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ὶὃ2022—2023ᳮᦪ⚗1.ᔁὃḄஹ!ὃ"#$ᑏᙠ⚪ᓱ)*ᔁᢣ,-./.2.2⌱4⚪5⌱678⚪ᫀ:ᵨ<=>⚪ᓱ/?@⚪AḄᫀ᪗#CD.◤ᦋHᵨIJKLM:N⌱CᐸPᫀ᪗#.2Q⌱4⚪5ᫀᑏᙠ⚪ᓱ/ᑏᙠR*ᔁ/Sᦔ.3.ὃ*UV:R*ᔁ)⚪ᓱWX2.ஹ⌱4⚪R⚪ᐳ128⚪78⚪5ᑖᐳ60ᑖᙠ78⚪[6Ḅ\]⌱⚗^_ᨵ⚗abᔠ⚪A⌕eḄ.1.ghᔠ4={1|%2-6q+8„},3={1,2,3,4,5},ᑣAc8=A.{2}B.{2,3}C.{3,4}D.{2,3,4}2.x,yeR,|“+3-1=0”a“-1=1”ḄA.ᐙᑖ⌕ᩩB.⌕ᐙᑖᩩC.ᐙᑖ⌕ᩩD.ᐙᑖ⌕ᩩ3.tan=3,ᑣ8cos28+2sin26=11A.B.-C.-2D.2554.⚪P"wR’sin?/-cos?xxsin"/-cos'x"⚪<7"Vx>0,x>sinx"ᑣ§ᑡ⚪©ª⚪ḄaAr^qB.P^Fc.p^qD.P7F5.ᙠAABC^«¬3c=4,A=X,C=2ᑣAABCḄ☢¯°±A.4B.4²C.6²0.873X'6.³ᦪy=±ᐸ^e©ᯠ?ᦪḄ¸ᦪḄᜧº»¼a
17.,½ᙠR/Ḅ³ᦪ/(x)ÁÂ/(1+Ã=/(1ÃÄÅÆ15/(X)=X2-2X+9,ᑣ/(2023)=()A.-6B.6C.-8D.88.gQ=1.25,=log34,c=log45,ᑣQ,0,cḄᜧ8ᐵÌa()\,a>b>cB.b>c>aC.b>a>cr>.c>b>a9.«¬³ᦪ/(x)=0sinx,³ᦪg(x)Ḅ»¼ÎÏᵫ³ᦪ/(x)Ḅ»¼ᐜᔣÓÔÕ7]ᓫ-×ØNᡠÚI71³ᦪ»¼ÛᢝÝᙶ᪗ßàᙶ᪗ß©áᩭḄ(>0)Úᑮx=a³ᦪg(x)»¼Ḅᩩ?äåᑣa>8Ḅᨬ8ç©()A.3B.6C.9D.1510.ᙠAABC^]ᑁéCᡠ?Ḅêᑖë©a,ìacos(c+'■îcsinA,q=2²ð=4,ᑣc=()A.2B.4C.2V13D.811.,½ᙠñò/Ḅ³ᦪ/(%),?ñòᑁḄó,ôᨵ.0ᡂö,ᑣä/(ᑜ©ñòO/ḄÔù³ᦪ.«¬/(x)a,½ú©[0,2]ḄÔù³ᦪìÁÂজVxe[0,2],J(x)..2xᔓ+)/(2x)+/(x)=2þঝVxeḄ()15A.lB.—C.2D.4812.ᦪ/(x)=e'-2inx—2ainx+G"2ᨵ$%&'(ᑣḄ+-()A.(-Ve,0)B.(-oo,0)C.(-oo,-V^)D.(-oo,-e) ஹ⚪(⚪ᐳ4⚪⚪5ᑖᐳ20ᑖ.)
