2023年新高考地区数学名校地市选填压轴题好题汇编（十二）（解析）

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2023
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12ᵫiu¡¢Mku¤/'¦x§=-41ruxe¦l,4©ាᨵ«¬¢k®=-ln4iy=“6=-413”¦1,4©²ᑗk´ᑗ¢¦x¦§,-41nxo§44ᑣᑗµ᳛*஺¸¦X஺§=AAᡠᑗy+4

13x=-A¦x-%§0X஺X஺ºᑗ¡»¢ᡠ41nx0=4nx0=e4kk5$=--eᡠi-g<&M-ln4ky=kx/¦x§=-41nxke¦1ᵨាᨵ«¬¢¿iuÀ¡¢¦;-ln4§k=-41n4V-:ᓽy=/¦x§=-41n~e¦l,4©ាᨵ¬¢kÄ஻x§=lnAjeᨵ¬¢Æke¦-1,-ln4.ᦑ⌱:D.20.¦2022•=>=BCD▤FGH§ÇÈᨵ஺ÉᳫËbÍᳫḄÎB¦஺ᓃᙳOÑw2§,ÒÓOÔÕᙢ×Ø᥎ÚAᳫ.Û“ÜAÓ᥎ᳫk᥎ᑮÉᳫ''A,"ÜAÓ᥎ᳫk᥎ᑮÍᳫ''&;"ÜÓ᥎ᳫk᥎ᑮÉᳫ”ß“ÜÓ᥎ᳫk᥎ᑮÍᳫà,ᑣáᑡãä┯æḄ¦$A.P(8J=%B.P(B,|A)+-P(^lA)=iC.P6+P(Bj=lD.A)+P(8j4)=1ூᫀ௃Dூ᪆௃ᵫ⚪LP(A)=rP(A,)=-^,a+ba+bP(4)=P(AE)+P(4ᓽ1+3.^^=êTa+ba+b-\a+ba-i-b-ia+babbb—\bP(B)=P(^B)+P(AB)=----------------------------1---------------------------2222a+ba+b-1a+ba+h-la+hÇëPì§+P¦g§=l,ᦑACíî;abP(A4)஻+/?A©°TP(AB?)_a+ba+b-l_)¿p¦ᓺA§=ভA§=P¦4§aa+b-lP¦4§aa+b-\a+ba+bᦑ-(41A)+P(sJA)=1,ᦑBíî;baP(AB,)_-ಘ4§=a+ba+b-l____P(A2)ba+b-1a+ba+bᦑ-(BjA)+-(4l4)=Hl,ᦑD┯æ.a+h-\a+b-\a+b-\

14ᦑ⌱;D.21.(2022•=>•=ôõᓭ÷BCD▤FGH)ᦪ/(x)f(x)+/(-x)=2,/(l+x)-/(l-x)=0,ixex0,l©k/(x)=x+l,ᑣᐵwxḄ/*)=$úᙠxex0,2022©ḄḄᦪ()A.1010B.1011C.1012D.1013ூᫀ௃Bூ᪆௃ᦪ/(X)f(x)+f(-x)=2,ᡠᦪ/(x)ᐵw¢(0,1)Jû,/(l+x)-/(l-x)=0,ᓽ/(l+x)=/(l-x),ᡠᦪᐵwx=lJûixex0,l©k/(x)=x+l,ᵫᦪ/(x)ᕜ,ᦪᕜ,7=4,ᵫwᦪx«2,6©Aᕜ,ᑁy=/(x)ÿ=⁰ᨵ2ᙠxe0,2y=/(x)=⁰ᨵ1ᡠ᪷ᦪᕜឋ"#$xe0,2022%y=/(&')=᳝)ᨵ2*++1=1011.ᡠᐵ/xḄ12/(3=4'ᙠxe0,202267Ḅ8Ḅᦪ91011.ᦑ⌱

151_1rk஻x)=x-lnx,ᑣ/(&=1m=nm$r(x)O,x>l,.•.f(x)ᙠ(0,1)ᓫXXq⌴s(1,”)ᓫq⌴tᡠ/(4)>/(3)>/(2),ᓽ"v/(a)>/(o)>/(c),waw4,6*3,cx2xஹz⌱⚪23.(2022?@GH|Fὃ~)ᦪ᜜&=28$2]-«6+஺)ᡠᨵḄᙶ᪗ᩭḄoᔣ஺(஺0)ᓫvᑮᦪg(x)ḄḄxeR,ᙳᨵg(x)Mg(ᔁ]ᡂᑣ()A.g(x)ᨬᜧ¡1B.9Ḅᨬ¢¡£C.g(x)ᙠ(*,¥ᓫq⌴tD.ḄxeR,ᙳᨵg(x)*gூ_ᫀ௃BDூ8᪆௃¦f(x)=2xᓃ¨^-ocosx+©sinx,5/3,11.(ª)]=——siirn■—COSJ:+1=sinx+—+1,22I6)ᡠ8(%)=$«(2%+29+¬]+1,ᡠg(x)Ḅᨬᜧ¡2,A┯®o¦g(x)4g[2]ᡂᡠg(x)ᙠx¯ᜐ±vᨬᜧ¡7TTT7Tᦑ20+]=2k/r+—,keZ,ᓽ0=ᦇ³+´ZwZ,7T¦µ0,ᡠ$¶=0%᜛±vᨬ¢¡஽B¹º;

16g(x)=sin2x+2kᐔ+—+1=sin(2x+yj+1,JTTT7Tk2kᐔ---<2,xH—<2¼H—,kQZ,232/½,57r.7t._fofk.7T-----0/>0
ḄஹÅᯖᑖÈὡÊᐸab7ᩩÌÍÄy=Gx,ÎÄ/ÏFÐÂÃÄCḄÅÑ/A,BÒM,NᑖÈÓ6ÔABFRḄ2ᑁÖᑣ¿ÁA.ÎÄ/×ØÙḄ±¡Û¿?,+ுB.MNÞßᐵ/xàáC.HÙâMNgÎÙHÙâD.HÙâãNᵨ☢æḄᨬ¢¡/ூ_ᫀ௃ACDூ8᪆௃¦ÂÃÄḄÒᩩÌÍÄḄ×ØÙᑖÈqÔ$ç"#ÎÄ/ÏÖÐÂÃÄCḄÅÑᨵÒ,ᑣÎÄ/×ØÙḄ±¡ÛA¹º;èᯖé2c,ê⚪"#=ëᦑc=2a,᝞Ï஻ᑖÈçὡA"îAîḄᚖÄ,ᚖðᑖÈDD,E,H,¦஻“ᱏᵨḄᑁÖᡠᵫᐰ+v|ὡ஺|=|ὡὡõὡ=ឍ÷|□=¦|ù|7|ᯠ|=ᡠûü—ឍh=wᵫh+|ýh=2c,vþE|=c—a=«,ᡠE¿a,0Á,Mᙶ᪗mhᳮ"vNᙶ᪗«஺$ÎÄ/¾ÿJ஺ZMF[ESE,B┯;

