪy=/(x)Ḅhᦪx=Q(y)ᙠyᜐ1+d(y)=Î$+ᓽhᦪḄᦪYᐸᦪᦪḄ᎔ᦪ஺/(x)3.ᦪÒ⊤(ᦟᩞ)஺4.ᔠᦪḄᦪ7u=(p(x)ᙠXᨵᦪ×+y=f(u)ᙠ{iuᨵᦪÙ+dxduᑣᔠᦪy=f[(p(x)]ᙠXᜐÛᨵᦪ+ᓽÜ=Ü.Ý=f/Þ)./(x)஺dxdudxß7§¨©ªᔠᦪ4?à¢á+â`Q:1Zᑏ×+ä⌕ᑖæᦪḄᔠᐵçᨩéÀâ+,êëìµ?×ᔠᦪḄᦪ஺{ᦪ4¢7ᨵFᦪᵨ{ᦪ4¢4í°î+ᐸᳮ\à¢ᵫìðᩭḄñ⚪-ò஺

15165,▤ᦪ7ô▤ᦪ:/"(X)=*=limaxx=xAr->0/\yQlimfix)--%)X—>XQX—XQᳮᦪ/'XᙠXᜐḄᦪJᦪ+=/XḄö▤ᦪéJj“X஺Z÷øù+ᦪy=/xᙠxᜐḄn-1▤ᦪḄᦪJᦪy=/xᙠxᜐḄn▤ᦪ஺ô▤úô▤ZaḄᦪûwJ▤ᦪ஺ñ7Wᵫüýþÿ

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1617⚪ᑖ2ᦟḄ⌕ᳮᦪᑖḄᭆᑖḄᐵᑖḄᑣ!"ᑣ•▤ᑖ%&Ḅ'(ឋ*+ᦪḄᑖ஺,-ᑖḄᭆᑖḄ!"ᑣ஺.-ᑖᦪḄᐵ--▤ᑖ%&'(ឋᑁ11.ᑖ234AcTO/(x°+Ax)Ḅ56".ᐜ9:;<=>y=/(x)=x2,ᙠ-Ḅ⚞AᑁB:CDAx,E!/(x)ḄCDAy஺Ay=/(x+Ax)—/(x)=(x+Ar)3—xF=•Ax+3x•(Ar)2+(Ax)30000«•Ax(4Ar—>0).HIJKlim3x()•(:)+(9=Hm[3x()•Ar+(Ax)2]=0«ᓽ3x()•(Acf+(Ar)3IAv->0A,Ar->0ᐵRArḄS▤TUV(4Ar70)஺WᓽAy—3xFAx=3x0(Ar)2+(Ac)ஹITUV(4Av7O),ᵨ3xFAtZ[\)E!]^_`abV஺cd2.2ey=/(x)ᙠ-X஺Ḅ⚞AᑁB:CDAr,fgḄ+ᦪy=/(x)ḄCDh⊤jKAv=/(x+Ax)-/(x)=Ax+0(Ax)(Ax—>0).00ᐸl,AIArTᐵḄnᦪlimᜐ஺=0,o(Ar)IᐵRAcḄS▤TUV(Ax70)஺©70\%ᑣu+ᦪ/(X)ᙠ-X஺ᜐhAAxuK+ᦪ/(x)ᙠ-/ᜐḄᑖwKdyᡈy1(x),B|idy=A*Axoz{AAA•IᐵRAxḄ•|+ᦪ4Ax—»0n}Ay~=AAxuK\y=4Ax+(?(Ax)Ḅឋ⌕ᑖ஺hhḄᐵ>y=/(x)ᙠ-X஺hᑣᨵ\y=A•Ax+o(Ax),Ay40(Ax)ᡠrcrl~^A+—~~-,ArAx

1718lim—=lim(A+°࠷)=limA+lim"+)=A஺Ax->0ArAx->0ArAA—>0AXTOArᵫᦪḄcdᑣᨵf'(x)=A0ᨵdy=A•Ax=/(x)Ar஺0ᩭe1ᒹ=/'(x),ᑣᨵᒹ=f\x)+a.4(Ar70a70HIᦈ00AS0ArAx᩽▲Ḅ:;cᳮᙠ)ᡠAy=/(Xo)Ar+aAx஺(4Arߟ0a-0)ry•ArJKlim2=lime=0,ᵫᑖcdᨵ—AxAVTOdy=ᔠcᳮ஺cᳮ2.3+ᦪy=/(x)ᙠ-x0hḄᐙ⌕ᩩ¡Iy=/(x)ᙠ-X஺h_dy^f\x)^x.0᪆<2.23:£ᙢ+ᦪy=/(x)ᙠ¥{-xḄᑖdy=/'(Xo)Ar.uK+ᦪḄᑖ஺᪆«ᔠ+ᦪy=/(஻),஻=9(x),RIᢥ«ᔠ+ᦪḄª&ᨵdydydu.../ஹ.....Ar¯=ᓝ¯=/5)᜛(x)=f³᝖µ¶9(x),axduaxᡠdy-f:(pkxS\(p(x)dx-f(u)•udx-f\u)du.h9'3I·(DU,¸I+ᦪ஻=9(x),¹ᨵy=/'(M)ºH:ᱯ¼uK:▤ᑖ%&Ḅ'(ឋ஺Hᙠ'c½ᑖḄ¾ᑖ"ln◤ᵨᑮ஺zhQh᪆<2.24

