2022年全国高考乙卷数学（理）试题

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ਭᵨOO2022ᐰὃᔁᦪᳮ⚪ᔁ᪗⚪ὃXXXὃ100ᑖ⚪XXX⚪ᑖᑖ⚗1.⚪ᑏ!"#Ḅ%&ஹ()ஹὃ*+,2../ᫀ12ᑏᙠ⚪ᓱ5OO6Iᔁ8⌱:⚪;.<=>ᦋ6IᔁḄᦻBCDEᔁᑖᐶ11.GᐰI{123,4,5},IᔠMRS0M={1,3},ᑣ()7A.2cMB.3eMC.4["D.50M2.^_z=l-2i,dz+f'+b=0,ᐸja,6mnᦪpᑣ8;A.a=\,b=-2B.a=-\,h=2C.a=\,b=2D.a=-\,b=-2OO3.^_ᔣstRS|£|=1,ᵫ=x,|£2᧤3,ᑣ£/=8;A.-2B.-1C.ID.24.{|}~ᙠᡂᨴ[ppᡂmᡃ6⚩□Ḅ⌼~pmẆ{|ᕜᙢᳫᕜḄpᵨᑮᦪ£U{஻}Ib=11¦I4=1+—p21p%+-----ᔆp…p«¬®pᐸjaOO3a"Np8°=1,2,…;.ᑣ8;A.

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cos/ᱏN£=wᑣ஺ḄKL᳛O.A.ᙠB.-C.D.—.2222.Pᔁ*2⚓ᐳ5⚓

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஺#1)Ḅ᩽§6᩽ᜧ.......§6.g±<%,ᑣaḄ³§µ¬..OO}ᔁ~ᑖ..-----------------ஹ¶·⚪......17.“8CḄᑁº48,CḄm»ᑖ«a,b,c,WX|sinCsin(4-5)=sin8sin(C-N)...非W“堞(1)¾|¿2a2=b2+c2i收..25....(2)#a=5,cos>4=—,ÀAN8CḄᕜÁ............18.᝞j☢Ä/BCDAD1CD,AD=CD,AADB=ZBDC,E/CḄ6.........一.O整O都..........氐K.....(1)¾|¿Æ☢8EO_LÆ☢/CDÉ......(2)Ê/8=8஺=2,1C8=6O஺&FᙠBD),ËÌCḄ☢ÍᨬÎÀCFÆ☢.......18஺ᡠᡂḄºḄ¡Ò§.OO.19.ÔᙢÖ>×ØḄÙ᛻ÛᳮWÝ₠ßᦋ⌼ᡂáâã☘ß.åæ᪍Ôè᪛ᩈḄ....ëᩞÍí⌱³á10îïè᪛ᩈðíñî᪛Ḅ᪷óôõ☢Í(ᓫ÷¿mDᩞ.Pᔁ*3⚓ᐳ5⚓

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4内o装o订o线(2(13.2))西次0-口~容比21？。唠8?,<:若上谕渔My湾.ಘ3，若有+向雄，谢演+H~・5a”•二洋百5苣洌“

5

6£ὃºᫀ^1.Aூ½᪆௃ூᑖ᪆௃ᐜᑏUÂᔠM,ᯠÅ⌲⚗ÈᓽÊூ˽௃ᵫ⚪HM={2,4,5}CmN⌱⚗HCAM<,BCD┯Ðᦑ⌱:A2.Aூ½᪆௃ூᑖ᪆௃ᐜUzCÓÔᐭCÖ1×ØD½yzÙᓽÊூ˽௃z=l+2iz+f/z+Z>=1-2i+a(l+2i)+/)=(\+a+b)+(2a-2)i\+a+h=Qᵫz+Ú'+6=0,2a-2=0ᦑ⌱:A3.Cூ½᪆௃ூᑖ᪆௃᪷STÛÜCᑭᵨᔣḄᦪÞ4½ᓽÊ.ூ˽௃½^'*\a-2b|2=|a|2-4a-b+4\b^,ß3à=1,|᧤y5,\a-2b|=3,.♦.9=1-4âB+4x3=13-4ᨌBC...▲B=1ᦑ⌱^C.4.Dºᫀ²1⚓Cᐳ21⚓