17/Ḅa,M,NᑖᓃAB//Ḅᑁᑣ2NM5E+2NNgE=/,ᡠ■7TNMF,N=Fc;2/.ஹ/&42,,,(,ᔆ+71a(eᔆa,\ME\=-------τ^ia\MN\=atan—+-------ᵫ(1)%'2Ltany?aஹ“51”ஹt,6ztuna=acty./<5ᡠ஻1+᪗La,67862.ᓽtan7=ltan—[an—22:;ᡂ=ᡠ>?MNgḄ☢AS2BxC?aa1,D.ᦑ⌱GACD.25.(2022•IJKLMNO>▤QRS)TUVP(l")ᨬXYZ[஻(஻eN*)ᩩ]^ᦪ஻x)=(x-l)e'Ḅ`abᑗᑣ()A.2+n<3B.6஻=24Ḅdef'C.iYg:h-4D.6஻=12Ḅidklju{°}ூnᫀ௃ACDqr᪆1etᑗV(%,(%-De*"),f'(x)=xe',ᡠᑗwxy-2=Xoe"(x-l),ᡠ(%—l)e""-2=xe'"(x—1),᦮ᳮ%A=—e"(xG-2x+1),o0uᡠ|g(x)=-e*(x2-2x+l),ᑣg'(x)=-e'-1),ᡠ|g'(x)=O%x=±l.ᡠ6x<-lᡈx>lg'(x)<0,g(x)<0,6-10,46x~h—g(x)~h0,g(-l)=——(g(O)=-l,g(l)=O,6x~h+a>g(x)~eh,ᡠ^ᦪg(x)Ḅ`ᜧ᝞`,

18

19A⚗x>log?x,ᯠy=x]/(X)ᨵf'VᦑBB⚗|/(x)=r,ᑣ/=lAf=Oᡈr=gᡈf=2n/(x)=0ᡈ/(=Bᡈ/(᜜=2=6rᦑ┯BC⚗|u-f{xj,ᑣ/(«)=/c(0,1)=%<0,஻2W(0,1),03e(1,2)=f(x)<0/(x)e(0,1)/(X3)e(1,2)nᧅe0Hlᨵ3rt26ᨵ2rᐳᨵ5rᦑBD⚗,|“(x)N0,!|/(஻)=x20,/(/(0))=/(1)=0,/(/(1))=/(0)=1,ᡠ0,1lwx/v(x))=xḄr6x>0,xwl/(/(%))=|log(|logx|)|=x,BP|log,x|=2X>^|logx|=2-x,222ᐳᨵ3rBᡠwx/(/(x))=xḄrᨵ5ᦑ┯.ᦑ⌱GAC2227.(2022•IJ•IᜧN▬MNO>▤QRS)C:£+£=l(a>>0)ḄᯖVᑖ",¡2,¢¢4,V¡(£,1)ᙠ¥ᙊC᜜VQᙠ¥ᙊC§ᑣ¨ᑡª«MḄᨵ()A.¥ᙊCḄ¬᳛Ḅidkl(.,1)B.£(0,-2),6¥ᙊCḄ¬᳛®|Q¯Ḅᨬᜧd3C.°ᙠVQ±%Ḅ•᝞=0D²³´Ḅᨬ5dூnᫀ௃ACDூr᪆௃᪷¶⚪¸Y஺=2,r22ᑣ¥ᙊwxᓃ+2v=1,4b2V¡("1)ᙠ¥ᙊC᜜'21'ᡠ¹+º>1,ᡠ஻2<2,4ᔉᡠ0<]<—,a22ᑣ¬᳛e=?=(:•)ᦑAB¾hB,6¥ᙊ஺Ḅ¬᳛3£=£==2a22

20

21À4A-4஺ḄMVTÁ=4ÂÃ04/141
,ᑣ¨ᑡª«MḄᨵÃÄA.>À┵¡-AEGḄÆAÇd-'2B.¹☢G-EF-AḄᑗdḄidkÊ2&C.64=gË☢EGGÌwÆᡠ%Ì☢:ῪÎ?D.6=1EG]Ë☢BCG4ᡠᡂḄᨬᜧ4ூnᫀ௃ACDூr᪆௃¾hA,Ï=4ÐY%VGlQBC§Ḅ'ÑVwÆABCD-ABCAMË☢8CG4஻Ë☢ACRABCuË☢8CGB1,ᦑ4c஻Ë☢AQRA,ᡠVGᑮË☢4C"AḄÓ¬ÇdÔ⎃£Ö=2,ᡠ>À┵×'£ØlÇd×=VF-^EGᦑ>À┵¡-AEGḄÆAÇdAB¾hB,62=1VG]VCÙᔠDiCiÛACEEA^EFÜl:Ὺ>?ME¡MVᑣᑣ¹☢G-EF-AḄË☢4C=Bm=£,ᔿ=-32+4-2=ÔÞ=4ß,ᑣRM°+WC2-AC2=-12<0ᓽàMCá,Û¹☢G-EF-AḄË☢ᜧh90஺ÛG☢G-EF-AḄᑗdâh0,ᡠBeB¾hCM64=gãᓃN=gOᓽVGäCḄMV᝞`ᡠå

