考研数三考研历年真题

考研数三考研历年真题

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时间:2023-07-15

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ὃẆᦪᨬᐰᝅὃẆᔊ⚪ᐰᡭᒹword᱐2004ὃẆᦪ()⚪᪆ஹ⚪(⚪ᐳ6⚪⚪4ᑖᑖ24ᑖ.ᫀᙠ⚪)sinxlim-----(cosx-b)=5iA(1)),+ijab=-^—.ூᑖ᪆௃6⚪789:᩽▲=>ᦪḄ@A⚪.Qinxlim-----(cosx-b)=5limsinx-(cosx-6)=0ூD௃EF,G1஺,ᡠJlim(ex-tz)=0“TO,MaNL᩽▲ᓄFlim—n'(cosx-b)=lim—(cosx-b)=l-b=5R°/R஺x—oxUMb=-4.EVUa—1,b--4.ூWX௃RYᙢU9:Gব=A,(1))g(x)T0,ᑣf(x)T0;(2))f(x)-»0,GAH0,ᑣg(x)t0.(2)cdᦪf(u,v)ᵫᐵijf[xg(y),y]=x+g(y)opUᐸrdᦪg(y)stUGg(y)*0,32f_g(v)ᑣHMvg2(v)ூᑖ᪆௃wu=xg(y),v=y,sMᑮf(u,v)Ḅ⊤zjU{=|}ᦪᓽs.U/ஹ—r+gWூD௃ਮu=xg(y),v=y,ᑣf(u,v)=g("),df_1=gீy)ᡠJU8஻g(n),g2(v)xex2f(x)=<22211f-1,x>-£/(x-1)<&=--বc2ᑣ2—jூᑖ᪆௃6⚪78=ᑖdᦪḄpᑖUᐜᣚᐗX-1=tU{ᑭᵨ᜻Ꮤdᦪ

1Ḅᑖឋᓽs.ூD௃wx-l=t,E3'J21xe'xdx+ߟl^=0+—ߟ=——=~22ூWX௃RYᙢU8ᑖdᦪḄpᑖUᢥᑖᑜᑖᑖ¡¢=.4N£¤/X|X2X3=X|+¥2¦+*2_*32+5+Xj2Ḅ§F..ூᑖ᪆௃N£¤Ḅ§ᓽ¨Ḅ©▣Ḅ§U«ᓽ᪗¤r®¯⚗Ḅ⚗ᦪU8±ᑭᵨ²³´ᣚᡈ¶¯·ᙳsMᑮ¹ᫀ.»DEF/XI,X2*3=*I+*2¦+¼½-A?+03+XJ2=2x/+2X2+2X2+2XJX+2XX-2xx232}32311ஹA=12-1-12,8±N£¤Ḅ©▣F'1-12ஹq-12ஹA->03-303-3,03-3>,000,ᵫ²³´ᣚM¾“/=2,ᓽN£¤Ḅ§F2.ூDN௃EF/¼¿U*2£=ᓛ+-22+¼¥2-Á32+%+%2=+2X2+2X2+2XX+2X1X-2xx2312323=2(X]+g%2+g%3)2+|"(ஹ2_%3)2O232=2Ã+-y211Ã=xi+/%2+5X3,ᐸry2=^2-^3ᡠJN£¤Ḅ§F2.

21(5)cÅÆ´ÇXȾ>ᦪF2ḄᢣᦪᑖÊUᑣP{X>}=ூᑖ᪆௃᪷ÐᢣᦪᑖÊḄᑖÊdᦪѯÒÓᓽMÔo¹ᫀ.DX=FூD௃ᵫ8ÕUXḄᑖÊdᦪFᦑூWX௃6⚪±×⌕ᑖÊUᓽᢣᦪᑖÊḄὃÙU7Ú6⚪¤.(6)cÛÜXȾÔ᝱ᑖÊN(஻iU/),ÛÜyȾÔ᝱ᑖÊN(஻2U/),M,ßàR”",ÑÁUâà"4ᑖã±ᩭåÛÜxÑyḄæᓫÅÆ᪵6Uᑣ22àê)+£—ë)Z(xj=l-2ூᑖ᪆௃ᑭᵨÔ᝱ÛÜìᵨíîÇḄᦪïᱯñᓽsM¹ᫀ.n1\R1”,_E[--£(^,.-X)2]=(72E[-óூD௃EF஽T0%ᦑ¨ô..ூWX௃6⚪±ìᵨíîÇḄᦪïᱯñḄὃÙ.ஹ⌱⚪(⚪ᐳ6⚪⚪4ᑖᑖ24ᑖ.⚪Ḅ⌱⚗ᨵ⚗"ᔠ⚪$⌕&ᡠ⌱⚗(Ḅ)*ᙠ⚪+Ḅ,-ᑁ)õஹIxlsin(x-2)JW=------------------2(7)dᦪx(x-l)(x-2)ᙠᑡúûᑁᨵ.(A)(-1,0).(B)(0,1).(C)(1,2).(D)(2,3).[A]lim/(x)limf(x)ூᑖ᪆௃᝞f(X)ᙠ(a,b)ᑁ᩽▲1/"#ᙠᑣ%ᦪf(x)