7ூ½᪆௃ூᑖ᪆௃᪷S᝞eN"("=1,2,…)CÓᑭᵨᦪᑡçè1%Ḅᐵ9ᑨëUègᔜ⚗ḄᜧâCᓽÊ4½.ூ˽௃½^íD%€N*(%=1,2,…)C,111--->----------ᡠQ஺|ᡭC%]q+——τ<%11cti+—>a+-------^-óᳮ%%+õCÊ&<4C2%1111->-----------j-----,a\+-------ö<஺1+-----------J-----ßíD“a+—a+—a+—,222%+—஺3a+23%a4ᦑ4<4C4>D3QùúûCÊ4>4>4>67>…C->/,ᦑA┯Ð3b>b>b,ᦑB┯Ð3]7s11üு12%+p,ᡭ<4,ᦑC┯Ð3%+…2஺6116+----------j—ுþ+---------j—%+-----ö஺2+…--------1C0b4cb7,ᦑDM<.%----a6-----%anᦑ⌱^D.5.Bூ½᪆௃ூᑖ᪆௃᪷Sÿᱥ
Ḅᑮᯖ
ḄAḄᙶ᪗Aᙶ᪗,ᓽᑮᫀ.ூ௃ᵫ⚪",#(1,0),ᑣ|/F|=|8#|=2,ᫀ)2⚓ᐳ21⚓

8ᓽAᑮ
x=-1Ḅ02,ᡠ3AḄᙶ᪗0-1+2=1,567Aᙠx9:;ᐭ/(1,2),ᡠ3|“@=J(3_1J+(O_2)2=2V2.ᦑ⌱HB6.Bூ᪆௃ூᑖ᪆௃᪷N᪾PQRSTᓽ.ூ௃᡻V)WXQR6=6+2஽=1+2=3,a=h-a=3-l=2,n=n+l=2,Z2[1\W2=-v-2=->0.01`/224᡻V)bXQRb=6+2a=3+4=7,a=h-a=7-2=5,n=n+l=3,3/>2-7212=-r-2=—>0.01`a25225᡻V)hXQR6=Z+2஻=7+10=17,a=b—஺=17—5=12,஻=஻+1=4,L211-y-2=lW2=.<0.01,nᓃpqr஻=4.a~12144ᦑ⌱HB7.Aூ᪆௃ூᑖ᪆௃stE#v☢8஺4ᓽᑨzA`᝞P3D0}~ᙶ᪗745=2,ᑖrv☢ᵨE#ABD,Ḅᔣ᪷NᔣḄᐵᓽᑨzBCD.}ூ௃ᫀ)3⚓ᐳ21⚓

9Hᙠ:Z8C3-44GAl,IC_L8஺DD11v☢ABCD,EFuv☢/5CD,ᡠ3EFLOR,0E,#ᑖ0ᨴ8cḄlᡠ3EFII/C,ᡠ3#_1.8஺7BDCDDஹ=D,ᡠ3EF_Lv☢7EFu:☢8=,ᡠ3v☢B,EF1v☢BDR,ᦑA`᝞P3஺0}~ᙶ᪗745=2,ᑣ(2,2,2),E(2,1,0),#(1,2,0),8(2,2,0),4(2,0,2),N(2,0,0),C(0,2,0),£¡0,2,2¢,ᑣEF=¡-1,1,0¢,£¡0,1,2¢,¤=¡2,2,0¢,9=¡2,0,2¢,¦=¡0,0,2¢,%=¡-2,2,0¢¨=©2,2,0¢7v☢#Ḅᔣ0ª=(«,¬,),in-EF=-X|+¬=0ᑣᨵ±=(2,2,-1),m-EB=+2z,=0}²ᳮv☢48஺Ḅᔣ0*=(1,-1,-1),v☢44cḄᔣ0µ=(1,1,0),v☢4G஺Ḅᔣ0Z=(1,1,-1),ᑣw?•஻]=2—2+1=1*0,ᡠ3v☢5Eᔆ¼v☢48஺5ᚖᦑB┯¿;0Á¼Â5vV,ᫀ)4⚓ᐳ21⚓