22PQBC1,FC[,EB,Û3Gc8|C=G,ᙠwÆMA3CD-44GA£bᑖÀAA4஺ḄMVY%E/஻A"஻BG,7EF=^BC,,ᙠAABEMY%BE=+4æ=2⍩,èᳮ஺/=ᵨêë"=2ìᡠíî?8CEE:ῪÎ?ᓽË☢EGGÌwÆᡠ%Ì☢:ῪÎ?ᡠC;¾hD,Nᵨ8ḄMV;ïðEN,GN,ᑣENLË☢8CGB1,BஹN=2,ᑣNEGNEG]Ë☢8CC4ᡠᡂḄ6ñ=B=BὡC=&,ᙠRtAὡ8cMNBBC=R,fe^G=J22+2-2x2x>/2x—=>/2,4V2ᓽBG+NG2=BN?,ᑣ/VG±B,C,gp2=-NGᨬâ4EN2ᦑtanZ.EGN=——=——-6NGᨬâtan4EGNᨬᜧ(NGNGᓽ64EG]Ë☢BCCᵫᡠᡂḄᨬᜧDᦑ⌱GACD29.(2022•IJ•IᜧN▬MNO>▤QRS)«heea>b,c>d,——=——=1.01,(l-c)er=(1-J)erf=0.99,ᑣ()a+\b+1A.a+b>0B.c-\-d>0

23C.a+d>0D.b+c>0ூnᫀ௃ADூr᪆௃A..'^—=——=1,01>0:.a>-1,b>—\f(x)=——(x>-l)ᑣI(û)=üýᡠr(x)ᙠ(TO)ᓫ⌴,ᙠ(o,+8)ᓫ⌴"0)=0,ᦑ஺>0,-1<஺<0.=ln/(x)-ln/(-x)=2x-ln(x+l)+ln(-x+l),xe(-l,l)I7ᑣ/?'(x)=2——-+—!-=2--^<0,x+\-x+\l-xᡠ'஻(x)ᙠ(-1,1)ᓫ⌴஻(0)=()(-1,0).<.ln/(i)-ln/(-Z>)>0:.f(h)>f(-h)f(a)>f(-b)a>-bᓽa+b>0ᦑ⌱⚗A/0B.•."(l-c)e<=(1-J)e0:.c<\,d<\6g(x)=(l-x)e*(x0:.g(c)>g(-c).\g(d)>g(-c)d<-cBRc+d<0ᦑ⌱⚗B┯FCvf(x)=?...g(-a)=Iஹ=W^>0.99,ag(-x)'/(a)101V7.-.g(-a)>g(d)N:ga)ᙠ(y,0)ᓫ⌴-a>d:.a+d<0ᦑ⌱⚗C┯FD,ᵫCSTg(-6)>g(c),-be(O,l)NW8X)ᙠ(0,1)ᓫ⌴:.-h>cᦑ⌱⚗D/0ᦑ⌱WAD2230.(2022•Z[\]^_`a▤cde)fTghi»1(஻>0k>0)Ḅmஹnop⚔rᑖtuA&,mஹnopᯖrᑖtuwxPughiz{4,4Ḅ}~rᑡᐸ^/0Ḅu()A.||-▏1=2஺B.i4%Ḅ᳛{a-C.PKEῪaḄrPᨵᨵ¡p

24D.¢S.£=¤ᑣᡠ•%=0ூ¦ᫀ௃BDூ©᪆௃ᵫ⚪~rPughiz{A4Ḅ}~r¬P(X஺,%),®{A^ᵫghiḄ¯Tᡠ'A┯F<®{B^ᵫA(-a஺)4(40),Sᓽ4•&°=•-%—=/3%+஽x-ax-a00NᵫJ-5=l,ᡠ'³S&´.µ&=5,ᡠ'B/0<®{C^¢ᙠ¶·▲ᑣ¹|Pf<|=2c»|¼=2c-2a,ὡ¾Ὺa<¹|¼=2c»\PF\=2c+2a,ὡx°Ὺaᦑrᙠ¶·▲¿/=<ÀῪaḄrPᨵop.ÁᳮSᙠ¶Ãஹaஹ¡·▲ÀῪaḄrP°ᔜᨵopÅƾῪaḄrPᐳᨵÈpᡠ'C┯F.®{D^ᵫS.%'=X+y:-É=஻x<+y<=c2,¤Êᡠ•%=*+/-஺2=0,ᡠ'D/0.ᦑ⌱WBD.(x+l)er,x<031.(2022•Z[•Ì]^_`a▤cde)fTÍᦪ/(x)=(x+lÏᑡ⌱⚗/0Ḅu()J2-*஺Ie'A.Íᦪ/(x)ᙠ(-2,1)ᓫ⌴B.Íᦪ/(X)ḄÑT+8)C.¢ᐵ{xḄÓÔ"(x)]2-a(x)|=0ᨵ3pwÖḄ×ᦪ᪷ᑣ×ᦪ஺ḄÙÛu(Ü,W)D.wÝ/(x)-Þ-஺>0ᙠ(-1,ß)ាᨵop᦮ᦪ©ᑣ×ᦪ஺ḄÙÛuூ¦ᫀ௃ACD(x+l)ev,x<0ூ©᪆௃•••"x)=(X+1)2,e*জஹ¹xvO»/(x)=(x+l)eJ,r(x)=(x+2)e*,¹xe(y,-2)»f'(x)<0,Íᦪ஻x)ᙠXG(—,—2)ᓫ⌴<¹xe(-2,0)»f(x)>0,Íᦪ“kᙠxe(-2,0)ᓫ⌴.¹x=-2»/(kᨵ᩽æ"-2)=-[,e~

25¹x<0»/(x)=(x+l)e\/(1)=0,.•.¹x<-i»/(x)<0<¹-i0,xéê{ëìíᜧ»J(x)éê{0.ঝஹ¹x..()»“ðñ/(k=ò1=(1-?ó),¹xe(O,l)»r(x)>0,Íᦪ/(x)ᓫ⌴<¹xe(l,y)»/'(x)<0,Íᦪ/(x)ᓫ⌴,.•.x=l»Íᦪ“X)ᨵ᩽ᜧ=JNீxéê{/ìíᜧ»,/(x)éê{0,Ã"஺»/(x)>0,f(O)=l®{A⌱⚗W]Íᦪ/(x)ḄõöSTÍᦪ/")ᙠ(-2,1)ᓫ⌴ᑣA⌱⚗/0W¿14®{B⌱⚗WᵫÍᦪ/(X)ḄõöSTÍᦪ/(X)ḄÑ-/qᑣB⌱⚗w/0<®{C⌱⚗Wᵫ÷“ᑗ2—ùম=0,S<("(|/(S|஺=0,ᓽ|/(k|=0ᡈ|஻x)|="üḄõö᝞W•••ᐵ{xḄÓÔ"(x)f-a/(x)þ0ᨵ3pwÖḄ×ᦪ᪷ÿ(
.ᨵ-1Ḅᦪ᪷,•••|/(-2)|=^,/প=%ᔠᦪ|f(x)|Ḅ,ᦪaḄᑣC⌱⚗#$%&D⌱⚗(."(x)-")஽>0,,./(xAaa+l),