213.ᦪy=log2[1+j)+Vl-x2Ḅ789.14.:sin(x+?)=g,ᑣsin(2x—=)=.15.ᙠAABC@(AA,BḄCDᑖFa,"c, b=2,IcosC=3-J(ᑣAABCḄ☢LḄᨬᜧ2416.PQ┵P-A5CḄPTUUᡠX(Iᐸ[ᳫḄ]^4,ᑣPQ┵-ABCḄ_LḄᨬᜧPஹab⚪(ᐳ70ᑖ.abeᑏgᦻijkஹlkmnᡈpqrs.)17.(10ᑖ)uvwᦪ/(x)=(x2+3?—3z"ᵨ|Ꮤᦪ.(1)~ᦪ/(x)Ḅa᪆(2)ᦪg(x)=/(x)-2x,xe[l,a],:g(x)Ḅᨬᜧ15,~ᦪḄ.18.(12ᑖ)uvᦪ/(=2&8511+3)+2Ḅᨬᜧ.(1)~ᦪ/(Ḅᨬᕜᓫ⌴(2)~ᡂḄxḄ+ᔠ.19.(12ᑖ)ᙠAABC@(ᑁA4BḄCDᑖFa,b,c,I_____.ᙠজbcos[^—c)=—Gcc°s8ঝ254e=¢6£,BCঞtanA+tanC-G=-gtanAtanC¦ABP%ᩩ¨@©⌱¢%(⊡ᐙᙠ☢Ḅ®⚪@(¯°ab.(1)~A5Ḅᜧ"(2):ABḄᑁA±ᑖ²³AC´(IBD=1(~a+4cḄᨬ.20.(12ᑖ)ᙠ┦AAABC@(ᑁAA,8,CᡠCḄDᑖFa,,c,I¶sinC+cosC=ᔳ0fJsinA(1)~A(2):AABCḄ[ᙊḄ]^1,~º2+2Ḅ+-.21.(12ᑖ)uvᦪ/(x)=xlnx+2.(1)~ᦪ/(%)Ḅᓫ;
32(2)lk"/(x)>x¢¢.x22.(12ᑖ)uvᦪ/(x)=——¾ᙠ$%'᳝,M,ᐸ@>0,eÂᯠCᦪḄÄᦪ.ax+1(1)~ᦪḄ+-3/ஹ/ஹ(2)~l"1H---(%)+/(J2)<6,2aÇὃbᫀÊËὶὃ2022—2023ÍÎËPÏÐ(¢)ᳮÒᦪÍ1.Dூa᪆ᵫY—6x+&,0a×2F"4,ᑣ4={ÙÚ4},Ü8={1,2,3,4,5},ᦑ4r^3={2,3,4}.ᦑ⌱.2.Aூa᪆lgx+lg(y—l)=lg[x(y—l)]=O=x(y—l)=l,Ix>0,y>1,ᦑ⌱A.ano2"8cos2e+4sin6cose4tand+8...zfc3.Dூa᪆8cos-(+2sin26=-------------=——----=2,ᦑ⌱D.cos2^+sin2^tanP+14.Aூa᪆âsin2%+cos2x=l(ᡠsin4x-cos4x=(sin2x-cos2x)(sin2x+cosஹ)=sin2x-cos2x,ãijsin!-cos4x=sin2x-cos2xC©åḄxeRឤᡂ(âèé⚪PᎷé⚪.᪀⌼ᦪ“x)=x-sinx,ᑣ/(x)=l-cosx.O,ᑣ/(î)ᙠ(0,+8)ᦪ(Ü/'(0)=0,ᡠïx>0ð(/(x)>0,ᓽx>sinr,âèé⚪óé⚪.ᡠºóé⚪(ᦑ⌱A.5.Bூa᪆ᵫô7ᳮ×õö■ö.ᡠAB=-——=4j3,sinAsinCsinAâ8ö%—¢4öJ(ᡠS=—x43*3><91118=4>^.ᦑ⌱B.ARrAAOIC62x36.Bூa᪆C©åḄx£R,e*>0,ᦑᦪy=—Ḅ789R,◀C⌱⚗.
4Yþ¢ïxvOð(y=—<0ïx>0ð(y=—>0,◀A⌱⚗.exexâ=ö1(3—ÿ)x<3y>0,ᦪ=ᓫ⌴eAe*e*3rx>3ylog5,ᓽa>c.ᡠ!4b>a>c,ᦑ⌱C.9.Bூ᪆ᵫ⚪2g")=J5sin(s-?)x=(%ᦪg(x)34Ḅᩩ6789ijTTTT7T—co——=—+kᐔ,keZ,ᡠ!/=6+8%,ᦇeZ,.;>(),ᡠ!Ḅᨬ?@6,ᦑ⌱B.842aC\7T\10.Aூ᪆ᵫABCᳮ-------FsinCsinA=sinAcosCᓝ.sinAwO,ᡠ!sinAsinCI6JsinC=cosC+—=—cosC--sinC,ᳮF3sinC=GcosCᡠ!tanC=X^.£(0,J)ᡠV6J223ᑍ!C=—.ᵫKBCᳮc?=/+22aᮞ;osCFcஹ2=12+16-24=4ᑣc=2.ᦑ⌱A.611.Cூ᪆Vxe 0,2j(2—x)+/(x)=2,ᡠ!ᦪḄ34ᙠ 0,2QᐵS(1,1)67Tx=lUF"1)=1..Vxe0,f(x)..2x,ᡠ!/(W..1%CXY 0,2ḄZᦪ/(1)=1,
