226ஹîïðjᑗs>0,V2s6'V2s6ឤᜧó0,ÐôV2S6ḄîõöóS÷3 8Ƕᔣ4ùḄ.Ðxr\l6=V226=l,ᡠüV2s6ᙠs>03ýᙠþjḄ ”,“el2.Rsᙠ0,s0ᑁᙠs0,+8ᑁ.ᵫ =!="#Ds>O(lim s+l=Rl=l,SSSTO*ᦑᨵlimr5=lim-0+D=+oos->0+ST0+Sᵫrsᙠ$0—ᑁ345limr5=+8.5->+oo6ஹ89ᦋᑏ⌴4=>? s=r-+1-.,3ABᦪ s89ᑮFᦪG◀IS=0,—1,—2,…L.SNஹᐸPQ> ᦪᑖ᪆3ᦟᫀ(1)Tx=V35 ম=£Xs-'e-xdx=2j[-%-](0).ody5>(2)Tx=pyᨵ=($)=(xs~'e~xdx=/?vyx-'e~pydy(.v>0,/?>0).dஹBBᦪ(0)ஹfghB(p,q)=i᮱-|(10l2m:op0,q>0.J0yz0>0,%>0,ᙠ>0|>0ᑁ~/"(10)2=0ᦈᦑJ0BBᦪᙠfghp>0,q>0ᑁ()ஹឋB(p,q)=B(q,p) ᣚx=1-yB(p,q)=(10=i(I-y)pTyq~}dy(d)ஹ⌴4=>B(p,q)=(p>O,q>l),(8)p+q-i
3p—1ஹஹB(p,q)=--------B(p-l,q),(pுLq>0),(9)p+q-i(P-D(q-1)B(p,q)=B(p-l,q-l)f(/?>1,(7>1),(p+q-l)(p+q-2)p>0,qு1q,B(p,q)=f'xp''(1-X)9-1dx=&—(1-A)—1+[x'^-^dxJop0pJH-xp-'x)q-2dxp%⚗ᳮᓽ5(8).(6)ஹᐸPQ>(1)Tᑍ=8$2ᑣᨵ:ᦪᑖ᪆3¤ᦟᫀB(p,q)=cbc=2(^sin20¿>0Àᨵᐵ´>(ÁLÂÃÄ)
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8ᐵ¡)YKLMNᑖÆONᑖY᪵ᐹᨵ%½YëV⌕ឋQ%☢ᑡ0j☢$)YKLMNᑖḄឋQ,¡mn)YKLMNᑖḄឋQ,íὅïðñæᑏ0.k1.Ü(®(⌚ô=1,2/-,2)öᙠ,q(i=l,2,…,ú¢ûᦪ,ᑣc,(x.y)ᩲÆöᙠ,Ýi=\IcicþEcJ-=XcJ-(%,<=1=1f=l"2.Lᵫ4&…✌ᡂ /(x,yWs(i=L2,…$%&ᙠᑣ£/(%,y)ds)&ᙠk£f(x,y)ds=2*+(x,y)ds/=13.Jj(x,yWs.(g(0,y)2%&ᙠᙠ£4/(5,y)Wg(x,y),ᑣ6ᦪ8ᑖ᪆3;ᦟᫀ4.j/(x,y)ds&ᙠᑣJj/(x,y)Hs)&ᙠ£f(x,y)ds5.