26ᑖ᪆(01y=a(x+l)89(ߟ1,0),=01y=a(x+l)89(1,>|@A0=B2_=2,I஻1-(-1)e᦮ᦪJK஺M1,ᑣD⌱⚗#$.ᦑ⌱(ACD.32.(2022•TUTV•WX▤Z[\)]^ᱥ1C(V=4xḄᯖ9KcA89FḄ01/MCeAஹ89(9Ahi)j▲)A/MCḄl1e஺9AmK1ZADḄn9Al1M*pḄe9KE,ᑣ()A.0/Ḅr᳛KGB.AB=2BDC.AEEB>0D.01AEM8EḄvrwx⊡ூ{ᫀ௃ABDூJ᪆௃᧕^ᱥ1CḄᯖ9Km(1,0),01/MxpᔠAᑣ01/M^ᱥ1Cᨵ)e9Aᔠ⚪ApAᑣ01/M^ᱥ1CḄl1Aᔠ⚪A01/ḄKB=+1(*0),9A(4,yJஹB(x,y),22ὶ[x=?+l,.2,ᓽ9-2),[x=Ty=Vm).tnK9mK1ZAOḄn9Aᑣᑣ2>0,>0,VrnjmK9Aᙠ^ᱥ1CAᑣ3=3x4=12,=A"3ᡠA01/ḄKx=*y+l,ᓽy=

27ᦑ01/Ḅr᳛K6AA&%■6L1=ὶ7"ஹJᡈ,3ᓽ943,26)ஹ8ஹ,—¡¢,£…=26=_ᓩI1133J᧕9஺(-1,-2@,ᡠA¦=()1)§¢,¨=£-(,-§¢,ᑣ©=2©AB&%I33JI331᧕9E(-1,O),ª=(-4,-26)A¨=«¢A133,---------164^AE-EB=--+4=--<0,C┯%2G=—=—A=-;■2-=)=Aᑣ╢=)¯ᓽAAF-421,2)ᓝ13ᡠA01AEHBEḄvrwx⊡AD&.ᦑ⌱(ABD.33.(2022•TUTV•WX▤Z[\)]ᦪ஻x)±²³KR,/(T)=-"X),f(2-x)=f(x),/প=1,ᑣ()A.“X)Ḅjᐵ01x=2&µB."6)=0C.஻x)Ḅjᐵ9(-2,0)n¶&µD.஻2x-l)KᏔᦪூ{ᫀ௃BCDூJ᪆௃&A,Ꮇ“X)Ḅjᐵ01x=2&µAᑣf(2-x)=/(2+x),K/(2-x)=஻x),ᦑ஻x+2)=/(x),ᓽ2KᦪḄ)ᕜºAᑣ/প=/(1-2)=f(-1)=1,ᵫ஻T)=-4x),f(l)=l-1,¼½,ᦑ஻x)Ḅjᐵ01x=2&µAA┯¾%&B,ᦪ“
±²³KR,f(-x)=_஻x),ᑣ"0)=0,ᵫ/(2-x)=஻x)/(2-x)=-/(t),ᑣ/(2+x)=-/(x),/(x+4)=f(x),ᦑ"6)=/(2+4)=஻2)=஻0)=஺ᦑB#$:&C,ᵫBḄᑖ᪆A/(—2—x)=/(2—x)=—/(—2+ÁASPf(-2-x)=-f(-2+x),ᦑf(x)Ḅjᐵ9(-2,0)n¶&µ,C#$%&D,ᵫ/(-
=-/(
4—2x—l)=—/(2x+D,ᵫ/(2—x)=/(x)/(2x+l)=/(l-2x)=-/(2x-l),ᦑ/(—2x—l)=f(2x—D,ᓽ/(2x-l)KᏔᦪAD#$A

28ᦑ⌱;BCD.ூ9Ã௃Ä⚪ÅᔠὃÇᦪḄ᜻ᏔឋÊᕜºឋË&µឋAÅᔠឋÌÍAJ{@⌕ÏÐ᪷ÑÒjᦪḄឋÓÔÕḄÖᣚAØÙᦪḄᕜºAJ{ḄᐵÚÛ$᝞ÝÞÛᦪᐹᨵ&µឋÊᕜºឋ.34.(2022•TU•WX▤Z[\)]a=5-81n2,b=4-41n3,L"à"()c=e4A.b>aB.c>aC.b>cD.a>cூ{ᫀ௃ABCூJ᪆௃ᦪ஻x)=e'—4x+l,ᑣr(x)=e-.ᵫ_f(x)>0.x>ln4%ᵫ/'(x)<0,xMln4.ᑣᙠ(y,ln4)ᓫâ⌴äAᙠ(In4,ᱥ)ᓫâ⌴å.11_Yg(x)=lnx—x+l,àij/(x)=1=^-.gீx)>0,Ovxvl%ᵫgl.ᡠg(x)ᙠ(0,1)ᓫâ⌴åAᙠ(1,y0)ᓫâ⌴äA333511ᡠg(x)Vgপ=(),ᓽlnx4x-l,ᑣln±4ç)1,ᦑln3l—(=é=x=l@Aêᡂ)AᡠIn—>1-eAᓽIn4>2——>—.xe444Ka=/(ln4),b=/(ln3),c=/(%),In3<(c>a.ᦑ⌱(ABC.)235.(2022•TUTV•WX▤Z[\)]mKíᙊC:+ï=1Ḅ¯ᯖ9Að8ñ9஺Ḅ01/Míᙊ168CeA.89ApAᚖóK஺(ñ9)AMíᙊCḄô)e9KE,ᑣ()A.ABA.AEB.☢öḄᨬᜧK4ùC.AWᕜúḄᨬûK1211625D-ü+ýḄᨬûKWூ{ᫀ௃ABDூJ᪆௃&A,ᑣÿ),஺(,0),E(X”M),⚪Mw°஻NX1,zn+X1ᱏ0,