1819⚪lÃcᳮÄÅÆ"ᑣ2ᦟḄ⌕ÈÉÊ*gᵨËÌcᳮஹÍÎᨽÐlÃcᳮÑÒlÃcᳮÈÉᵨÄÅÆ"ᑣÓc&᩽▲Ḅ]"஺ᦟ,-ËÌcᳮÍÎᨽÐlÃcᳮÑÒlÃcᳮḄᵨ஺.-lÃcᳮḄᮣÕᵨ஺:ஹlÃcᳮÖת&(ØᐭÖ×ÚᦪlÛ)1.(ËÌcᳮ):᝞f(x)ßà:পᙠ³a,b¶äå.(2)ᙠ(a,b)h.বf(a)=f(b)ᑣçèéᙠ-(a,b),êf/(&)=0<>g(x)=x(x+l)(2x+l)(3x-l)ᑣᙠîï(T,0)ᑁ]ñg'(x)=0ᨵ2;ó᪷Fᙠ(-1,1)ᑁg஻(x)=0ᨵ2;᪷2.(ÍÎᨽÐlÃcᳮ)᝞f(x)ßàজᙠ³a,äåFঝᙠ(a,b)äåᑣéᙠ(a,b),êf(b)-f(a)=f•/ড(b-a)஺ø3᝞ùᙠîïIf1x)û0,ᑣf(x)=c஺zᙠÍÎᨽÐlÃcᳮl᝞ù/0)û/ভᑣÍÎᨽÐlÃcᳮþÿᓄᡂᳮᡠᳮᨽᳮḄᱯ஺3.(ᳮ)᝞ᦪ/(x),g(x)$%&(1)ᙠ)*+ಘ-./0(2)ᙠ2*+(36)ᑁ678g(x)H0ᑣᙠ2*+ಘᑁ<=>ᙠ?@Je(a,b),EFg(a)-g(b)g'4)IᯠKg(x)=xMᳮᓽOᨽᳮᡠᨽᳮᳮḄᱯ஺4.PQRSᑣ&᝞TḄᦪ᩽▲WXY஺0...x-sinx",1ஹ?`&᝞&lim--------`&0sotanx-x2ஹ?`&᝞&lim--a>0aoox3ஹ0*8`&᝞&limxa•

19xa>0XT+oo

20204ஹoo-oo`&᝞&lim(-------)sinxx5ஹ0°`&limxarclanxx->+016ஹ8°`&᝞:lim(ctgx)inxXT+07,r`&᝞&lim(ᜐ3310xpqḄrstuᵨᦪ᩽▲ḄwᑣxsSᑣ,8pqy⊤{|`}ᨵᐹ஺003l)s-(?)`ḄPQRSᑣXTa(ᳮX78)08ᳮ&ᦪ/(X),g(x),᝞&(1)lim/(x)=0,limg(x)=0xTax-(x->8)(x—»oo)(2)ᙠN(a,3)ᑁ(x>X)ᨵ7ᦪg',8g'(x)ᑁ00(3)lim/3>ᙠ(ᡈ)ᑣᡂ&(X)g(X)UmJm(X)8(x))g(x)2)ஹᐸp|`஺?2τOO1)10110-02)8—OO->-----------<--------000x03)y=0"TIny=OxlnO(0,°°`)1oo04)y=i,y=8S3)ᳮ&ᦪ/(x),g(x),᝞:

2121(1)lim/(x)=8,limg(x)=oo.x—>ax—>a(x—>8)(x-»)(2)ᙠN(a,3)ᑁ(x>X)ᨵ7ᦪ7g',8g'(x)HO0(3)lim.(),>ᙠ(ᡈ)ᑣᡂ&jg'(x)limJim¡L)g(x)£¤g(x)0OO¥&(1)PQRSᑣ6./Eᵨ¦§¨EᵨSᑣ©Qª«¬ᔲ®¯Y`ᡈ?`,08±t²tuEᵨPQRSᑣ஺(2)᝞ᨵ6³´µᡈᨵ¶·᩽▲Ḅ¸¹´µᑣ6ᐜ³»ᡈ¼½ᓄ¾s¿À;/V)(3)Krhm$—t>ᙠMÄtuÅrᐶt>ᙠÇM3EᵨᐸÈÉSÊ஺g(%)g(x)

2222⚪Ì&ᦪḄᓫÎឋ᩽ÐM&2ᦟÒÌḄ⌕Ê:ᳮᦪḄ᩽ᭆÕÖ×ᵨ7ᦪᑨÅᦪḄᓫÎឋÊᦪ᩽ḄÉS,Ö×ᦪᨬᜧᨬḄÊSÛᐸ½ᓫ3ᵨ஺Ü@&ᦪᨬᜧᨬḄÊSᑨÅᦪḄᓫÎឋÝ@&Êᦪ᩽ḄÉSᦪᨬḄ½ᓫ3ᵨᑁÞ&1.ᦪḄᓫÎឋ&ᳮ2.6ßᦪy=/(x)ᙠa,b-./ᙠ(a,b)ᑁ67ᑣᨵTàáâᡂ஺(1)᝞ᙠ(a,b)ᑁ/'(x)>0,ãäᦪy=/(x)ᙠa,b-åᓫÎæ0(2)᝞ᙠ(a,b)ᑁç(è<0,ãäᦪy=/(x)ᙠa,b-åᓫÎê=஺ëì¾{íîïð᪷ò-☢ᳮᑨᦪ/(x)ḄᓫÎឋ²6ᢥTᑡ¿Àᩭ÷ø஺(1)ù/(x)Ḅ஺(2)úÊE/'(x)=0/'(X)t>ᙠḄ@x,Äûü@Oᑖþ@ÿ
ᑖ஺(3)'(X)ᙠᔜᑁḄᔠ(ᵨᑡ⊤)!"ᑨ$/(x)Ḅᓫ&ឋ(r(x)>0,()*ᦪᙠ,ᑁ-.ᓫ&/01/'(x)<0,()*ᦪᙠ,ᑁ-.ᓫ&34)஺5᪆73.383.62.*ᦪḄ᩽ᜧஹ᩽>?@1)
@᝞ᙠX஺Bᑁឤᨵf(x)ீf(xo),(f(x)>f(x)),ᑣGf(x())0*ᦪf(x)ḄH᩽ᜧ(>)?஺IJ᩽?Kf/(x)LMᙠḄKNf/(x)=OḄK஺(OK)OKH᩽?K3.ᑨPQ*ᦪ᩽?ḄR⌕ᩩU@V*ᦪf(x)ᙠKX஺ᜐIXYZᙠKX஺ᜐᨵ᩽?(᩽ᜧ?