5ᡠ!xe1,1/(x)=l.ᦪ/(X)Ḅ34ᐵS(1,1)67,3aᨵx)=l,ᡠ!/cᡠ!1,-1+1=2,ᦑ⌱C.12.Dூ᪆/(=6-2▲2.11%+0?=/-2l+0(%2-2⊈)ᨵnopq0rst(x2-21nx)=0ᨵnovwḄ᪷.Tf=g(x)=x2-21nx,ᑣ2202(X+1)(1)QO,ez+=0.g'(x)=2%——=—xXXxe(O,l)g'(x)O,g(x)ᓫ⌴.ᡠ!rmin=g(X)min=g(l)=lᓽᵫe+R=0F=T(.)=->ᑣ/(/)=_¥(,)ᑣᙠ+8)Q%ᦪ(l)=-e.ᡠ!ᔠᦪ(g(x))ᙠ(0,1)Qᓫ⌴ᙠ(1,+8)Qᓫ⌴ᨬᜧ@-e,ᡠ!⌕ᦪ/(x)ᨵnopqᑣ◤e,ᦑ⌱D.,2x+2C1+—=---->0x>0<-2,13.(0,1]ூ᪆ᵫ⚪2xxFᓽᡠ!ᦪḄCXY(0,1].2—k1,l-x..O,7ூ᪆rsin2x2=-coscஹ7ᐔ1cJc7114.2xH—-cos2x4--=-cos2x+962I36=2sin[Y.ᦑ¡ᫀJ1TCrT=x+—,ᑣsin%=—,x=;ᡠ!636sin(2%-^-=sin=sin(21-9=-cos2r=2siR-1¤.ᦑ¡ᫀ1
615.73ூ᪆ᵫKBCᳮUFcosC=""+4——=3£,ᓄ§F4=/+2aᑣ4a24cosB=a+C~4=-,.Be(O,»),ᡠ!B=&,^4+ac^a2+c2..2ac,ᓽac,,4,c=c2ac23¬®ᡠ!¯ABCḄ☢²S=´QcsinB=Y3aG,6ᦑ¡ᫀ2464r-\6.—ூ᪆ᵫ¶·32¶¸┵P—ABC3ᡠ¼AC=26a,48=8C=2a,NC48=30"¾01AABCÀᙊḄᙊÂÃÄᵫ---------=—ߟ=2r,$r=2asin/CABsin30ᵫ⚪2B41Z☢ABC,¾ÆA=f«>0),¶¸┵P—ABCÀᳫḄᳫÂᑣ01Z☢A8C,00=(ᑣ+4/=16,ᵫ;É+4/=]6F,=2,16—4/Rj?ᡠ!0/3ax2axsin/BAC-^-a2t=a2^4-a2-4"\j4aA-ab.Pp-AABRCC32333i^/(x)=4x4-x6,xe(0,2),ᑣ/'(%)=16^-6%5,Tr(x)=0,F*=Ì€(0,2)xjo,Ã]/'(x)>0J(x)ᓫ⌴/Ã,21/'(X)717.(1)ᵫ⚪2Óa+3l-3=1ᓽ+3l4=0FÓ=-4ᡈÓ=1.l=-4f(x)=x-\v%ᏔᦪÖ×Ó=1/(x)=x2,%ᏔᦪØÙ⚪Úᡠ!x)=Y.(2)ᵫপ2g(x)=f—2x,g(x)34Ḅ678x=l,ᡠ!g(x)ᙠÛLaÝQ%ᦪᑣg(x)max=g(a)=/2a=15,F=5ᡈ=-3,.>1,ᡠ!=5.18.(1)/(x)=20cosx(sirucos?+cosxsinßÝ+m=2cosxsinx+2cosஹ+m=sin2%+cos2x+m+l=>/2sin+m+1,ᵫ/(X)max=3+Ó+1=àF᪷=1,ᡠ!/(X)=\/^sin(2x+5),2ᑣ/(X)Ḅᨬ?Aᕜ'T=ß=4.nJTj7T7TT—+2k7r^&x+——+2kᐔ,kwZ,F----+ᦇã1k——bkᐔ,z£Z,2428834j6ᡠ!/(X)Ḅᓫ⌴æç--+k7T,—+k7r,k&Z.oo(2)/(x)=/sin(2x+?)..l,ᡠ!sin(2x+().ᑍᑍ\TTTTᡠ!2è+—é,x+—2kᐔ+——,keZ,Fê%ᨽ*kᐔ+—,kGZ,4444ᡠ!ᡂíḄXḄ¬@îᔠ{xlᓃḄbr+?,%ez}.19.(1)⌱òজ¤bcos■°)=-6ccosB,ᓽ/?sinC=-MccosB,ᵫABCᳮFsinBsinC=-8sinCcosBᙠ¯ABCöCe(0,^),sinCwOᑣsin3=-øcos3