3ᙠ(a,b)ᑁᨵ(...)ஹsin3..r,ஹsin2lim/(X)=------lim/(X)=-----------ூ/0௃1x20,1,24f(x)5--618,1஺-,4,limf(x)=s'n2lim/(x)=8limf(x)=gx->0+4,xT,x-»2',ᡠA%ᦪf(x)ᙠ(-1,0)ᑁᨵ(ᦑ⌱(A).ூDE௃FGᙢ᝞%ᦪf(x)ᙠIJKLa,bMNᑣf(x)ᙠIJKLa,bMNᨵlim/(x)lim/(x)(O᝞%ᦪf(x)ᙠPJK(a,b)ᑁ᩽▲—+"#ᙠᑣ%ᦪf(x)ᙠPJK(a,b)ᑁᨵ(.limf(x)=a(8)Rf(x)ᙠ(-8,+8)ᑁᨵSTX-8,I°x=O,ᑣ(A)x=0XYg(x)Ḅ[F\K]^.(B)x=0XYg(x)Ḅ[`\K]^.(C)x=0XYg(x)Ḅ^.(D)g(x)ᙠ^x=0ᜐḄឋ"aḄdeᨵᐵ.LDMlimg(x)u=—ூᑖ᪆௃ὃh᩽▲XT)Yᔲ#ᙠ᝞#ᙠYᔲjkg(0)ᓽmnoᣚᐗX,limg(x)lim/(x)mr᩽▲I0sᓄuX—8'.limg(x)=lim/(—)=limf(u)u=—ூ/0௃vuJ஺x-ox"-8=a(zx),{g(0)=0,ᡠAlimg(x)=g(0)1a=04xro,ᓽg(x)ᙠ^x=0ᜐ1aW04limg(x)Hg(O),XT஺ᓽx=0Yg(x)Ḅ[F\K]^vg(x)ᙠ^x=0ᜐḄឋ"aḄdeᨵᐵᦑ⌱(D).ூDE௃⚪k⚪⌕ὃhᑖ%ᦪᙠᑖ(^ᜐḄឋ.(9)Rf(x)=|x(l-x)|,ᑣ(A)x=0Yf(x)Ḅ᩽e^(0,0)Yy=f(x)Ḅ^.(B)x=0Yf(x)Ḅ᩽e^(0,0)Yy=f(x)Ḅ^.(C)x=0Yf(x)Ḅ᩽e^(0,0)Yy=f(x)Ḅ^.