2323ᡈὅ᩽>?)]ijRᨵf'(x)=O*ᦪ᩽?ḄdHᐙᑖᩩU@V*ᦪf(x)ᙠKx0ᜐghᙠKX஺ḄjHklBᑁIX@ᑣᨵmᑡnᡂp.(1)᝞rf/(x)ᙠX஺Ḅstឤuᙠvtឤw()*ᦪ/(X)ᙠKX஺ᜐxy᩽ᜧ?/(X஺)1(2)᝞rf/(x)ᙠX஺Ḅstឤwᙠvtឤu()*ᦪ/(X)ᙠKX஺ᜐxy᩽ᜧ?/(N)1*ᦪ᩽?Ḅd{ᐙᑖᩩU@V*ᦪf(x)ᙠKX஺ᜐᐹᨵH▤{▤XᦪZ/'(%)=0,/(/)஺0,()ᨵmnᡂp@(1)᝞r/(%)>0,ᑣf(x)ᙠKX஺ᨵ᩽>?஻N)1(2)᝞r/"(/)<0,ᑣf(x)ᙠKX஺ᨵ᩽ᜧ?(%)1*ᦪ᩽?Ḅ@(1)*ᦪ/(x)Ḅ
1(2)*ᦪḄXᦪOKXᦪLMᙠḄK1(3)ᵨ᩽?ḄdHᐙᑖᩩUᡈd{ᐙᑖᩩU᩽?K1(4)᩽?Kᐭ/(x),$᩽?Yᢣ$᩽ᜧ(>)?஺5᪆73.7-3.101.*ᦪḄᨬᜧ?ᨬ>?V*ᦪy=/(x)ᙠa,bgh᪷gh*ᦪḄᱯឋI*ᦪ/(᜜ᙠa,bHᨵᨬᜧ?ᨬ>?஺᝞rᨬᜧ?ᨬ>?ᙠᑁxy(),ᨬᜧ?ᡈᨬ>?H*ᦪḄ᩽ᜧ?ᡈ᩽>?஺᜜,ᨬᜧ?ᡈᨬ>?IJᙠḄKxy,ᡠ/(x)ᙠa,bḄᨬᜧ?ᨬ>?ḄQ@$IJ᩽?KḄ*ᦪ?Y¡¢NKḄ*ᦪ?£¤¥¦ᐸ¨ᨬᜧḄ©*ᦪḄᨬᜧ?ᨬ>Ḅ©*ᦪḄᨬ>?஺ᵨQ5᪆73.11-3.162ஹª«Ḅ¬ஹ®K¯°±«

2424ᙠIf(x)IX᝞f஻(x)>o(0x=l,x=-2,f(x>Qx=lX(-8,-2)-2(-2,0)0(0,1)1(1,+°°)y+0-+0+y”---ÄH0+yᓫ&/᩽ᜧ?ᓫ3ᓫ/®ᓫ//(-2)=Km(1,_270)~~4°±«@ª«CḄÈKPÊḼª«¶▲ÍÎÍKÏKPNj-ÐÑ«LḄÓÎÔ±ÕÖᑣGÑ«Lª«CḄ°±«஺᝞f(x)=aᑣGy=a×Ø°±«(X—>-oo)᝞XJ-ijPf(x)=8ᑣGX=XoVᚖÑ°±«Þ-»Hᡈà-«6)°±«IJâᨵᡈãᩩ஺

2525⚪å@LæᑖḄᭆèឋéêÏ@2ᦟìåḄ⌕@ᳮ5î*ᦪᭆèஹLïᑖḄᭆèðñLïᑖḄឋé஺òK@î*ᦪLïᑖḄᭆèóK@LïᑖḄឋéᑁô@î*ᦪஹLïᑖᙠI,᝞F(x)=f(x),Gf(x)F(x)ḄX*ᦪGF(x)f(x)Ḅî*ᦪî*ᦪNX*ᦪHö÷⌮ᐵú஺᝞F(x)f(x)ḄHî*ᦪᑣF(x)+Cf(x)Ḅᐰüî*ᦪ஺ýJf(x)dx,ᓽJf(x)dx=F(x)+Cᑖឋপ(|f(x)dx)=f(x)ᡈdJf(x)dx=f(x)dx(2)|F(x)dx=F(x)+C(3)|kf(x)dx=kjf(x)dx(4)J(f(x)±g(x))dx=jf(x)dx±jg(x)dx:ᦪᦪᨵ"⌮ᐵ%&...ᵫᦪ⊤*+ᑖ⊤஺-ஹ/0F(x)123Ḅ56ᦪ&X78dF(sinx)98F'(x)=^X:.ஹdF(sinx)..Insinx1dF(sinx)=----------dsinx=--------cosxdxdsinxsinx-ஹf(x)Ḅᦪ1sinx&ᑣf(x)Ḅᦪ-sinx+c.x+c^(JஹBCDEᦪ)

2626⚪G8H5IᣚᐗL&HMIᣚᐗL&ᑖNᑖLOP84ᦟRGḄS⌕78UVᑖḄWXYZ&UVᑖḄឋ&UVᣚᐗᑖLᑖNᑖL஺[\8ᣚᐗLᑖNᑖLḄ]ᵨ_\8`ᑖabᣚᐗLḄcᵨᑁe8fghLᐜὃkᑖJcos2xJx஺mᯠ&opqᑭᵨWXᑖYZ[cosxJx=sinx+Cot2ᑍ=%,BPx=—,dx=?du0|1}ᦪᓄBJ22cos2x=cosu,jcos2xdx=-jcosudu஺11P&Ḅᑖ5=—sin஻+C,஻ᣚB2x,+ᑮ22[cos2xdx=-sin2x+CoJ2H5IᣚᐗL(ᑖL)8Jf(஻)d஻=E5+C,஻=8(x)ᨵᦪ&ᑣJf[p(x)]8'(x)dx=F[(p{x)\+CoEᵨᑖZdkx=kdxd(x+c)=dxexdx=de'-dx=dlnxX-4dx=d-cosx=dsinxX-X—Ddx—dVx^sec2xdx=dtanx2Vxdx=darcsinx,Xdx=dVl+x21-x2ViZT7sin2xdx=dsin2x-sin2xdx=-dcos2x