10ᡠ3v☢ᵨEF¼v☢44c5vVᦑC┯¿;0ü஻35vVᡠ3v☢ᵨļv☢4G஺5vVᦑD┯¿ᦑ⌱HA.\Æ/AEBX8.Dூ᪆௃ூᑖ᪆௃7Çᦪᑡ4
ḄÊÇ0g,g#o,᧕4*1,᪷N⚪"r✌⚗¼ÊÇÞ᪷NÇᦪᑡḄÌ⚗ᓽ.ூ௃H7ÇᦪᑡÎ஺“ÏḄÊÇ04,4X0,Ð4=1,ᑣ%-%=0¼⚪"ÑÒᡠ34b1,%(1-Zfa,=96ᑣrτÔ+r+&=…-----=168,“×/ØÙa-a=aq-aq=42225]ᡠ3Ú=4᜛'=3.ᦑ⌱HD.ᫀ)5⚓ᐳ21⚓

119.Cூ᪆௃ூᑖ᪆௃ᐜstàá┵Ḅ⚔Oᑮä☢ABCDᡠᙠåᙊWçpä☢ABCD☢èᨬᜧë02r2,ᑮá┵è⊤íîÞᑭᵨᙳëçᳮñá┵èḄᨬᜧëᑮàòá┵ḄèᨬᜧpᐸôḄë.ூ௃7òá┵ä☢0õöABCD,õöABCDᡠᙠåᙊ÷ø0Æ7õö/8COù
ᜳ0a,ᑣS஻BCO=`.ZCBDsina<^-AC-BD<^-2r-2r=2}¡àüàõöN880:öpýᡂ¢ᓽàá┵Ḅ⚔஺ᑮä☢N8CDᡠᙠåᙊWçpä☢☢èᨬᜧë0£+@=/àüàr=2h2ᓽÿ
ᡂ,ᦑ⌱C10.Dூ᪆௃ூᑖ᪆௃ᑣ.ᑖᙠᵬ"#$Ḅᭆ᳛Pw(ᙠ)"#$Ḅᭆ᳛஺)(ᙠ+"#$Ḅᭆ᳛P+.,-.ὅ01"2ᓽ45ூ6௃ᑣ7ᙠᵬ"#$Ḅᭆ᳛8ᑣpᵬ=2(1-p)pp+2pp(l-p)=2PM+;)-4Plp2]J2l}7ᙠ)"#$Ḅᭆ᳛P)>ᫀ6⚓ᐳ21⚓

12ᑣP)=2E1-P]HPR3+2P1P2E]KP3H=2P2EP|+P3H-4P|PW37ᙠ+"#$Ḅᭆ᳛P+ᑣP+=2E1-AHᵨ8+2R8E1-஺2H=2REA+H-4RpP2ᑣP,v-PL=2Pg+P3H-4Plp22-[22ER+;H-4Plp2P3]=2EPi-%HP?Y0PL-Pp5=2p2EP|+P3H-4p/2P3-[2p3EP|+P2H-4p/2Pj=2EP2-P3HPlY஺ᓽpᵬYp)p)Yp+ᑣᙠ+"#pᨬᜧ.⌱⚗Dᑨcde(⌱⚗BCᑨc┯i(Pᵬஹ)ஹ+Ḅ"#klᨵᐵ.⌱⚗Aᑨc┯i.ᦑ⌱D11.Cூ᪆௃ூᑖ᪆௃o⚪qrstuvwᯖyᙠx{t|ὡ~ᙊ஺ḄᑗwᑗyG,4ᑨcNᙠuvwḄt/KNg=a,AFFN=/3,ᓽ4sina,sin/?,cos£,ᙠAg£Nᵫ2X5/ᨴ2=5E஺+᜛H5/ὡ"ᵫdᳮ1gI||,ᨬ᪷uvwḄᑮ2b=3a,ᓽ4(ூ6௃o⚪qrstuvwᯖyᙠx{t|£~ᙊ஺ḄᑗwᑗyG,3ᡠ¤OGLNF(,¨cos/ὡ4=©ª0,ᡠ¤NᙠuvwḄ,ᡠ¤|OG|=a,|08=°,\GF\=b,t/ᨴNg=a,NgὡN=᜛tᵫcos/6N7^=—ᓽcosa=-,ᑣsina=—,sin/?=~,cos(3=K,55SeeᙠAFENsinZ.FFN=sin(;r-a-£)=sin(a+P)}2´.´463a3஻+4b=smacosp+cosasinp=—x—+-x—5c5c5cᵫdᳮ2c·=I=Ml_5csinZgN~2>ᫀ7⚓ᐳ21⚓