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9ூᑖ᪆௃9⚪yzᑮ|}~ᑮᵨᐰᭆ᳛CDUg}Ḅᔜ||@ḄᓽᜓLᡈ᪵9Ḅᑜᑖ.[F]P[Y=2}%0=\}P[Y=NX=\}P{X=2}P[Y=2|X=2}+P[X=3}P{Y=2|X=3}P{X=4}P{Y=2|X=4}++1111ஹ13-x(0+-+-+-)=—.423448(6)$%Y~K(X,Y)Ḅᭆ᳛ᑖY0100.4a1b0.1¢£~¤X=°¦§¤X+ேl¦@©ªᑣ@=0.4,b=0.1.ூᑖ᪆௃✌ᐜᡠᨵᭆ᳛®1,a+b=0.5,ᐸ}ᑭᵨḄ©ªឋ°g±Dᵫabca,bḄn².ூF௃ᵫ⚪$£a+b=0.5°¤X=O¦§¤X+Y=l¦@©ª´µᨵp¤x=o,x+v=1¦=P¤x=Q'P(x+y=1¦ᓽa=(04+஻)g+6),ᵫaa=0.4,b=0.1%ஹ⌱¹⚪(9⚪ᐳ8»⚪¼»⚪4ᑖ½ᑖ32ᑖ.¼»⚪¾¿ḄWX⌱⚗Áᨵg⚗Âᔠ⚪Ä⌕Æᡠ⌱⚗ÇḄÈÉÊᙠ⚪ÌḄÍÎᑁ)(7)ÑanÒᑡÓX²Ô'ᦪ/(Ö=2×3-9Ù2+12Ú-4ាÜᨵ|XÝḄ_Þ.(A)2.(B)4.(C)6.(D)8.[B]ூᑖ᪆௃ᐜ¿â᩽²Þqᑭᵨᓫåឋ§᩽²æ¿'ᦪ]AçᓫèéêIᑖ᪆ÑាÜᨵgX᩽²_Ô'ᦪf(x)ាÜᨵ|XÝḄ_Þ.ூF௃/(X)=6X2-18X+126(X-1)(X-2)£â᩽²Þx=l,x=2,U=>/প=5-“,/(2)=4-4,îÑa=4Ô'ᦪf(x)ាÜᨵ|X_ÞᦑA⌱ï./,=jjcos^2+y2

10஺ô஺/),+/<1},ᑣ(A)3>2>/](B)A>12>13(C)12>11>3(D)A>A>2[A]ᐵöᙠ´÷øù?+/ஹ1+/§(/+û2)2ᙠüýQ={(x,þ2+y2<]}ÿூᑖ᪆௃Ḅᜧ.ᙠ0={8*+41},ᨵ0+41,ᨵூ௃ᵫcosxᙠ"ᓫ$%&ᦪ()00,஻=1,2,…(ᦣ,(9)M=lᦈE,ᑣGᑡIJKLḄ)(A)gᦈE(I>ᦣ.(B)«='ᦈE,(R>ᦣ.8Eᦣ((gᦈE,aZ“2"1:«-1+2n)h஻=]i஻=]ᙳ>ᦣ(᣸◀(A),(B)⌱⚗(l஻m>ᦣ(no᣸◀(C),£(p,1-஺2“)ᦑ3⌱(D).rs(tᦪIḄuᑖvᦪᑡ᩽▲yᙠ.(10)7஻x)=xsinx+cosx,Gᑡ|⚪~KLḄ)f(0))᩽ᜧ,)᩽.(B)f(0))᩽,)᩽ᜧ.

11(C)f(0))᩽ᜧ,)᩽ᜧ.(D)f(0))᩽,)᩽.[B]ூᑖ᪆௃ᐜ/'(x)(/“(x),ᵨf᩽ḄᐙᑖᩩᑨᓽY.r(o)=o,.r(^)=()ூ௃/'(X)=sinx+xcosx-sinx=xcosx(ᯠ2r(o)=i>o,rQ=-^-

12=\A\E=>\A[=Ên|H=஺ᡈM=1Á(lMl=Ð4+312+6343=3/Ò0,)Ó=1,ᨴ""»,ᦑKL⌱⚗"(A).(13)74,4)¤▣AḄÕªÖḄᱯØ(Ù3ḄᱯØᔣÛᑖÜ"Ý2,ᑣ%,4%+஺2)ÞឋᐵḄᐙᑖ²⌕ᩩ)(A)4=0(B)4=°.(C)4Ho.£4Hoூᑖ᪆௃âJãäåᔣÛḄÞឋᐵឋ(Yᵨ¾æᡈ®ᓄ"ᐸèᓽY.ூ௃éaÂêë0+&஻(a+஺2)=0,ᑣka+%24al+ë=஺((î+%24)«+ë242a2=஺]]ᵫa?Þឋᐵ()ᨵ1ᓃ+ë24=஺([kA-0.22ñò(ᯠᨵ%=°(ë2=°,0ò4,4%+஺2)Þឋᐵó\[ᩭ(<6,“(«+õ)Þឋᐵ,ᑣ²ᯠᨵ"#°(,ᔲᑣ,3iZ(a+%)=4aÞឋ´ᐵ)(ᦑ3⌱(B).,,ù14-+%)]=[/(/1²+4%]=a(%]ூéaúÂᵫযõü(14஺=4w0.Yþa,4a+஺2)ÞឋᐵḄᐙ⌕ᩩ)°%'ᦑ3⌱প).(14)ᢇḄ᝱ᑖN(஻஻)ᐸ஻ᙳ.16!"#᪵%ᙳ&'=20(0"),᪵%᪗/0s=l(cm),ᑣ஻Ḅ6780.90Ḅ67:;<4)(20-5஺஺5(16),20+50஺5(য).B(20-(16),20+஺C(16)).(20-i/(15),20+!%05(15)).(20-i/o.!(15),20+^/(15)).0050Jூᑖ᪆௃NOP0QRSḄ:;TUᵨWUX:

13Z-5-1)S/_ூ]^௃ᵫ᝱NO᪵ᑖḄឋa,nᦑ"Ḅ6780.90Ḅ6(x--7=^a(஻-D,X+—j=t(n-1))(2O-i/OO5(15),2O+1/OO5(15)).a7:;<5Q5,ᓽᦑg⌱iCk.2006lὃẆᦪpi'kq⚪^᪆ஹ⚪31—6⚪⚪4ᑖᐳ24ᑖ.ᫀᙠ⚪.lim----=Li1k—஻7ூᑖ᪆•௃wᐸxᦪឤzᓄ"=|"Q^.lim(——஻+1ஹ("=limeIn1f—n)]=Llim(-IfIniW—\fl]஻T8ூ]^௃limIn4=0lim(-l)MIn|R=0ᦪᑡiTk’1ᨵ,A?4-1ᦑni2kᦪ/iXkᙠ"2Ḅᑁ/'ixk=e'["2k=1,ᑣ/"i2k="ூᑖ᪆௃ᑭᵨᔠᦪQᓽ.ூ]^௃ᵫ⚪/'ixk=e"\xxQ#/஻¡/ব/£¤¥k¦xXQ#ᔆপ=2e2""ixk=2e3Mk,ª/ফ=1,ᦑ¬ফ=2e3/i2k=2e3i3kᦪ"k®,¯°ᑣz=/i4-²ᙠ³i1,2kᜐḄᐰ®ᑖ¶q2)=4dx-2dy.ூᑖ᪆௃ᑭᵨºᐗᦪḄᐰ®ᑖ¼½ᡈ®ᑖ¿½ÀÁឋUÂ.

14—L=fX4x2-y2),8xL=4ூ]^௃PÄÅÆ8aC1,È2)=4--/)-(-2?)|,=-2(12)ᡠÊdzR)=Ë஺0+È2=4dx-2dyPĺÅxz=/(4——Ì)®ᑖ#dz=f\4x2-y2)d(4x2-y2)=/z(4x2-y2)(8xdr-2ydy)dz|=f(0)(8dx-2dy)=4dx-2dy(12)RX.•_(11ஹAভÏ▣J2AE82▤ᓫÔÏ▣Ï▣8ÕÖ8/=8+2E,ᑣ×1=2.ூᑖ᪆௃wÏ▣PØᦋᑏ84X=8ᡈ=8ᡈ/Û8=஺Ḅ¿½¦ᵨP▣ÜÝḄÞᑡ½ឋaßÞUÂᓽ.ூ]^௃ᵫ⚪ᨵB(A-E)=2EI|_11_oà<ᨵá"â=4,'"71,ᡠÊ×1=2.(5)ÁXXãÛÜäåæᙳ:;ç°”êḄᙳᒴᑖᑣ1ì{max{X,Y}Wl}=9ூᑖ᪆௃ᑭᵨxãÛḄåæឋðᑖUÂ.ூ]^௃ᵫ⚪xãyᐹᨵÜáḄᭆ᳛ô1,0