2727-:1ஹߟ--dx=--f---d(3-2x)=--ln|3-2x|+c3-2x2J3-2x2112ஹXdx=JVlnxdInx=(Inx)2+c3ஹcosxsin3xdx=jsin3xdsinx=~sin'x+c2V1-x24ஹ•/xdx=--fdVl-x+cVbV2J5ஹJx2exdxJe'd(-x,--e'3+C36ஹ13.-1X~~dx——J—arctan—+ca+xaJa1+12x7ஹd2x=—arctan------Fc9+4x223?+(2x)26a------------dx=f----------------d(x+l)c+2x+5J(x+1)2+41x+1=—arctan--------Fc229ஹ.——rdx=arcsin—+cJVa2-x2adx_pdx+12x-9x/0-,5-(2-3xY12-3x—arcsin+c3V511ஹfsecx==(-d(tanx+1)=24tanx+1+cJJtanx+1JJtanx+112ஹjtan4xdx=jtan2x(sec2x-l)dx

2828=jtan2xdtanx-j(sec2x-l)dx=-tan3x-tanx+x+Cjarcsin4xdarcsinx=-arcsin5x+C514ஹjexsin(ex+l)dx=jsin(ex+l)d(ex+1)=-cos(ex+1)+C15ஹjC0^2^ds=2jcosVxdVx=2sinVx+CarctanVx,,arctanVxMfdx:2[(l+x)VxJ1+x=2JarctanVxdarctanVx=arctan2Vx+C1rl+es-e\-------dx=f-----z--------dx1+e*-l+ex=[1------dxJl+ex=x.23J1+e*=x-ln(l+ex)+Ce*—1/de'de,---------dx=f--------------r---------------e2x+4Je2x+4Jex(e2x+4)1e=—arctan-----249e2x+4j=—arctan-———+—ln(e2x+4)+C2248

2929x-+cosxi13x_+3cosx,19ஹr—8-------dx=--rr--------dxx+3sinx3x+3sinx4¡“£+c98jxx(l+lnx)dx=jexlnxd(xlnx)=ex,nx+C=xx+C20ஹ98flnsi,Xdx=[insinxdtanxJCOSXJ..rCOSX.=tanxlnsinx-Itanx----dxJsinx=tanxlnsinx-x+CSinXtanxif.21ஹvtanxe-tanxdtanx—T—edx=icosx=-jtanxde-tanx=-tanxe-tanx+e-tanxdtanx=-tanxe-tanx-e-tanx+C22>Jxf(x)dx=arcsinx+C,ᑣ®=--+c¯☢ᩭẆ³9´µIᑖḄhL஺fgḄ&B¶9´µ6_⚪◤⌕¸¹º|3☢ḄᣚᐗhL&»1tx=/(t>o),µ᪵»ᨵG=t,½¾dx==2tdt,¿ÀÁÂᐭᡠ7ᑖÅ&»+ᑮ=2[f-ln(l+r)]+C>ᵨÇÈᣚ3ZÅḄ=2t,ᓽ*+ᑮᩭḄᑖ+C஺mᯠ&3ÉÊ⚪Ḅ9´¡1ËÌᣚᐗḄ⌶ÎᩭÏÐḄ&Ñ1&µÒḄᣚᐗLÓ☢ḄᣚᐗhL1ÔᐰºḄ&9´X⚪ḄᣚᐗX=஻Å&Ö×Øt1cBÙ×ØᩭÚÛḄ&3ÉH5I

3030ᣚᐗᑖLÅḄÖ×ØM1cBᦪÝÞ»oḄ&¿µbᣚᐗ7ᑖḄhLßBHMIᣚᐗᑖL&ᐸᳮâÉ᝞¯8HMᣚᐗLäḄå'("&=ç(஺+C,x=8")ᐹᨵᦪ&¾d(f)H0,t=9T(ì1í=e(r)Ḅîᦪ&ᑣᨵ=ç3T(x))+C஺HMIᣚᐗLḄcᵨᙠ|ðᑖJ/GMx᧕7+P&*ÝcÂᣚx=9(f)(⌕7x=ô)ᙠõ`öᑁ÷øᓫú&ᑣt=᜛5ü)5ýᙠ)[f[x}dxᓄBJf[ôå3þὅ᧕ᑖ,᝞3=஺+஺x=°(஺Ḅᦪt=9T(x)t!"(p-\x),#$%&\f[x}dx='3T(x))+Co◀+,-ᑖ.᜜ᐸ12ᵨ456ᣚ(1)9ᦪ:;ᨵ=>᪷@Va2—x2,Ex=asinfVa2+x2,Ex=atantVx2-a2,Ex=asect᝞MJax2+bx+CPQ—>Ju2+aT,Gu2-aT,JaT-u2U1ஹdxEx=sint,dx=costdtJx2XY!@=jc°YT..costdt)/-Jcot2tdt=j(csc21-l)dtN\l\-x2=-cott-t+C71-x2-arcsinx+Cx

3131U2ஹf-1BY=aX.Jx'Jx-4x-2seer%=4cosx(2)9ᦪ:;de᪷@dxU3ஹ1+Vx+2XYE-X+2=tx=t3-2dx=3t2dt-1+—^)dt!@=I+ta______=-3(x+2y-3Vx+2+31n1+Vx+2+CU4ஹJ----1jdxEx=t6dx=6t?dt!@==6Jmn=6j(t-l+^^n=6(y-t+ln|l+t|j+C=3Vx-6Vx+61nl+Vx|+CU5ஹJ7ex+ldxXYEJe*+1=tex=t2-1x;ln(t2-1)dx=•,tnt2-l!@=Jt'PT7dt=2J(1+?TT)dt=2t+ln—+Ct+1