29wi44=,44=,•▲+ᓟ"ᓽ(஻+X)("%)112ᓽ&"L-](/n+x))(/H-Xj),,2nn,n..1.111,11KkAB_-c—_(K஻—•஻K—஻K—஻BD_C»,-BE_BD_CKAB2mm2m2ᑣMAE=-5*A8ẑ£=—1WᦑA45:2278B,ᵫAḄᑖ᪆>-+?=1,@ABAᙠDE▲ᑣF>0,஻>஺16822I22"ᡠK1=2-+2~22j2-x—,.”஻K4QRSTRM=2U,஻=2VWXY168V168S^ABD=^mx2n=mn<4>/2,ᦑB45\78C,ᵫ⚪C^3+V_=lbᯖBde(-2f,0),gᯖBdFT-2f,0),a=4,b=2Y,168ᑣ᪷klᙊḄ7nឋIBF|=|AF|,ᦑAABFᕜsd2a+1A31=8+1A31,uIAFḄᨬwxdlᙊḄyzs3=4Qᵫ⚪{@|}lᙊyz~ᔠ,ᦑAABFᕜsᜧ88+4\C┯\78D,ᵫCḄᑖ᪆|Aᵨ+|BeRAᵨ+|AF'|=2a=8,ᦑ+E=(+)(1AF|+|BF|)=-(17+BF1(5M1)|AF||■8\AF\\BF\8AF4(17+2J὜)=X,RSTR|AF|=■1,|Be|TVWXYD45,8\AF\\BF\855ᦑ⌱^ABD36.(2022••᡻▤)¡ᦪ“X)Qᐸ¥¡ᦪe(x)Ḅ¦§¨ᙳdR,S/(x)ª᜻¡ᦪg(x)=7'(x),஻(x)="x-4)+x,ᑣK®¯45Ḅᨵ()A.¡ᦪg(x-2)Ḅ±Eᐵ8³´x=-27nB.µg(x)Ḅ¥¡ᦪdg'(x),¦§¨dR,ᑣg(0)=0

30C.஻(x)Ḅ±E¶ᙠ7n·D.ᦪᑡ¹5ºdX»ᦪᑡµ4+>+…+᝞=44ᑣ¾(4)+஻(>)+…+¾(¿)=44ூÁᫀ௃BCDூÄ᪆௃7A,ᵫ¥ᦪḄÅ{§Qf(x)Ḅ7nឋf(x)ᙠxÇ-xᜐḄᑗ´Êᐵ8ËB7nᐸÌ᳛ÎXᦑg(x)=g(-x),g(x)ªᏔ¡ᦪg(x-2)7nzdx=2,A┯\7B,g(x)Ḅ7nឋg(x)ᙠxÇ-XᜐḄᑗ´ᐵ8Ðz7nᐸÌ᳛Ñdᦪᦑg'(-x)=—g'(x),g'(x)d᜻¡ᦪÒ¦§¨dR,g'(O)=O,B7;7C,/z(x)=/(x-4)+(x-4)+4,ᵫ/(x)d᜻¡ᦪ஻(x)=/(x)+xd᜻¡ᦪ±Öᐵ8(0,0)7n஻(x)K×Øᵫ“(x)ᢥᔣgÛÜ4ÝᓫßàᔣáâÛ4ÝᓫßuᡠKḄ±E¶ᙠ7n·(4,4),ᦑC7^7D,ᵫC⌱⚗Rà+w=8V,3)+஻ম=8,ᵫX»ᦪᑡឋå4+%=8,\./?(4)+஻(ᓽ)=8,çᳮ஻(%)+஻(4())=8,h(a)+h(a)=Sᦑ39/j(a)+/?(a)+---+/j(67)=|[[^(«)+/?(«,,)]+[/j(a)+/?(a)]+...+[/?(a)+/?(a)]+[/?(«,,)+^(4/,)]º12ll1210l02=-x8xll=44,D45.2ᦑ⌱^BCD37.(2022••ìíîï▤)78¡ᦪ=ᑡ⌱⚗45Ḅª()XA.¡ᦪf(x)Ḅ᩽wxBd-e,᩽ᜧxBdeB.¡ᦪḄᓫò⌴ôõd(-oo,-e]u[e,+o>),ᓫò⌴øôd[-e,0)5஺,e]c.¡ᦪḄᨬwxdᨬᜧxd:D.¡ᦪú(X)¶ᙠÝûB1Ç-1ூÁᫀ௃ADூÄ᪆௃Rx<0V/஺)=ᔢÊý¥^/(þ)=á*ÿ
x>0/(x)=—,XXX
x<-eᡈx>ef'(x)<0,
e0,ᦪf(x)ᙠ(-8,-e],[e,+8)ᓫ"⌴$ᙠ[-e,0),(0,e]ᓫ"⌴%ᦪ/(&)ᙠ&=-0ᜐ(᩽*+ᙠX=eᜐ(᩽ᜧ+A/01ᦪf(x)Ḅᓫ"⌴$34ஹ%346789:;<Ḅ34:=ᵨ?@AB;CB:/0;ᦪ“X)Ḅ᩽*+G-᩽ᜧ+G1
x<0:/(x)Ḅ(+@ᔠG-1+8),

31
x>0/(X)Ḅ(+@ᔠGᑣ/(X)ᙠLMNOᨬᜧஹᨬ*+C:/01ᵫ/(x)=0,ᓽT=0b|=1,W&=±1,ᦪ/(x)Yᙠ89Z[1\t,D/0.ᦑ⌱AD38.(2022•ef•gh▤jkl)mᦪ஻x)="^W(x>0),r"x)ு/tឤᡂwᑣxyᩩ{Xᓝ1Ḅ/᦮ᦪk=7()A.2B.3C.4D.5ூᫀ௃ABூW᪆௃
x>0/(>£ឤᡂwᓽO<(x+l)l+M(x+l)ᙠ(0,y)ឤᡂw,8(᜜=(*+1)1+ᵨ!*+1)(*>0),ᑣ&VgznG),g(x)=x1*"x),1y/j(x)=x-1-In(1+x)(x>0),ᑣ/f(x)=1--——■=—>0,ᦑ஻(x)ᙠ(0,y)ᓫ"⌴%GM2)=2-l-ln(l+2)=l-ln3<0,/z(3)=3-l-ln(l+3)=2-ln4>0,ᡠ஻(x)ᙠ(2,3)YᙠZ[%,%-1=111(1+%),ᡠ
0x஺஻(x)>0,ᓽg'(x)>0,g(x)ᓫ"⌴%1ᦑgmin(x)=g(X஺)=(3+I)l+M(x<>+1)=(/+1)1+/T=G+1,“0¦0G2