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23ூ4௃Y(x,y)ôõÒöo᝱ᑖÓ'ᑣx«y:Pᐵ«x«îï¥ÿḄ.ஹ⚪•ூᑖ᪆௃⚪ᑭᵨ“ᢕᜧᜮ”!"#ᨵ%&'(!Ḅ)*.X3X213.2.1—-4——4——nூ34௃5(lim-——=lim----=—=0,1sinx4-cosx\<2,XT+oo2X4-5-X1XX5Y24-1ᡠ#lim-------(sinx+cosx)=0.XT+82*+XூJK௃!ḄLᐵឋOP(1)ᨵ▲R!ḄSᦪ(!U(2)ᨵ▲R!Ḅ"V(!U(3)!Wᨵ%X&Ḅ"V(!.12.ூᑖ᪆௃⚪YᦪḄZ▤\ᦪᑭᵨ⌴^ᡈYᦪḄ`aὁ᪍de.ூ34௃f=*‘hi?ᑣlಘ=n◤’ᦑl(°)="t.2X+3(2x4-3)(ZX+3)3ூJK௃⚪(vẠ⚪x.13.ூᑖ᪆௃⚪(ᐗzᔠYᦪ|\}~ᑭᵨᓽ.ூ34௃ᑭᵨ\ᓃ>Iஹேdzdzᡠ?xAB=1*oxOyூJK௃ᐗzᔠYᦪ|\.ᨬX&KḄឋ.14…..ூᑖ᪆௃⚪(Ḅ4஻=.Xூ34௃஻=ᑣX(du1dwdr஻+x—=u—u3——=----.dx2u2xVᑖ

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31(D)ூᫀ௃D.ூ᪆௃V⚪$WXᑖḄEᵨB[ὃ᪶ᵫ:=/(x)ḄST!^ᐸS`abcdecஹx=x஺ᡠḄSTḄiᦪ☢X$ᡠ%Iᦪ/(᜜lm!nopqr☢Ḅᱯt:জxe[0,1]9{(x)W0,}ᓫ⌴.ঝxe[1,2]9{(x)ᓫ⌴.ঞxe[2,3]9/(x)$Iᦪ.টxe[-l,0]9{(x)W0$ឋIᦪᓫ⌴.ঠᵫF(x)$Iᦪᔠᱯ!^@⌱⚗$(D).(5)H48ᙳ$2▤▣ᑖ$48Ḅ▣I=2,181=3,ᑣᑖᙽ▣13Ḅ▣$'O38*ஹ'O28*ஹ(A)'2Z(B)'*'O3/]'O2ஹ(O&*(A*ூᫀ௃B.*..C*=|C|C-1,C-1=lC*r7ூ᪆௃᪷¥࠷=§"©

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33()P(AB)=Q()P(AB)=P(/)P(B)ABয{(♦)=1ÅP(B).(p)P(Au5)=1ூᫀ௃D.ூ᪆௃Ç$“IÀÁÂᡠµP(/8)=°)P(AB)=P(A\JB)=1-P(AUB)Ç${(ZUB)ÅWi,ᡠµ(A)@.(A?ËCP(4),P(8)$o9(B)ᡂᦑ᣸◀.(C)ÐᨵC48À$Ò¾¿Ḅ9᎛Ôᡂᦑ᣸◀.(D)P(7UB)=P(AB)=1-P(AB)=1,ᦑË@.(8)HÕÖ×XaØÁÀÙ}XÚl᪗Ü@᝱ᑖÞN(OD,YḄᭆ᳛ᑖÞ$P[Y=Q}=P{Y=1}=—T?(7\Z7/7\2,æçè)$ÕÖ×z=ATḄᑖÞIᦪᑣIᦪ£(êḄMëqᦪ$()(A)0.(B)l.(C)2.(D)3.ூᫀ௃B.[᪆]B(z)={(XY

34ஹ⚪39~14⚪⚪4ᑖᐳ24ᑖCDᫀᑏᙠ⚪FᢣHIJ.c—COSX)e-elim---=——(9)a஺#]+——I3ூᫀ௃2e.12e--xe(l-cosx)2ec-e_cosx=lim=limlim.———x->0A—>022-x2[᪆]1°ᓛ7—15Vl+X-1r3dz(10)Hz=(x+e>)"ᑣa(1,0)ூᫀ௃21n2+l.ூ᪆௃ᵫz=(x+"),ᦑz(xO)=(x+D*y-=[(x+lf]=[exln(1+x)],=erln

352In2+ù)=21n2+liᐭx=lndx(11)úûᦪ2n~Ḅᦈýþÿ2ூᫀ௃qey-l)">0ூ᪆௃ᵫ⚪,YTn+l(i\஻+lrTYT—>e(nT8)(஻+l)2(஻+IpᡠᦪḄᦈ$%&'(12))*+,Ḅ◤./ᦪ஺=஺(2)ᐸ45672Ḅ8ឋ:=°2ᑣ=◤.>