3232=2je+l+ln(7ex+l-1)-ln(Vex+l+1)+Cᑖuᑖ.ீwᳮு᝞u(x)ஹv(x)ᙳᐹᨵ|}Ḅ~ᦪᑣJudv=uv-jvduYᑖuᑖ.Ḅᵨᙠ᝞wᑖJvd”ᑖ᧕%&ᵨᑖuᑖ.$ᓄ"᧕஺U1ஹjxcosxdx=jxdsinx=xsinx-jsinxdx=xsinx+cosx+c-XxU2ஹJxedx=-jxde-=-xe-x+|e-xdx=—xe-ஹ-e-x+CU3ஹJ(arcsinx)2dxj=x(arcsinx)2-Jx2arcsinx■,ூdx=x(arcsinx)2+2jarcsinxdVl-x2=x(arcsinx)2+2V1-x2arcsinx-|dV1-x2•dxV1-x2=x(arcsinx)2+2V1-x2arcsinx-2x+CU4ஹ…Inxdg)

3333jlnjnx_jinInxdInU5ஹ=Inx-InInx-finx-d-dxJInxx=InxInInx-Inx+cU6ஹjxtan2xdx=jx(sec2x-l)dx2=jxdtanx--2x=xtanx-Jtanxdx--2=xtanx+In|

3434=exsinex-Jsinexdex=exsinex+cosex+c22x2^(1-cos2x)dxU10ஹjxsinxdx=Jx2dsin2x=————x2sin2x+—[xsin2xdx642Jm-Uin2xTJxdcos2x64X12•31c1.C=--------x-sin2x——xcos2x+-sin2x+c6448xarcsinx2U11ஹdx=-JarcsinxdV1-xA/1-x2=-Vl-x2arcsinx+x+c

35355.1wᑖḄᭆY2ᦟḄ⌕%YᳮXwᑖḄᭆwᑖḄឋ¡¢஺£¤YwᑖᭆḄ¥~¤YwᑖḄ¡¢ᦟᑁ§Ydஹw¢ឋ¨f(x)dx=lim£f(g)Ax,X-maxீw¢ுYXd,®®஺¡(1)ᑖ®¯ᨵ▲9ᦪᨵ±T(2)“ᑖ.”ஹ“´.”µᐵ;(3)wᑖḄ·ᑖ45Ḅ⌱´µᐵ(4)f(x)ᙠ¹ºᨵ±Mf(x)ᙠ»a,bº$Ḅ¼⌕ᩩ¾f(x)ᙠ»a,bº|}Mf(x)ᙠ»a,bº$Ḅᐙᑖᩩ¾஺(5)ÀÁᦪᙠᐸw¢®¯mÂM|}ḄÃÄÀÁᦪᙠᐸw¢®¯mÂM$Ḅ஺ீÅ¡¢ுYLÇ"”ᙠÅm⊤ÊËÌ=°,Ì=Ç)x=a,x=bͯᔜuᑖ☢Ḅ6ᦪÐ஺᝞ÑÒᙠOxÔḄÕQᑣᑖ"Ö᝞ÑÒᙠOxÔḄmQᑣᑖ"×஺⊡ᐙÙw¨ÚÛ=°JTf(x)dx=-fTf(x)dxீឋ>ឋ(1)d(9)(1—7ḕᶍ)ᐸ:(8)"ßàwᳮYᙠá$m‘f(x)WM,ᑣm(b-a)

3636éY.,9/1Ì9$+X-x.=___X_____Iri4ë2ìᙠ[0,1Jmᨬᜧ·"+ᨬÚ·"22[¨]•.3V2+x-x2I2rl]1-3

37375.2-ᑖòówᳮ5.3wᑖḄᣚᐗ.ᑖõᑖ.Y2ᦟḄ⌕%YᳮXö÷øùúᐻü@ýᵨᣚᐗ.ᑖuᑖ.%ᑖ஺£¤Yö÷øùúᐻü@¤YwᑖḄᣚᐗ.Ðᑖuᑖ.òówᳮö÷ߟøÿᐻ1°▲ᑖᳮf(x)ᙠa,bX(a,b)!"#$ᑣ&x)=Jf(t)dt+,-.ᦪ0B(x)=f(x)ᓽf()dt=f(x)34jf(x)Ḅ#78.ᦪ஺tdx:3ஹ=>ὡ(x)=J@e+dt,F2(x)=Je-Fdt,F3=J=XG?F4(X)=IZe%t,F(X)=JXtf(t)dt,5OF(X)=fXxf(t)dt-F(X)=JX(x-t)f(t)dt607OR:F(x)(i=l,2,……,9)XE(x)=e-"E(X)=2X6'R(x)=sinxg`E(x)=cosx^"rx+sinxexE(x)=x,x)E(x)=J@f(t)dt+xf(x)IE(x)=(xFf(t)dt-Jotf(ಗ=Jf(t)dttlntdtcosxlncosx-sinxcosx:4ஹlim=limx-»0X4XTO4x3

38381#sinxFIncosx=—hmcosx-lim-----lim-----4x-M
x—>0xXTOx2-sinx1_=—lim4J°2x•cosx8:5ஹy=J(t-1m#dtᨵ᩽ᜧqḄ$A.X=1B.X=-1C.X=+1D.X=0:6ஹ᝞F(X)=J^dt+J7xW0WFxxy=BcᐔA.0B.#c.-D.2e23:4ஹf(x)ᙠ(#848)0F(x)=J@(x-2t)f(t)dt,|4}f(x)Ꮤ.ᦪᑣF(x)+Ꮤ.ᦪ஺|F(-x)=J(-x-2t)f(t)dtfx(-x+2u>'(-t)d(-1)o=JX(-x-2t)f(t)dt0=F(x)2°ᑖজᐻீᳮF(x)ᙠa,b஺F(X)F(X)ᙠa,bḄ!"#78.ᦪᑣᨵ

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4040ᐔ="xcosxsinxd-Jnxcosxsinxd2xdsin2x2JT21+x2x<0:12ஹf(x)=JᑣJ:f(x-2)dx=Xx>0i1Aஹe3Bஹe+-cஹ—Dஹ2e33Jf(x-2)dxjτf(t)dt=|(1+x2)dx+j'exdx2^=dx=f2x2:13ஹ1dx°72^7Jo#x-1=sintJI2¦x=2sin2t8{3HJI3=8f5sin4tdt=8*'.—='nJ04!!22:14ஹf(x).ᦪ0f(x)=sinx+J@f(x)dxRf(x)XJf(x)dx=Aᑣ«*)=$ᵫ*+A