32ᡠfÑxÒᐵ»[Ñ2»/Ñ2ÒÒᡂ¼½¾A/01½஻xÒ/'ÑxÒ=3#-i2ax+c,tÔᦪ/ÑxÒ½¾Õx=2,Ö34Ñ0,1ÒÆÑ3,4Òᐵ»ᦪ2½¾,“ᙠÑ0,1Òᓫ"⌴%,ᓽ
x«0,lÒ/rÑxÒ>0,,
xeÑ3,4Ò,f\x$>0,ᑣ/ÑᙠÑ3,4Òᓫ"⌴%B/01
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à<á<ßf\x$<0,ᑣ/ÑxÒᙠâ,ãᜐᑖå(᩽ᜧ+\᩽*+,
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î
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3#2,A<0,ðñòᨵÉWy=ar3-6ax2+cx+dy=(c-12a)(x-᳝))+/(x)VxeRðñò()ᙳᨵÉW7,ஹoy=ax'-6ax2+cx+dᡠÀÁÂᦪGÃÄ^=Ñ஺-124Ò@-öÒ+/Ñ÷°ÒÆÇÄy=/ÑᨵÉÊᐳ[D/0.ᦑ⌱ABD40.Ñ2022•efeøùgh▤jklÒ᝞úᡠûmᓫüᙊÆxÕḄ/þÕÿ
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ஹ-e,+8B.ᦪ/-xḄJ-e,lC.ᐵ
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xḄ¢£-ὡ-¯-¯0ᨵ5¦§#¨Ḅ©ᦪ᪷ᑣ©ᦪ஺Ḅ¬J®,1,1ூMᫀ௃ACDூP᪆௃°
A⌱⚗:xf-x=H;•ᑣ:-ᑗ=ᔆ<°

34:ᐭ21>,·ijr(x)=^k^l,ᵫr(x)e,XXᡠᦪ/(X)Ḅᓫ(e,l)ஹ(e,+8),A°_°¼B⌱⚗:xvl>;஻x)=l+½<1,x—1:xNl>00,ᵫ/2(x)-4/(x)|=஺¹º/(Ä=0ᡈ஻x)=aᡈ/'(x)=-a,ᵫ¾¹¢£/(Ä=0ᨵ2¦§¨Ḅ©᪷¢£/(x)=-“Âᨵ¦©᪷ᐵ15Ḅ¢£/2(x)-H஻x)|=oᨵ3¦§#¨Ḅ©ᦪ᪷ᑣ஺>|,C°_ᐵ
xḄ¢£(Ç-4஻ᑘ=0ᨵ5¦§#¨Ḅ©ᦪ᪷ᑣD°.ᦑ⌱ACD.42.(2022••ÉÊᓭÌ▤)ᦪ/(x)=(x+D(e'-x-l),ᑣ&ᑡ()*+Ḅᨵ()A./(x)ᙠ(0,Î)ᓫ⌴ÐB.x=0f(x)Ḅ¦᩽¯JC.ÒᨬᜧJD.7(x)ᨵÓÔூMᫀ௃ABCூP᪆௃R⚪T/'(x)=(x+2)e*-2x-2,Õg(x)=(x+2)e_2x-2,Ö׺g'(x)=(x+3)e<2,:x>0>ÕØ(x)=(x+3)e-2,ᑣ/f(x)=(x+4)e>>0,ᓽg'(x)=஻(x)ᙠ(0,+co)Ù⌴Ðg'(x)>g'(0)=l>0,ᑣ/'(x)=g(x)ᙠ(0,ᵪ)Ù⌴Ð,rW>r(0)=0,`ÁAx)ᙠ(0,+a))Ù⌴Ð,A*+_

35:-le(x)=eஹ-Û?Ö׺9'(x)=e'-hJ,àᯠᦪâᙠ(1,0)Ù⌴Ðã᜛'(-1)=1-2<0,9'(0)=1>0,ᑣäᙠ᳝,a(-1,0),æºç(%)=0,e2:§£(᳝),0)>஺0)ு0,ᦪêëᙠ*0,஺)Ùᓫ⌴Ð:XE(Xo,O)>9(ë<᝖0)=0,2x-i-2ᓽ:x«%,0)>ex<——ᑣ/*)=(ï+2ð'-2Ø2<0,`Áx=0/পḄ¦᩽¯JB*+;f:x>0>,Õ஻(x)=eஹ-x-l,Ö׺஻'(x)=eஹ-l>0,ᦪ஻(%)ᙠ(஺,+°°)Ù⌴Ð:ᜩó2>,u(x)>e2-3>1,ãy=x+iᙠ(0,+8)Ù⌴ÐJ(1+8),`Á:XN2>/W>X+1,ᡠ/*)ÒᨬᜧJC*+_`/(-1)=/(0)=0,ᓽ-1õ0,ᦪf(x)=(x+D(e*—x—1)ḄÔD§*+.ᦑ⌱ABCஹ÷ø⚪43.(2022••ùὃû)ᙠü┵S-ABC.þ☢ABC,02GḄ
SA=AB,”S4BḄᚖCM,☢SAB,ᑣ┵S-45cḄ᜜ᳫḄூ"ᫀ௃9&ᐔூ(᪆௃᝞+,SM-./0AB1D3M5SA016ᑣSO_LAB,BEYSA.:CMJL☢S4B,ABu☢S4B,ᡠ>CM_L4T:CMcSD=M,CM,SOu☢SC£),ᡠ>/W_L☢SCO,CDu☢SC£),ᡠ>C£)_LAB,ABCD
ᦑ஺ABGH&4=AB,ᡠ>S48DKLSA=SB=AB=26(᧕NS£»=CZ)=3,£>M=gsO=l,SM=BM=2,CM=\ICD2-DM2=272-ᡠ>SC=yJSM2+CM2=2>/3>W᜜ᳫO,ᑣ஺ᙠCMh,Z[r,ᙠASCMGᨵ(CM-OC^+SM?=OS2n(2&-r^+2?=r2,(Nᔆ=⌳2ᦑ᜜ᳫe=fᐔx(hi=9jᐔ.ᦑ"ᫀf9&ᐔ