3610000?@67AB1ᐗDE+,ᦈFABᐗ.ூᫀ௃8000.ூ᪆௃ᡠ.ᓽ3)'=8+°:="=-02,I‘°ᡠ0'2KL042஺ᡠ(02)'=-020+0=0.80N0=10000Oᐭᨵ(஺0)'=800஺‘300ஹ000(13))&஽=(1°)',UV▣XYZ100°J,[\=ூᫀ௃2.'300'000ூ᪆௃Ḅ]XYZ10°°^᪷`XYV▣ᨵXaḄᱯcdeᑮg]Ḅᱯcd3,0,0.h஻᜛V▣Ḅ4jᐗklm••^+o=3+0+஺.-.k=2,(14))p,ᓰ…£ᩭuK⚗ᑖxyz8(஻,p)Ḅ{ᓫ}~᪵mS'ᑖ᪵ᙳdm᪵>T=^—S2,ᑣET=2ூᫀ௃L᪆ᵫE7=E(X-S)=EX-ES1=np-np(\-p)=np-

372010ὃẆ⚪ᦪᔁL⌱⚪(1)lim[--(--a)e]=lim[-(l-er)+ae:]=lim+alime=-1+a=1)1TCXXIT஺xXT,Xx-0Ia=⌱C(2)᪷`ᨵ"+jjp(x)=q(x),2j]+j¤pa)=q(x)஺Z¥N/.y\+4§m4i-fiyᑖOᐭ¨o©e2(/Ji+ᜐJ+P(x)(4+®?)=(+°ব(²-4y¤)"+p(xXzvj-//y)=(z-஻)q(x);/.\\+ᜐ¤¨n/+஻=L/.\\-aᐸº¨n/-,஻=0,e2=4=!஺⌱A(3)᪷`e¾%)=0,g⛷Â0஺I[B(Ã]Ä"(g(x¤))gভ=஺ᦣ⌕ÈXÉ(ÊḄ᩽ᜧdÍÎ◤ᓽÏ஺ᓽ[ᵨ(Ê]1y§ᕮÒভ௃¤+§ga¤))gD=rভg'G)Â஺஺IÎ◤/3)0஺⌱B

38(4)Ö×ØÙÚ10IÛÂB)ÂÜ)⌱C(5)ÞA,ßàᑣᔣ>âLãäឋXᐵ⌱⚗BஹDæç¤ᔣ>â140)ஹQ஺)ᔣ>âHê(1¤0)ஹ(2,0)஺⌱⚗Cæçᔣ>â1(L0)ஹ(10),ᔣ>ân(L0)(6)᪷`▣ᡈᱯcd5íîï+&0,ð=0ᡈ-1஺ñr(J)=3oIHḄᱯcd0(Ló)m-1(ó)஺ᦑ[XY[-1ஹ_1Z⌱DT:0;(7)P(X=1)=F(l)-7(1-0)=1-e-1-1=1-g-1,⌱C(8)᪷`úû/ᦟḄឋý,

391=]/(x)&=]þ(x)d"|"(x)dx+⌱j-xJ-xJo*14A⚪(9)f'Jdt=[xsinrdtffix•...஺-(1+$)=|sinr^+xsin/o•V*ᐭx=0--.(1+J[.)=0n1+12y1|.=-1zox0(10)451=(6/7”9:;ᣚ7)•*n=>?@AB)A/,7arctan!?==—')4(11)CDᖪFḄᦈIᦟKR(P),ᦈOPឋK1+RᐸTKFVWXYᓽ)=1,ᑣ(P)=\▬^_*:ᵫcdeᨵgRXᓽKPF(ᑖjk:)P[lnAZ+Clln^=lnP+—+Ciopqrᨵ3-XᓽF3

40\]CTR-CPvwᨵx’-,z{eᓽ|}*~,w∍M12᪷ᩩe⊝L=஺Xj[=QoᐸT6x+2a°ᑮ+41,☄3-6+2a=0*13᝞+ᓽ=A+ὶ|.ஹ}|/+}|A3.22:3.14EX[=DX[+EX”^_ஹ1|1||||ET`E-'ᱏ-'£T=T0'+=/+/஻J’஻ஹ1