13ᐭml5c.5c3a+463a+46..5c5ca5aᡠ¤WE|=^smN/£?ᱏr?gN=7x—^—=——)|7V^|=—sin^=—x-=—NZDCZZNCNEI—LI3஻+4b5a4h-2a-½¾ᵨK|ឋ|=K^-—-=^—=2a,ᡠ¤2b=3a,ᓽ2=2,a212.Dூ᪆௃ூᑖ᪆௃᪷-ÀឋÁÂÃᩩÅᑮ/(x)+/(x-2)=-2,ÆÇᑮ/(3)+/(5)+…+/(21)=-10,/(4)+/(6)+...+/(22)=-10,ᯠ᪷ᩩÅᑮ“2)ḄÉᵫ⚪qᑮg(3)=6ÆÇᑮ/পḄÉᓽ4.ூ6௃¨y=g(x)ḄËÌᐵÍÎwx=2-Àᡠ¤g(2-x)=g(x+2),¨g(x)-/(x-4)=7,ᡠ¤g(x+2)-/(x-2)=7,ᓽg(x+2)=7+/Ï-2),¨/(x)+g(2-x)=5,ᡠ¤/(x)+g(x+2)=5,>ᫀ8⚓ᐳ21⚓

14Ðᐭ/U)+[7+f(x-2)]=5,ᓽ/(x)+/(x—2)=-2,ᡠ¤஻3)+fম+…+f(21)=(-2)x5=-10,/(4)+/(6)+...+/(22)=(-2)X5=-10.¨/(x)+g(2-x)=5,ᡠ¤/(0)+gফ=5,BP/(O)=l,ᡠ¤஻2)=-2-/(0)=-3.¨g(x)-/(X-4)=7,ᡠ¤g(x+4)-/(x)=7,½¨/(x)+g(2-x)=5,ὶg(2-x)+g(x+4)=12,ᡠ¤N=g(x)ḄËÌᐵÍy(3,6)Ø-À¨Ùᦪg(x)ḄÛR,ᡠ¤gব=6¨/(x)+g(x+2)=5,ᡠ¤஻l)=5-gব=-1.ᡠ¤Ý/(Þ)=ß)+/ফ+[஻3)+/(5)+…+/(21)]+[/(4)+/য+...+/(22)]=-1-3-10-10=K24஻=1ᦑ⌱Dூyá௃âᨵ-À{ᡈ-ÀØḄä⚪ååᩩÅ"2◚çὃé◤⌕᪷ÂÃᩩÅ01ាíḄîᓄᯠᑮᡠ◤ḄKðᦪÉᡈᐵñòÆÇ⚪.313.—##0.310ூ᪆௃ூᑖ᪆௃᪷ôᐺᭆö÷øᓽ4ூ6௃Æ5ùúûüý⌱3ùḄþÿᦪ
C=10ᵬஹᐭ⌱Ḅᦪ
C=3,ᡠᵬஹᐭ⌱Ḅᭆ᳛='3ᦑᫀ
5ᫀ9⚓!ᐳ21⚓