3644.(2022•mnopGqr▤tuv)Wwᦪf(x)=gx?+2or(“>0)Ḅ+y5g(x)=3/Inx+AḄ+yᨵzᐳᙠzᐳᜐḄᑗ~ᔠᑣoᦪᓃḄᨬᜧ.3-ூ"ᫀ௃-e32ூ(᪆௃Wzᐳᙶ᪗,%),f'M=x+2a,g,(x)=^-(x>O),0oo3a2ᵫᙠzᐳᜐᑗ~N+2a=ᓽ+240-3/=0,(N=3஺()ᡈ%=4,X஺H=/(x())=g(%)ᓽ3ᱏ+20=3a2lnx+b()ᡠ>b=+2”-3a2lnx=-1(72-3a2lntz(tz>0),0Wwᦪ=-3/Ina(a>0),//(a)=5஻-(6alna+3a)=%6olna=2Q(l-31na),Ḻ)=0N4=3XE0,e3/?'(«)>0,“£,+0))A'(Q)<0.ᡠ>wᦪ஻)ᙠ,,eᓫ⌴¢ᙠᓫ⌴£,ᡠ>¤¥ᨬᜧ¦§ᐭ6=£j3a21na,14—VH-VQ3-ᑣN*,=13.32ᦑ"ᫀf-e\245.(2022•mn•mªᜧq▬¬Gqr▤tuv)®P,A,B,CDZ[2Ḅᳫ☢Ḅ,

37PA=PB=PC=2,NABC=5BᙠACḄ¯°D,ᑣ┵ḄᨬᜧDூ"ᫀ௃b8ூ(᪆௃jrᵫ⚪²PA=PB=PC=2,ZABC=-,³®´ᙠ☢ABCḄ¯°GABCḄ᜜ᓽACG2ᑣᳫḄᳫᙠPGḄ./~WPG=hᑣ0G=2—h,ᡠ>OB2-OG2=P82-PG2,GR4—µ2-h
2=4—஻2,(Nh=l,ᑣAG=CG=6¶B·BD_LAC1D,WAD=xᑣCD=2G-x,¸WBD=y,ᵫ³N¹ᡠ>º»¼½¾♦BDC--ADB,ᑣg¿=gJ-d+2c3,f(x)=-x4+2y/3x3,ÀI1/(x)=-4d+6Gx2ᵫ/(x)=0³Nx=g/ᡠ>X=f£L=Nᡠ>ADB☢ḄᨬᜧLx%Á=2Á248ᑣ┵P-ḄᨬᜧDÂஹÄஹ1=ÅÁ.388ᦑ"ᫀÆ846.2022•mn•ÇÈGqr▤tuv¾®wᦪ./•x
=Asin5µA>0,µy>0¾,ÉÊËÌᙠÍÎÏKḄoᦪz஽«Ò,2ÓÔN/•&¾+/µÕ¾=2A,ᑣoᦪ஺Ḅ¥×D一95---ூ"ᫀ௃—42一-ூ(᪆௃•••ÊËÌᙠÍÎÏKḄoᦪᜧ,9ؼ2ÓÔN/a¾+/w
=2A,AjrÙ>2T=wᓽ3>4ÚÌᙠÍÎÏKḄoᦪ%,9Ó2ÓÛÜ⚪²;Ò<27,ᓽ0vgv4ày,2ày],

38

39--k-1+4XiitPNfAx-y+4=0,ᵫ2=1,N45z-844+32=0.\Jk2+i32X15kpR.kpN=A(ᑣ%á=ÏN4=âc15c9l9n2^=—"3=-,À=f2247ᦑN¤c7•äᙊḄæ᳛e=—=ᐭ.a97ᦑ"ᫀf-48.2022•mn•ÇÈGqr▤tuv¾Éwᦪ/µ¤=i108“Ø-10<஺<1
ាᨵÍÎêᑣ஺Ḅூ"ᫀ௃a=eூ(᪆௃ᵫjf(x)=a[log“x|-1=0,Nllogarl==ᓽlogτ.Vaaᵫ⚪²,wᦪy=log,X5Ḅ+yᨵÍÎ0,a0

40ᦑ"ᫀf.,-;e2249.(2022•mnmª•r▤tuv)®äᙊC:0+?=l(a>2a),ᙊO:/+/=ᔠ+2,òᙊCḄâóᯖᑖö÷ø.ù~y=û0äᙊ1P,0ᙊ஺1MஹNÍ.dPMPN=6,ᑣºὡÿ=ூᫀ௃8ூ᪆௃ᵫ⚪|஺ὡ|=|஺=஺"=2,ᵫᙊḄPF\+PF1=2a,᝞ᡠᙠVP஺ὡᵫ!"ᳮ$PF^=OP2+Oὡ2-2•OP஺ὡcosNPOKজᙠVP஺0ᵫ!"ᳮ$PF^=OP2+OF^-2OPOFCOSZPOF@,2212ZPOF\+Z.POF=n,ᡠ3cosZPOFஹ=-cos/506ঞ,2ὶ:জ@ঞ$Pk+P/V=2Op2+2c2,ᓽ?ὡ+”)2_2C5D=20E2+2,2<7HIᨵ4a2-2PFPF=20Pঝ+2c2,ᡠ3OP?=/+஻-5ὡ.pN=/+4-PF,-PF,x22ᵫᙊ0:/+Q2=/+2,$ᙊ஺ḄRS2ᔆ=1+2,12MஹNXYᙠᙊZᡠ3|0MT°N|=r=J/+2,ᡠ3PM=7a2+2-OPPN=J/+2+OP-efDPM-PN=6,ᡠ3PMPN=(Ja2+2-Op)(Ja2+2+op)=a2+2-op2=6,22-a2-4+PF,-PF=6,$a+2PF,PF=8.2ᦑᫀ2b8.50.(2022•dedf•gh▤jkl)mnᦪ”>0,qrᦪ஻x)=e'+acosx(x>0)ᨵvwᨵ2x᩽zYᑣ஺Ḅ|z~I.ூᫀ௃(/#)ூ᪆௃12஻x)=e"+acosx(x>0),ᡠ3:(x)=e*-asinx,⚪/'(x)ᙠ(0,+)ZᨵXxYg(x)=r(x)=e*-asinX,xe((),+b»),ᑣ(x)=ex-acosxg'Cr)=e*-acosx=0,(x>0),