&ᙠLḄBCDs,ᑣ&ᙠEᦪc,FG1/(x,y)ds=csIJinff(x,y)9A*=J(d)+(d)ZVj0Ḅ&ᙠS>0,F4<6ᨵJ"2(7)+"(/)-Jd2&)+9)10ᵫ±²x=(p(y),ye[c,d]⊤¶ᙠ4ᨵbc·`ᦪ(3)kᡂDy)ds=y)Jl+-)dy(6)º1YL»¼ᙊᕜLs7="c°s'',ÂTUPQRSᑖf(i+y2Msy=asmtJLº2YL»V=4x((),0)ᑮA(l,2)Q(20T),ÂTUPQRSᑖÈjyds=j'yJl+^-dy=2-(l+^-)2|^=^(2V2-1)OJLJOV43413Ë᯿Vᳮ20.1,ÍSᑖফLᵫÏб²x=8(f),y=e,z=%প/w[a,/3]⊤¶ᐸTUjkD£/(X,y,z)ds=/(ᡃt),?t),7«))]"e+e+/e+º3TU[x2ds,ᐸvLDᳫ☢x2+y2+z2=a2ÛÜ☢x+y+z=0ᡠÝGḄᙊᕜÈiÞឋl£x2ds=£y2ds=£z2ds,i20ᡠyßx2ds=-£(x2+y2+z2)ds=^-£=-Tia',6ᦪ8ᑖ᪆3;ᦟᫀàáὃ⚪ஹåæ⚪:1(2)(4)(6)çèé⚜à⌕ëPORSᑖ
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12ᦟaḄ1⌕cdef "ghijᑖḄk`:lmnoKpq $ஹ"ghijᑖḄrs.ᦟuvKwvduvd "ghijᑖḄk`:lmnowvd "ghijᑖḄlmnoᦟᑁyd2 "ghijᑖ$ "ghijᑖḄ`ᙠᱥᳮ~ᑮ$gḄhijᑖ⚪$vF(x,y)Ḅᵨ☢hiLvAᑮvB,cF(x,y)ᡠḄ(20-2)¡ᙠhiᑁ¢ᐭ—1§ᑖvA/””?K…K14=®0,3=®“$±²ᨵᔣhi4ᨴᑖᡂ§ᨵᔣ¶hi3“$®,«=1,2/$,)K¸¹¶hi3.Ḅº»¼,ᑣᑖᒘTḄÀÁ|IT||=maxAvÅ»1111l13ì=ZwK=Zp©K7)ñ+EK)Ýó/=1/=!/=1õÀÁ||T||TO KFoö÷:oḄ▲úûüßᡠcḄýgḄ:oḄ▲úß%☢ᡠ⌕þÿḄᑖ1ᦪP(x,y)Q(x,y)ᙠ☢ᨵᔣ !"LḄ$%ᑖᒘT,()Lᑖᡂ,-.M,_,M,(z=1,2,4..,«)ᐸ89=A,M,=B:ᔜ-.<_▬,.Ḅ> ?@AᑖᒘTḄB|”=maxGTḄᑖHM,.Ḅᙶ᪗?(ὅ,L)MN:ᙠO,-.!$P%H(,7)MR▲UᙠVᑖᒘTH(6,7)ḄPXYᐵMᑣ\]▲?ᦪP(x,y),(^>)`ᨵᔣL!ḄᑖM:?jP(x,y)dx+Q(x,y)dyᡈJ*P(x,y)dx+Q(x,y')dy(1)!fᑖ9 ᑏh£P{x,y)dx+£Q(x,y)dyᡈJjHyMx+LQEyMy?lᑏmnopM(1)qrmᑏᡂjPdx+QdyᡈJ”,Pdx+Qdysᦪtᑖ᪆3wᦟᫀRL?z{ḄᨵᔣMᑣ:?£Pdx+Qdy(2)R:F(x,y)=(P(x,y),Q(x,y)),ᩲ=(dx,dy),ᑣপq ᑏᡂᔣ~q£F-dsᡈ-ds(3)MAF(x,y)=(P(x,>),Q(x,y))`ᨵᔣL:A©"HᡠhḄ?