4141ª«ᑖfHfitJ஺f(x)dx=Jo(sim^A)dxA=-cos<+A^A=&1-ᐔ2f(x)=sinx+----1-ᐔ:15ஹ(f(x)ஹg(x)ᙠO,20f(x)=3$+J@g(x)dxg(x)=-x3+3^£f(x)dRf(x)ஹg(x)Ḅ⊤°஺±ᫀf(x)=3x2-4g(x)=-x3):16ஹf(x)=fxdtx>0,)Jl1+tRf(x)+f—/Xf(x)+f'L)=Jµdt+J@¶dt

42421+xx(x+l)Xf(x)+=j^-dx=^ln2x+c·x=lc=0(•.•f(l)=0)f(x)+f——ln2x2:17ஹf(x)=fx.sint¸Rfnf(x)dxJon_tJoXrnrnJf(x)dx=Jof(x)d(x-7T)o=(x—ᐔ)f(x@#J@(X-7T)df(x)=F(x-n)•S*nXdx=f"sinxdx=2Jo'JT.Jox:18ஹ=>f(x)ᙠo,2¦▤,-0fফ=1,f'(2)=0Áj@f(x)dx=4RJ@x2f2x)dxX8¾J@x2dft2x>-x2ft2x12xft2x)d>22021,1111H'J஺xdf(2x>-xf(2x)-Jf(2x)d;+oNN0N1%…11=——+-fRt)dt=——+11=—24Jo22:19ஹf(x)ᙠ(-8,+8)

4343|4J@4u)(x-u)du=jJgx)dxdu|«=ujf(x)dx_=Judj@f(x)dxo=xf(x)dx-J஺'uf(u)du=xJ஺f(u)du-J஺uf(u)du=F(x-u)f(u)du:20ஹI(a)=J|x—a|e'dxRI'(a)XI(a)=J(a-x)edx+[(x-a)edx=aFexdx-xd

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6564040⚪JX=ᐸÆA,Ñ஺0,0i=l,2,…,஻.ÀXᑭᵨᩈ⚪_ÓÔÕ.4.14▣4=(%):Ö×Ø▣᝞`iᡠs஻äᡂ3.®5⚪äJ¡ᩭìí59ÈÇ×Ø▣ä+᪵ᡂ3.4.15JA“X஻▣î.2).56AA*=|A|£.+H0,ᵫÈï|=|A|n,ᑣভ=ὶ;ó=0,ᑣ,]=0ᔲᑣA*⌮A=44*(A*)T=|A|E(A*)T=0,õö)ᑣ_Óäᡂ3.ᡈὅ|ù=0ᑭᵨ4.12úÓ5).n,&(A)=஻4.16J4+Ç.56R(A*)=<1,R(A)=஻-1,0,R(A)<”1.ᶍR(A)=஻ᑣ|Aû0n|Aü0nR(A*)=஻A(A)=n—1,ᑣA*0nR(A*)21C4¾ᙠ஻1▤ýþÿ)AA*=0,ᵫ⚪4.12ijR(A)+R(A*)WnnR(A*)Wl,ᑣR(A*)=1R(A)<”-1,ᑣA*=0G4Ḅᡠᨵn-1▤ᙳ)ᑣ

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6766Em0ஹ'hBஹh,Bஹd<=mE„)IAE,JI0Lᑖ4ABᑡᓽ#.E-ZAB)n9.1%▣Ḅ*+,ᣚ9.2%▣Ḅm9.3nឋ=pqḄrstu4ᦟwxḄy⌕:{|%▣Ḅ*+,ᣚᳮr%▣ḄmIᐸឋ~rnឋ=pqḄrḄᭆIᑨMMᳮ஺u%▣Ḅ*+,ᣚu%▣Ḅmᦟwᑁu3.14ᑁ,…,஺Ḅᦪ”8u%=(14…/I),i=1,2,…,nឋᐵḄ.81ᔣ=pX1/+xa+•+xa=0$¡¢nឋ=pq22rrX14-x4----Fx=02rZ]X1+G©2+,,,+,Xr=0+ª-ஹ2+…+fixr=0ὃ⇋ᐸ®7°=pqᡂḄ=pqX1+xH----Fx=02rtX+txH----F/X=0]i22rr(U)//´+᜛V+…+¶V·஺(II)Ḅ¸ᦪBᑡºℳBᑡ+,¼½¾ᨵrᡠ¿(I)"¾ᨵr¼rÀ(I)rÀ(II)ḄÀ)Á,"2<,Ãnឋᐵ.ᶍ82AᔣqÄ=(14,…,L),i=1,2…/84,Á,…ÅnឋᐵÆÇ…,Ãnឋᐵ.ᶍ83Aᦪ:/…஺É32,…஺??Ê%=(1஺…I)j=r+1,…,஻8Ë஺2,…,ÌnឋᐵÆÇÍ,Î,…,Ãnឋᐵ.

68678¿42,…,᝕nឋ3.2ÐѪ"2,…,4(1)Ḅmr,8u•••,«,ÔÕÖr°nឋᐵḄᔣ×᪀ᡂÙḄ<᩽ᜧnឋᐵq.8Ü,,%"<,6,(2)পḄÕÖr°nឋᐵḄᔣ᪀ᡂḄßᑖqà%,&2,…,1r(3)জḄ<᩽ᜧnឋᐵqÕAᔣᙠ(1)ÔãᙠঝÔ)ᑣᔣq%&,<,4,%(4)#ᵫঞnឋ⊤Ëdr+l>r,ভênឋᐵMᳮ2),ᡠ¿ফ"᩽ᜧnឋᐵq.3.3%%…4পḄmÜÍ,(2)(1)ÔḄr°ᔣ,ɺপÔì°ᔣ×#í(2)nឋ⊤Ë8u(2)(1)Ḅ•᩽ᜧnឋᐵq.à%a2,…,ïবপḄ••᩽ᜧnឋᐵqবyQ)êᯠ+ó,¼½ÙôᨵḄm,ÆÇ(2)"nឋᐵ.3.4ᵨõᐗG÷ᑡᔣqḄ᩽ᜧnឋᐵqymu%=(6,4,1,-1,2),a=(1,0,2,3,-4),%=(1,4,-9-16,22),%=(7,1,0-13).2Ἕr1ᔣ=pÁ+Xa+ú313+ú414=0(1)22$᝞÷¡¢nឋ=pq6X]+x+x+7X=02344X]+4X+x=0340-11557-13-16-105-25--105-25-13JJ-4223,0—840ஹo002,<12-90q2-9001-5-201-5-2T000-15T000100090000ஹ0002w0007(2)r=pq