8.sinBwO,ᡠ!tan8=—ᑣ8=-^-.⌱òঝ¤2s,Rr=-y/3BABCᵫ¶úûḄ☢²üýàᦪþ²Ḅÿ 2x'acsinB=6cacosB,ᓽ/Vov2sinB=->/3cosB27r3e(O,)sinBwO,ᡠtanB=—bᑣB=3-.⌱ঞtanA+tanC-73=-^tanAtanCᓽtanA+tanC=-73(tanAtanC-1),tanA+tanCᡠtanB=-tan(A+C)=-=—..1-tanAtanC27rᙠABC5£(0,4)ᡠ5=—^—.2TCTC(2)ᵫ(1)8=,ᑣ^ABD=NCBD=—,S^+S^=S^ABDCBDABCᓽ,xcxlxsin+Lxaxlxsin&1.2ᐔ=—xcxaxsm——,232323ᓄc+a=cci,ᓽ—i—=1.Clca+4c=(a+4c)-+-j=5+—+-..5+2./—x-=9,\ac)ac\ac4cci3=,ᓽa=3,c=!"#$ac2ᡠa+4cḄᨬ'()9.20.(1)ᙠA/WCV3sinC+cosC=-nZ?+S-C,sinAᳮGsinCsinA+sinAcosC=sinB+sinC=sin(A+C)+sinC,ᓽVisinCsinA+siivlcosC=siivlcosC+cosAsinC+sinC,
9ᡠV3sinCsinA=cosAsinC+sinC5)sinCwO,ᡠJ^sinA-cosA=l,ᓽ^^sinA-cosA=ᡠsin(A—1]=7222I6J25)0K,3326'J1ᙠ┦MAABCB<~,ᦑ<8<.262hr.ᵫOPQᳮ----=-----=2R=2,ᓽb=2sinB,c=2sinC,sinBsinCᑣb1+c2=4(sin2fi+sin?)=-2cos2C-2cos23+4=-2cos(T-IB-2cos2B+4=V3sin2B-cos2B+4=2sin(25-2J+45)2<8<2ᑣW<28—(ᒹᡠ5<2$Z(23—1+4,,6,62666I6[ᡠ\+2Ḅ"(^)(5,6].21.(1)/(x)ḄQab)(0,+8),r(x)=lnx+l.c/'(x)=0ᑣe=,e!/xe(g,+8)!/'(x)>0,ᡠ/(x)Ḅᓫi⌴klm)(0,nᓫi⌴olm)
10(2)/(x)=xlnx+2,x>0222ᑣ/(x)>x——ᓽHnx+2ுx——,ᓽxlnx+2-x+—>0.XXX22c(x)=x
11x+2-X+—(x>0),ᑣ/(x)=liu——-2,214cu(x)=lnx——-(x>0),ᑣ□'(x)=+>0XXXᡠ“(x)ᙠ(0,+8)Kᓫi⌴o."(1)=-2(0,“y)=1-z02ᡠ{ᙠ|Ḅ)e(l,e),}'(%)=17=0,.᳝)xw(O,x(J!'(x)<0,(x)ᓫi⌴kXG(/,+OO)!,'(x)>0,(x)ᓫi⌴o,ᡠ(x)min="(ᐭ0)=Xo1nA0+2-/+-2=X0'2~+^~X0+22---cF2-2XQH---%%)4c45-(e-l)2=2—^—>2-eH—=->--0------%ee2ᡠ7i(x)>0,ᑣ.f(x)>x——.eA(izx2-2ax+l)22.(1)ᵫ⚪r(x)=T—~L,XER(ax2+l)/(x){ᙠ(,#22+1=()ᨵ#Ḅ᪷᳝,0,◤A=4t?-4a()ᓽᑣᦪaḄ"(^)(2)ᵫ(1)᳝+=20,=0,¡¢M¤2ᑣ0¤᳝¤1¤¤2,aax2—2ar+l=0¥¦§)ax2+1=2axᑣ:+1=2axaxf+1=2ax,]2ᡠ/(xJ+/(X2)=-^+~^=\+p=eJ2[—aax+1ax+12ax2ax2}2]2
12¢«ᦪ8(¬=6'-([/+*+]),ᑣ,(x)=e'—(x+1),¢(x)=e'-(x+l),ᑣx>0!'(x)=eX-l>0,ᡠ(x)ᙠ(0,+8)Kᓫi⌴o,//(0)=0,ᑣx>0!/z(x)>0,ᓽg'(x)>0,ᡠg(x)ᙠ(0,+8)Kᓫi⌴og®=0,ᑣe>0!g(x)>0,],ᡠx>0!e">—X"+x+1.211o,5¯/(%)+/(%)>—2Xi+᳝+121/\c11(33n+1.2᳝/(᳝+*2)+2X/2+᳝+21=]+22/°+±)=^^^=²³2´+(2µ[,cm(x)=xe2-v+(2-x)ev(00,ᡠm(x)ᙠ(0,1)Kᓫi⌴o,m(%)