14W=LP(x,y)dx+Q[x,yydyRL?ᨵᔣ M(x,y,z),Q(,y,z),/?(x,y,z)?ᙠ£!ḄᦪMᑣ ᢥ!fXᙢ`ᨵᔣL!ḄᑖMN:?P(x,y,z)dx+Q{x,y,z)dy+R(x,y,z)dz,ᡈmᑏᡂPdx+Qdy+Rdz)F(x,y)=(P(x,y),Q(x,y),R(x,y))Kds=(dx,dy,dz)hᔣ~M(4)q9 ⊤ᡂবqḄᔣ~qᑖLḄᔣᨵᐵ"%MᔣAᑮ8ᦋ?ᵫ8ᑮAMO%-.Ḅᔣ¡ᦋ.¢£ᡠ¤ḄAxj,Ay9¥¦ᦋ§¨MᦑᨵPdx+Qdy=—Pdx+Qdy£%ᑖḄª⊤«q¬ᦪ/(x,y)> ḄM(LḄᔣYᐵ®¯°ᑖḄ%,±⌕³´%ᑖMᑖ9ᨵ¶%·±⌕ឋ¹1.RLº&A(i=1,2,…,QUᙠMᑣ(Zc/dx+ZGQ9UᙠMV£ZqE¼+EQi=Eft.Pdx+QdA\i-i7ᐸ86=1,2,@%½)?rᦪ2.RᨵᔣLᵫᨵᔣ¾,…4✌ÀÁ£ᡂMᨴÄÅ+A=1,2/%«)UᙠMᑣ£Pdx+Qdy9UᙠMVjPdx+Qdy=ZJ,Pdx+Qdysᦪtᑖ᪆3wᦟᫀᑖḄÇÈ%ᑖ%᪵Mᑖ9 ᓄ?ᑖᩭÇÈ☢ᐸ8Í,Lt)ᙠ[a,Î!ᐹᨵ%▤ÑÒÓᦪMVHA8Ḅᙶ᪗ᑖ´?(da),(a))((ব,(ব)
15GP(x,y)(x,y)?L!ḄÑÒᦪMᑣ`L¢Aᑮ8Ḅᑖ[P(x,y)dx+Q(x,y)dy=ÕÖ(L),[Å'Í+((,%যJLJaÛ᯿18ᳮ20ÄḄXᑖ´ßà[P(x,y}dx=ÕP(p(r),(/)%'(/W,[Q(x,y}dx=ÕQ(MG“(/))'(,,’ᵫ]å ¤¼q(6),®æçèéfê"`z{Ḅᑖ(2)ḄÇÈM ᙠL!$ë⌱P%Hh?oHM`LᡠᢣḄᔣîïMᨬñòᑮ®%Hó1ÇÈ(Pô+(y—x)Mᐸ8Lᑖ´`ö20—38÷(i)ùABû(ii)ACB(ýᱥ¹y=2(x-l)2+1)û(iii)A³4(ᕜ)X=1+fre[0,1]o{y=\+2tᦑᵫ(6)Jxydx+(y-x)dy—J[(1+f)(1+2/)+2/"/=J(1+57+2%^dt——(ii)()ACB*+ᱥ)y=2*-1)2+1,1WxW2,ᡠ1xydx+(y-x)dy=j112(3-1)2+1]+12(x-1)2+1-x]4(x-1)5=J(1Ox-32x"+35x—12^dx-(iii)9:L<ᩩ>?()ᦑ@ABCDᵨFGḄឋJ2,ᑖLMNO8AFḄ)QᑖᯠSTUᓽᑮᡠMX()QᑖᵫYNZ)AO:3=x,y=1(1WxW2)Ḅ)Qᑖ*\ᦪ^ᑖ᪆3`ᦟᫀjxydx+(y-x)dy=xydx=[xdx=-1Nc)DB:x=2,y=y(l16NZ)84Ḅ)Qᑖᵫ(i)d(5)ᑮ25\xydx+(y-x)dy=xydx+(y-x)dy=--ᡠ1£xydx+(y-x)dy-(y-x)dy=-1+0+2583e2fgxtfy+y9:L:(i)N+ᱥ)y=2/,@ᑮ3ḄG(h20-4)E(ii)NZ)GO8:y=2xE(iii)N>?