41cosx=0g'(x)wO,ᡠ3cosxwO,ᑣᵫ⚪ᨵ஺=ᐭrᦪ$e*(l-tanx)=0,ᓽtanx=l,COSXᦑg(x)Ḅ᩽zY2=?+br,ZeN,᧕2Ꮤᦪ2᩽zYZ2᜻ᦪ%2᩽ᜧzYv᩽ze"-asin/¢ḼḄ¤ᜧ¥¤ᜧ¦g(0)=1§஺(7r\?.7Cg—=e©஺sin©ª0⌕¬rᦪg(x)=esinxᙠ(0,+8)ZᨵXxY◤ª44,(94).9°±£——=e4-as

42——§0rl4)4$³e´aீ¶·ᦑᫀ2b(0¸,ᢈº)2251.(2022•de•gh▤jkl)mὡNᑖ¼I½¾¿E:E-q=l(a§0)ḄÂஹÃᯖYÅᨴḄÇ¿º½¾¿EḄÂஹÃXÈᑖ¼ÉHA,Bhi,qËᵨÍ=5:12:13,ᑣMBDḄ☢Ñ212ூᫀ௃5ூ᪆௃᝞12ÒᑮÔb|Õ1=5:12:13,ᡠ3ÖÒÍ=5x,|AB|=12x,$I9|=13X,ᵫÒᒓ©ÒÙ=|ÚÛ|Ô|,$12x+1AK|-5x=l3x-\AF\tᡠ3Hᵨ=3x,ᑣÒᵨ=15x,ᵫÒὡÝ+ÒÞE=ÚᵨE$25(*=4°2,[\BF.\-\BF\=i0x=2aKஹ,,2¦ஹ'':7(ᡠ3/=2,C2=5,ß=ᔁ[c=a2+325117ᦑAABFZḄ☢áS=^\AB\\BF\=30/=?.2

4312ᦑᫀ2by52.(2022•dedf•gh▤jkl)ᙠâáABC஺A3஻C£),45=4,BC=CD=DA=2,/\ACDãACᢚåæç80,$ᑮhè┵D-A8C.hè┵஺-A8CḄêÑ|$ᨬᜧzìhè┵Ḅ᜜çᳫḄ⊤☢Ñ2.ூᫀ௃20%ூ᪆௃ÅYCðCE"ᚖò2E,•••ABCD2óῪâáAB=4,CO=2j.BE^~,B=-23ᵫ!"ᳮ$AC2=AB2+BC--2AB-BCcosy=12,ᓽAC=26AB2=BC2+AC2:.BCVAC᧕õ☢ACD_Lõ☢ABCh.è┵Z)—ABCêÑᨬᜧöõ☢AC஺᧕ZD=y÷஺2᜜çᳫᳫøRS2R•.•BCLõ☢ACO,OB=OC•••Oùõ☢48Ḅúûü"=gsc=lAC=9¦Ḅ᜜çᙊRS'©,.2ᐔ©'2sin——3/.R2=r2+d2=5-,S=4TTR2=20TTᦑᫀ2b20ý1

44253.2022•de•᡻ÿ
▤ᱥV=4xP4,4
ᩩPBᙠᱥḄ᳛!"#4,ᑣABឤ"—.ூ)ᫀ௃3T/2\/2\y,-4_4ூ,᪆௃.“JB/0(ᑣᙠ1I474442ᳮkPB=--,kAB=--------%+4444!50•73=4,ᡠ:——7=4,%+4%+4ᡠy»+4y/+y2+12=0.ᡠyiy2=-12-4“+”
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▤)\]ᙠR_Ḅ`aᦪ/*)bc/(x)-/(-x)+x]±+e')=O,ᙠ(0,zo)_ᨵYಘ>-4ᡂk.l!ᦪ஺bc/(l-a)-/(a)+e"T-ae"n-ae-">0@ᑣaḄ$%'oeூ)ᫀ௃(8,y]Y1—Xூ,᪆௃ìg(x)=஻x)+Wᑣg'(x)=ra)+eeᵫ/(x)-f(T)+xg+e[=0Jf(x)+==f(—x)+VeJeeᡠg(x)!ᏔYᦪìð஺)=Ij/z'(x)=1ee4!cx<2d//«<0,cx>2d஻'(x)>0ᡠcx=2d᱐òᨵᨬ#2)=-ᓰp4!ᙠ(0,”)/'(x)>ᓽ/পߟõ>0ee1—Y1ᡠg'a)=ra)+—>r(x)-->oee~ᡠg஺)ᙠ(0,+8)ᓫ¸⌴ºᵫ÷(1஻)f(a)+e"7—ae">0J/(Ia)+■^^2/(஻)+=eeᓽg(l—a)Ng(a)ᡠ|1—4dᓽ(1஻)2஻2,,Jᦑ)ᫀ!K(-CO,-159.(2022•QR•QýTᓭÿ
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49u/ফ=0,/(0)=/(4)=1@ᡠBav0v/2v2vcv4,/®=/(c)@ᑣ6+c=4,Ba+2Z?+c=a+Z?+4,==f«0,1),ᑣa=Inf,b=2-2t,ᡠBa+2Z?+c=a+b+4=ln7-2r+6,g(f)=lnf-2f+6,/«0,l),ᑣg'(/)=¤—2,rg'(f)=0,p>f=J,wK@g'(f)>0,g§ᓫ©⌴:@wK@g,(r)<0,g§ᓫ©⌴ª@ᡠB8(/)ஹ&(¤)=1¬-1+6=5-1112,BPa+2b+c=a+b-^4=

50t-2t-^-6<5-

512,ᦑ*ᫀ(TS@5-ln2].