1514.&X-2)2+&^-3)2=13^&X-2)2+&JV-1)2=5BKI+
yூ1᪆௃ூᑖ᪆௃5ᙊḄ7
x2+/+Dx+a+=0,᪷=ᡠ⌱>Ḅᙶ᪗!Aᑮ7C!1AᓽE;ூG1௃1H⚪J5ᙊḄ7
ᑗ+=0,L=0=0MN&0,0),&4,0),&-1,1),ᑣ,16+4஺+=01A!D=-4,1+1-O+E+=0E=-6ᡠᙊḄ7
x2+y2-4x-6y=0,ᓽ(x-2)2+(y—3X=13F=0F=OMN&0,0),&4,0),&4,2),ᑣ!16+4஺+=0,1A.D=-4,16+4+4D+2E+=0E=-2ᡠᙊḄ7
x2+/-4x-2y=0,ᓽ&x-2)?+&y-l)2=5F=0F=0QMN&0,0),&4,2),&-1,1),ᑣl+l-O+E+b=0,1A஺=-§16+4+4஺+2£+LQ14ᡠᙊḄ7
_2+/`ab`?c=0,16l+l-D+£+F=01A,D=-^-,MN&T1),&4,0),&4,2),ᑣ16+4஺+/=016+4+4D+2E+F=0E=-2169ᡠᙊḄ7
x?+y--—x-2y--=0,ᓽ25"ᫀ10⚓!ᐳ21⚓

16ᦑᫀ
(x-2)2+(y-3)2=13ᡈ(x-2X+(y-l)2=5ᡈூ1᪆௃ூᑖ᪆௃✌ᐜ⊤jkT,᪷=/'(7)=mnk9,o᪷=x=p
qᦪḄr>!ᓽEnk஺Ḅst,uvA1;ூG1௃1w
/(X)=COS(3X+O),(ty>o,0<஺(ᐔ)ᡠᨬᕜ=(!w
/(r)=cos=cos(2ᐔ+(p)=coᓽ=710<9<ᐔ!ᡠe=7!ᓽ/(x)=cosCOX+—x=W
஻Ḅr>!ᡠ+F=W+1Aᗂ=3+9,keZ,9962w
0>0,ᡠ=00mM=3;ᦑᫀ
3ூ1᪆௃ூᑖ᪆௃ᵫᓰ,ᑖqᦪ/(x)=2a*-ex2Ḅ᩽t>᩽ᜧt>!EAxe(-<»,ᓛ)஺p,+8)!/'(x)<0,xe(x,,X2)!r(x)>0,oᑖa>l0!᪀⌼qᦪg(x)=lna"*,᪷=´ᦪḄµᔠJ·µᔠ¬ᓽEAkᫀ.ூG1௃1f'{x}=21na-ar-2ex,ᫀ11⚓!ᐳ21⚓

17w
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&%,lna/),ᑣᑗÕḄ×᳛
8'Ø)="0.*,ᦑᑗÕ7
y-Inad஺=h?a.*&x-x0),ᑣᨵ`Ina•a"=-xIn2a-axT>,01Ax0=J—,InaᑣᑗÕḄ×᳛
ln%s±=eln%!w
qᦪy=lna-a*«qᦪV=exḄ¬ᨵ¡©b¯Ḅ°>!ᡠeln%

18ூ>à௃á⚪ὃãäqᦪḄ᩽t>å⚪!ὃãä´ᦪḄæçJ·!ὃãäèᓄêëìᑖí¥¦êë,ᨵ`îḄïð.17.&1)ñ1᪆(2)14ூ1᪆௃ூᑖ᪆௃&1)ᑭᵨ¡ôõḄö÷øᓄù!o᪷=öîᳮûöîᳮᓄô
ü!uvᓽEAý;&2)᪷=&1)Ḅµ¦µᔠûöîᳮnkþ!uvEnAb+c,ᓽEA1.পýÿ:
sinCsin(4-8)=sin8sin(C-%),ᡠsinCsinAcos2-sinCsinBcosN=sin8sinCcosN-sin8sinAcosC,a2+c2-b2~b2+c2-a2,a2+b2-c2ᡠac-----------2bc------------=-ab----------lac2bclaba2+c2-b2/,22\a2+b2-c2Hᓽn-----------2+c-a2)=------------,ᡠ2/=+஺2;ফ25!
a=5,cos4=§yᵫপ&/+஺2=5'(,ᵫ)*+ᳮ-&/=/+c?-cos”,0ᫀ213⚓6ᐳ21⚓