()0480i(i)£xdy+ydx=[22X(4JC)+2x\lx=£6xdx=—=2«(ii)£xdy+ydx=(2x+2x)dx=4~=2<>(iii)ᙠ04GFy=0,017ᐸL<()1="cos/,y=asinf,z=@=0ᑮyFḄ•Giᵫ(7),1=(3cosrsin2t+a2cos2t-a2sinrcost+a2hcos2t)dt=—a2C)Jo2=--a3sin3t--a~sin2r+—6f2(l+Z?)[r+—sin2/j_322k2JJ0=—~(1+b)ᐔoe4Mᙠ¡/(y,—£ᑍ+y+z)¥ᵨ(i)JᵫAN)4ᑮ8ᡠ¥Ḅ¦(h20-5),ᐸ§:x=acost,y=asint,z=bt.O±-xdy+(+y+z)dy(i)ᵫUdx=-asin1V,dy=acosfdf,dz=bdt,ᡠ1W=f(-a2sin2t-a2cos21+abcost+ahsintb2t)dt=27r(7ib2-a2)Joo(ii)²Ḅ*x=a,y=0,z=t,018µ¶·ὃ⚪ஹ¥»⚪¼1(1)(4),2½¾⚜¶⌕yÀQᑖᭆÂÃÄÅÆdᦟ^ᦔÈᑖ᪆Éᡂᦟ^ᑁÌÍΫ½ᦟ^^Ïs«½¾ÐᣴḄÒÓÔ«ÕÖ×ÙÚ^▾Ü᪶p^▾Þß²àáâᨴä\ᦪ^ᑖ᪆3`ᦟᫀ
19ᣴ¾åu2006.11.30x23½¾xyᓝçé¾ᦟêᣴ¾ç⁚íîᦻஹᦟᣴx⁚dëìᦟ^ðÐᣴ¾åò3kñGøùêᜧ^öü\ᦪ^ᑖ᪆ýFஹþÿ ᱐ᦟ᱐2001᱐ôᵨᦟᩞOᔺ℉ᦪᑖ᪆ᢣ ஹ!"ᦟ᱐2004᱐ö⌕ὃ÷$%&℉ᦪᑖ᪆Ẇ( )*ᜧ᱐1996᱐ᑢ᳝0℉ᦪᑖ᪆12 ᱐ ஹ!"ᦟ᱐1982᱐ᦟ4Ḅ6⌕891:;<=>ᑖḄ?2@ឋB<=>ᑖḄC>ᩩE2GHᨵJKLM ḄNOPᦪḄC>ឋ3GHR☢TUC8☢>Ḅᐙ⌕ᩩEᦟ=TWT9=T9<=>ᑖḄ?2@ឋBWT9<ᐗPᦪC>ᩩEᦟᑁZ9§1<=>ᑖᭆ]^ஹR☢_`Ḅ☢>aGẆ(?2ᙠR☢_`ᓽR☢TU PᦪḄ>ᑖᡃe✌ᐜhiR☢ᨵJ_`Ḅ☢>j⚪.ᡠn^oR☢_`PpᨵJḄpᢣ᪀ᡂsoR☢_`ḄTUpR☢ ḄᨵJTUᓽtᙠ^u`R,XYPuR.vPp^R☢ᨵJ_`ᵨy^Rz{ᙶ᪗~Ḅ^Tᑖᒘso_`.sTḄ--Ku`,Cᑖa9i ḄTpPḄᑁTii6 ḄTpPḄT,ᓽcP=0iii6 ᨵḄJT.ᡃeᡠᨵ{TḄiu`_▢ᑖḄ☢>ᩭso@ᦪaS/T,ᑣᨵSpT3s¢AR⊤¤ᒹPḄ¦ou`RḄ☢>¨ᡠᨵi6iiiu`_©ᡠªᑖḄ☢>ᩭso@ᦪaSpT,ᑣᨵ¬TWSpT.ᦪᑖ᪆3 ᦟᫀ
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