412011ᐰắ_Ẇ¡¢ᐭ£¤¥ὃ§ᦪ£§⚪©ªᫀ¬ஹ⌱⚪318⚪⚪4ᑖᐳ32ᑖLᑡ⚪Ḅ⌱⚗ᨵ⚗"ᔠ⚪$⌕&ᡠ⌱⚗(Ḅ)*ᙠ⚪+Ḅ,-ᑁ.(1)®¯x->0qX°ᦪ/'(x)=3sinx-sin3x¯cd±V²³Xᑣ()(A)A=l,c=4(B)஻=l,c=-4(C)A=3,c=4(D)A=3,c=-4ூªᫀ௃¶⌱(C)(ᑖ᪆௃ᵫ¸¹º»©²³▤Ḅ½¾¿஺r327r3ூ¬¥௃sinx=x--+o(x3),sin3x=3x---—+«(^)3!3!x39A?x..3sinx-sin3x..—À++°'4/.rhm------3----=lim---ஹ-----=hm-?-=1x-»0z^*x-»0x-*0CAᡠÃc=4,%=33sinx-sin3x..3cosx-3cos3x..3-2sin2.rsin(-x)-----------=hm------------=litn----------------ᡠÃA-l=2.d=12,ᓽA=3,c=4(2)C®(x)ᙠx=0ᜐ¿XH./(0)=0,ᑣlimg/3*2/(x')±$()7XT(A)-2/(0)(B)(C)/(O)(D)0ூªᫀ௃Çi(B)ூᑖ᪆௃᪷ᦪᙠDÈḄÉÊ.(¬௃lim/W")=lim1/஺)i—W)Ì2/(0)X*x^OAK/(K)ÍX=0ᜐ¿XᡠÃ

42.3^Î=.Î᧾®TimÑQÓ=.no)-2no)=-/r(o)(3)ÔÕ%×ᦪᑡXᑣᑡÙ⚪ÚÛḄ()(A)ÜᦈÝXᑣX(Ḅz+%.)ᦈÝ"In«l(B)Ü£(஻*1+Ḅ“)ᦈÝXᑣ“ᦈÝ“I/II(C)ÜE>“ᦈÝXᑣ£(%.1-Ḅ“)ᦈÝ(D)Ü£(%_.%)ᦈÝXᑣ“ᦈÝ“”-1ூªᫀ௃¶⌱(A)ூ¬௃2"“ᦈÝXᑣáḄâ⚗äåæçᡠᡂḄéᦪêᦈÝX⌮Ù⚪ì¥ÉÚÛXᡠ«■(Ã⌱(A).(4)Ô/=j7lnsinxdr.J=J7lncotxdr.K=J7Incosxdx,ᑣ/,KḄᜧᐵñ(A)I

43⌱(D).(6)(A)4x3▣*,+,-./0ឋ1234X=/7Ḅ450ឋ6ᐵḄ*kஹ,k)89:ᦪ*ᑣ4Y=0Ḅ<)()2(A)ᶇ“A(B-4)7I2C•+F(%-/)©-%+4I-/)+&(K-/):(D)+⁎%-/)+k-%).ூᫀ௃⌱(C).ூ௃ᵫ/,,%,-./0ឋ1234M=᜛Ḅ450ឋ6ᐵḄ*%-%!%-7)4¥=0ḄᡊẠQ.S./0ឋ123Ḅ0ឋ3ᔠUQᦪV)I,B./0ឋ123*"#WX)4¥=᜛Ḅ,ᵫ-./0ឋ123ḄY᪀*[2+4(%\4)+&(B\7))4r=£Ḅ<*ᦑ⌱(0.(7)(£(x)6(x))^5ᑖ`aᦪ*bcḄᭆ᳛fg/7(X),+(x),hiaᦪ*ᑣj)ᭆ᳛fgḄ,()(A)£(x)஻x)(B)2஻(xk(x)(C)Il(x)(D)£(x)l஺)+4(ᨴᔙ(ᑘூᫀ௃⌱(D).ூq᪆௃ᵫᭆ᳛fgḄឋ*ᭆ᳛fgjstu(vw=1ᦑᵫxJM[/বyx)+&Xz({|=}'(x)g(x)=6ব8(x)|M=Iᦑ⌱D.(8)(FX"ᦪ)(4ு0)Ḅᑖ`*X”,…,(஻22))ᩭ᝱FḄḄ᪵*ᑣḄ=,£,77=—1£+,ᜩtu()”H"\1H஻(A)ET>ET^DT>DT(B)ET>ET,DTO4(D)ET^ET^DT^DT,ூᫀ௃(D).ூ᪆௃ᵫ⚪£¥,=AM=W=1,2…,஻),ᦑᨵ