6968x+2X-9X=0{23*x-5X-2X=0(3),23Ax=04(3)ᨵ,ᑣᔣឋ"ᐵ.%&'xa+xa+xa=0(4)xx2244()*&'6x+x+7X=0}244X]+x=040001-13-16-10000<2-4223,ஹ0000,ᵨ0OḄEFGHᣚ5ᑣ'617ஹq20ஹ40101-2B=120—>001-13-1000<2-43,ஹ000>ᑣ?APQBPRST?5U,45%VQW5U54V55X/6ᑖ@᩽ᜧឋ9ᐵ•3.5Z[\᝞]ᔣ^IP`aᵫᔣ^IIPឋ⊤d5ST^IPḄ?efg^IIPḄ?.

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7271ᨵ5ÇᙠᨵÄÈià.¿À£ᦪÉ▣ḄGᑡ¥.3.10Z[\áẠ£FḄឋ9ᐵᔣsáẠ£.ãZh7,%…,7(1)@i¬äåឋ&'ḄiáẠ£5ᔣ5…,4(2)পF,kឋ9ᐵ.ᵫæᣚçᳮ,ᑣs=t,k(2)@iáẠ£Ḅឋᔠê@);vziᔣ஺5ᑣa`ᵫ(1)ឋ⊤d5STa`ᵫQ)ឋ⊤d5ᡠa(2)@áẠ£.⚪h&'fa//=0«=1,2L,5)Ḅ£ᦪÉ▣Ḅ?@ì5Z[\ᱏI&'Ḅv¸஻-rnឋ9ᐵḄxsᐸiáẠ£.häåឋ&'Ḅ஻irnឋ9ᐵ@~5•••(1)5ÁᐸiáẠ£o,%,…,r)_(2)5vz஻5ᵫᵫæᣚçᳮ5ᑣᔣnr஻µឋ"ᐵ,ᑣ஻`ᵫ(1)ឋ⊤d.3.11஻ÁÂTÃÄ5&'M+%+%3++ï5=13ð]+2X+ï3+.4-315=a2x+2X+2X+6X=32345+4X4-3X+3X-x=h2345ᨵ?ᙠᨵḄòó5Ç•à.ஹ"111111ஹ'1111113211-36/012263ᶍA=T01226300000aஹ5433—1Tஹ00000b-27Ëa=0/=2Ä5R(Z)=R(A)=2,ᑣ&'ᨵ.Ä&'0*X]++*3+*4+%5=1প5x+2X+2X+6X=32345(1)Ḅôd@@+x+x+x+x=0^2P2345x+2X+2X+6X5=0234ᑖõÁRᵫ¼ð3,ö5/@(i,a0),(ft1,0),(aa1),÷ᐭ(2)ᑣ`ùôdḄáẠ£@

7372o=(1,-2,1,0,0),%=(1,-2,0,1,0),%=(5,-6,0,0,1)5ØÁRᵫ¼3ö,5@(fta0)÷ᐭQ)ᑣ`ùᱯ@%=(-2,3,0,0,0)5STià@%+ᓃ7+ü஻2+᝕3஻3þ,᝕2ÿ
3.12%,-x=a,x-x=a,x-x=a,x-x=a,x-X]=%(1)2123234345455ᨵḄᐙᑖ⌕ᩩZa,.=0.ᙠᨵḄ!"Ḅ#$./=1ᶍ&(I)Ḅ*ᦪ,▣Ḅ./,▣01234ᣚGJ1—1000qஹr1—100001—100a201—100a2001—10%A=001—10—>0001—1%0001—1%5710001“5,00000i=l755<=>

747310.16nhᔣj10.26ᔣjḄkឋmᐵឋ10.36ᔣjḄ@10.46kឋḄḄo᪀q?4ᦟsTḄt⌕:vwᔣjḄkឋmᐵឋḄᑨyz{ᔣjḄ@|kឋḄḄo᪀஺}~ᔣjḄkឋmᐵឋ~kឋḄḄo᪀ᦟsᑁ3.1G…,mḄᦪ%=(U”…i=1,2,…,r,kឋᐵḄ.1ᔣjxa+xa+…+xa=0&`kឋx{22rr%i++…+x,=0ᑁ+txH------l-/x=022rr(1)4+…+t
X=0rt"'X|+'-^2+…+=0ὃ⇋ᐸrᡂḄX]+xH—+x-02rtx+tx+---+tx=0}y22rr(ll)