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452013ÓὃẆᦪÖ×4ØÙ⚪᪆\ஹ⌱⚪1.ᫀÚD᪆:Û4=Ü\஺0")0(Ý)o(x)஺(/)B----------=\.\^-T0XXXo(x')+o(x‘)o(x")o(x")C0×/+஺×/Øoxor,+n2,ஹ“஺yØ+஺×/ØnD2=2+2áÆâ0᝞ÚX=஺×åØᑣ2->1XXXXᫀÚ(B)Ixr-1ei,lA|xln1z1᪆Úlim------------------------=lim-------------------------=lim-------------------------=1.—ix(x+1)In|x|*஺æx+1)mIxI°4-1)In|x|xIn|x|1hmÝhm=—I*->•x(x4-1)hiIxI2lim7Txlim.-----------------------------------=co+tt*->-1K(K+l)ln|K|#è6éê*ᦑx=0k=l)ëìíîï.3ᫀÚ(B)᪆ÚL9I14”CJ.=ff(y-x)dxdy=fdQf(rsin8•cos8)rdr=—f(sin8-cos8)d8JJJ(l-I)j<1Jo3132122=-f(sin8-cos8)48=—(cos8+sin8),yᐭ{|=0,1=—>0,/=0,7=--<03333ᦑ⌱B஺4

46ᫀÚ(D)R]B᪆}~Z—(?>1)ᦈlimᙠᑣZ%ᦈ஺ᦑn⌱D஺naln"n"l5ᫀ3(B)᪆Ú'.'BoTiE.'.A(b--b)=C=”00(H)=R(B)A-»05-a08=000000000xz£7=0v&wRᨵR(A)=P(B).a=0ᨵ8᪆¡P(-2<஽<2)=ফ-ᑣ-2)=2ফ-1|-0P,=P(-1<-—<1)=2প-12(1p=P---<-------<-1=—(1)4>ᓃ.P>P>ᨴ133Jবtt8

47ᫀ3(C)m᪆3P{Z+K=2}=P{X=1,Y=1}+P{Z=2,Y=0}+P{J=3,Y=-1}1111111=P(J=l)P(K=l)+P{^=2}P{K=0}+P{Z=3}P{K=-l}=-.-+_•.+-83836/0⚪9(.2ஹfJ-2«J-/0)-2n+2limV=lim------------=hmnTr¦+2J“trn+22“Teᐔ+22n+2ᑐ+27஺)-2n=lim-----.lim-=-2/r(l)=-2nTx+2z2n+2?ᫀ-210ᫀ32-21n2m᪆:஺,2)®ᐭ(z+J)"=-{z(l,2)=0ᙠ(z+j)=XJ¯°K&±᧕ᦪᨵraz-|*I—|az(z+j)*|ln(z+j)+*-dx—|=´D*=1,µ=2,z(l,2)=0®ᐭ{=2-2In22+J|axLJ11?ᫀ:ln2InxInxdx᪆:r————dx=+I---------------J(1+x)&1+#),(1+X=0+In=O-ln—=In2.1+X1212

48ᫀ3J=e'(%+jx)᪆▤·¸¹ᑖºtḄᱯºt~1-2+—=o,m{aτ=4=—,421ᡠ?»¸ºtḄ¼m~J=0½(g+Cᵨ13ᫀ3-1᪆•••a„+A,=0A(=-%A=-Ar=>AA=-AAr=ভ£¿ÀᑡÁ{3-Mr=izr=,1ᨴ|=0ᡈ1ᨴ|=-Â|H|=O,n-AAr=0,nA=0ÐÑÒÓ).1A|=-114[--᪗ÄÅ᝱ᑖÇḄÈ᳛ÊHf(1)=7=µᫎ1--1-♦«-'''ÔÕ?=-=fm?Jx=Hx-=e'dx-2e38

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