7574(H)Ḅ*ᦪ3ᑡdGℳ3ᑡd2,ᨵᡠ(I)ᨵG(I)G(II)Ḅ)¡,12#ஹ¢kឋᐵ.ᶍ2£ᔣj¤=(1/,…,Di=l,2,…/ª᜛2,…¬kឋᐵ^a,.kឋᐵ.ᶍ3£ᦪ*ª+2-¯°32#¯±±²%=(15"1)j=r+1,…,஻/,஺2,…,´kឋᐵ^«"2,…,a,.kឋᐵ.᜛”22,…ὡkឋ3.2¶·«,4,…,%পḄ@G/a,a,---,aº
rkឋi2sᐵḄᔣj»᪀ᡂ"Ḅ#᩽ᜧkឋᐵ.¾,,«¿…,6,(2)GQ)Ḅ
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7675'6117ஹ‘12-90)’12-90ஹ40410-840103-15—6A=12-90T0-11557T0-11557-13-16-105-25--105-25-1-4223,0-8403)002,<12-90’12-90ஹ01-5-201-5-2->000-15-»000100090000ஹ0002ஹ0000,(2),%1+2X—9X=023x-5X—2X—0(3)9234X4=0(3)ᨵè,ᑣéᔣjkឋmᐵ.êxa+xa+xa=0(4)}}2244&`6V+ᐭ2+7X4=04Y+X4=0x+2X=0(5)[2—X]+3^2—X4:02x-4X+3X==0l24^(5)êx+2X=0}2x-2X=0(6)24X4=0(6)ᨵᑣÀᑖa,a,akឋᐵ,᪀ᡂéḄ᩽ᜧkឋᐵ}23,ᑣéḄ@G3.ᶍ20᝞Ø1234ᣚ’6117ஹ'12-90ஹ404101-5-24=12-90T0001-13-16-10000J—4223íஹ0000,ᵨîḄ1234ᣚᑣ

7776'617ஹ’120ஹ40101-2B=120—»001-13-1000-43
ஹ000,ᑣ@C4ðñòBðW,@^,a,a,a,a2,%^Àᑖ234Âa2,a?G᩽ᜧkឋᐵ.3.5᝞õᔣjòIðVᵫᔣjòIIðkឋ⊤!òIðḄ@öXòHðḄ@.ᶍòIðḄ#᩽ᜧkឋᐵGò1,ð=òIIðḄ#᩽ᜧkឋᐵGòIPð,òI'ðVᵫòII'ðkឋ⊤!êòI'ðkឋᐵᑣòI'ðºḄᔣjᦪöXòII'ðºḄᔣjᦪ,ᓽ@পöX@òIIð.3.6/,%…,a“প#”hᔣj,পkឋᐵQ#nhᔣj»VÌòIðkឋ⊤!.ᶍò=ðý஻hᔣja,ᑣa,%,þ,…,a“kឋmᐵs+1஻ᔣIឋᐵ,ᑣaIឋ⊤.uᵫ⚪ᑣᓫᔣ£2,…,£“11ᵫIឋ⊤%&nᔣ'ᓫᔣឋ⊤ᑣI(ᵫIIឋ⊤ᡠ*III+,,-./I011=஻ᓫᔣឋᐵ23Iឋᐵ.4⚪ᔣ/a?•,•,a*a*+i,•••,a,“ឋᐵ:a2,•••,a*,/3k+ii=1,2,•••/஻_2ឋ<ᐵ,=>?a,a,---,a,a+3a+£,“i2kk+]mឋᐵ.@A=>Bᔣ+,.3.7=>?EF

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7978111](11-24ஹ-21-2-»01-124)10001-2EFQ.2=1,1111ஹ,1111ஹ11117000011J10000,J1EFᨵQQ]X[=1-2-32%3%|•4⚪“22,cW0,4a|L~ax+bxH—+bx=c{2nbx+axH-------f-bx=c?¢ẠQX+,Ḅឋᐵᔣ(W¢ẠQX.¤=a4,…]-_`¥¦ឋEFḄ&¢ẠQXᔣ«,%/ফপ+,ឋᐵ.ᵫ¨ᣚªᳮᑣs=f,ফ(]-Q¢ẠQXḄឋᔠ¯]Q;%°•Qᔣ஺ᑣ஺ᵫ1ឋ⊤-.a(ᵫ2ឋ⊤ᡠ*2(]¢ẠQX.4⚪EFZ%/=0஻=1,2,…,SḄXᦪ▣Ḅ/]=>:j=\EFḄ%r/?-rឋᐵḄQ'Wᐸ&¢ẠQX.@A¥¦ឋEFḄឋᐵQ]µ,6^,…,a,—஺|ᐸ&¢ẠQX7,%7,,-r2%°Q஻ᵫᵫ¨ᣚªᳮᑣᔣ/,a?,a_,஻mឋ<ᐵ,ᑣ஻ᵫ1ឋ⊤.nr3.11a,6|}.~,EF

8079X1+º2+º3+4+º5=1311+2X+»+º4—3X=a25x+2X+2X+6X=323455xj+4X+3X+3X-x=b2345ᨵQ?ᙠᨵQḄ¿À,&¡Q.ஹ"ill1r‘1111113211-3a012263ᶍQᐭ=T01226300000aஹ5433-12ஹ00000b-27஺=0/=2R(m=R(A)=2,ᑣEFᨵQ.3ÈEFcQÉX]+ᑍ2+ᐔ3++%5=1পx+2º3+2º4+615=32(1)ḄÌ]X]+%2+%3+%4+=0x+2X+2X+6X=02345ᑖÎ|Ïᵫv`131415]Qa0),(ft1,0),(ftftD,Óᐭ(2)ᑣQÔÌḄ¢ẠQX]7=(1,-2,1,0,0),7=(1-2,0,1,0),7=(5,-6,0,0,1),Õ|Ïᵫv`»,Ö4*5]Q஺o)ÓᐭপᑣQÔᱯQ]%=(-2,3,0,0,0),-.&¡Q]To+ᓰ஻1+.஻2+%3஻3,ᓃ'&2'"3%r.3.12=>?EFx—x=a,x—x=a,x—x=a,x—x=a,x—x=a(I)]2}2323434545155ᨵQḄᐙᑖm⌕ᩩVW=°•ᙠᨵQḄ¿ÀtḄ&¡Q./=1ᶍQKEF(I)ḄXᦪ▣Ḅ▣Þß+Zàᣚ

8180q—1000qஹ—1000%01-100a01—100a22001-10a001—10ciy-t30001-1a0001-1%45á10001w5700000/=1)Iã=0/ᵨåA,ᑣপᨵQḄᐙ⌕ᩩVW=0./=1/=!&¡Q]234(0,-4-£%,&£஻”_6)+%(i,U,U),k%r./=1Z=1i=lè>?⚪é311312&¡êëyz/NᭂAQî4⚪p39ïᐜᑖ᪆XᦪZᑡ\òᔠ〉.

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