19JU!|50——-be=25,31ᡠ>==,2ᦑ@+஺)2=஻+஺2+>஺=50+31=81,ᡠ6+c=9,ᡠA48cḄᕜFa+6+c=14.18.(1)HIJKL᪆(2)CᡝOP☢48஺ᡠᡂḄSḄT*UV7ூ᪆௃ூᑖ᪆௃(1)᪷\]^ᐵ`HIgbC8஺6&ᑮd8=CB,fᔠhῪjSkjlᔠm&ᑮᚖoᐵ`6fᔠ☢☢ᚖoḄᑨ++ᳮᓽ-HIq(2)᪷\rs+ᳮ⌮ᵨ&ᑮ8E_L£)E,z{|}~oSᙶ᪗`6fᔠl☢SḄᑣᓽ-.(1)
4D=CD,EZCḄ6ᡠZCLDEqᙠbZ8Z)ACBD6
=CD,ZADB=ZCDB,DB=DB,ᡠ[\4BD]\CBD,ᡠ/8=C8,
E/CḄ6ᡠ/CL8Eq
D£,8EuP☢8£7),DEcBE=E,ᡠ/C_LP☢BE஺6
dCuP☢ᡠP☢8ED_LP☢/CD.(2)EF,ᵫ(1)^61CJ■P☢8,
EFuP☢BED,ᡠᡠ[SaFc=g4c-EF,6Eᨬ6ᓽbdCḄ☢ᨬ.
bC2஺6ᡠC8=/8=2,
4C8=60஺6ᡠhjSk6
EZCḄ6ᡠN£=EC=I,BE=6,0ᫀ214⚓6ᐳ21⚓

20
4£>_LCD,ᡠ஺E=1/C=l,ᙠADEB^,DE2+BE2=BD2«ᡠ[BELDE.Eᙶ᪗{|᝞¢ᡠ£Ḅ}~oSᙶ᪗`E-¤z,ᑣ4(1,0,0),8(0,¥,0),0(0,0¦),ᡠz=(-1,0,1),§=¨1,6,01©P☢48஺Ḅmªᔣ¬3=(x,y,z),ᑣ_ᔆ,®y=6,¯3,6,3,n-AB=-x+43y=0''
c(T0,0)°"ᡠ²ᵴᡠ஺஺ᓽ6´=᱘=¶64®x©bOP☢dᓽᡠᡂḄSḄT*Uᑴ,ᡠsin஺=|cos(஻,C77'=,ᡠCFOP☢480ᡠᡂḄSḄT*U⌳.719.(l)0.06m2;0.39m3ফ0.97(3)1209m3ூ᪆௃ூᑖ᪆௃(1)»᪵½Ḅm¾᪷¿ÀÁ☢ḄPᙳUÃm¾ᩞ¬PᙳU6ᓽ-ÅÆ᪍ÈÉÊ᪛ᩈPᙳm¾Ḅ᪷¿ÀÁ☢OPᙳm¾Ḅᩞ¬q0ᫀ215⚓6ᐳ21⚓

21(2)Íᐭ⚪ÐÑᐵ`ᦪÓÔÕᓽ-Ö&᪵½ḄÑᐵ`ᦪU!(3)×\᪛ᩈḄᩞ¬Oᐸ᪷¿ÀÁ☢ÙÚᡂTÛ6ᑡÝKᓽ-Ö&Æ᪍ÈÉÊ᪛ᩈḄÞᩞ¬ḄÅU.(1)᪵½10¾ÉÊ᪛ᩈḄ᪷¿ÀÁ☢ḄPᙳUß=᱅=0.06᪵½10¾ÉÊ᪛ᩈḄᩞ¬ḄPᙳUá=*=0.39\ã-ÅÆ᪍ÈÉÊ᪛ᩈPᙳm¾Ḅ᪷¿ÀÁ☢0.06m2,Pᙳm¾Ḅᩞ¬0.39m6(2)1010Z(x.-j)(ä-ᑓ»ç-1ᔙé—ê?ë!_ᕣí2_ᓽ)=0.2474-10x0.06x0.39—0334î0.0134”0§77(0.038-10x0.062)(1.6158-10x0.39?)^0.0001896-0.01377ᑣrx0.97(3)©Æ᪍ÈÉÊ᪛ᩈḄÞᩞ¬ḄÅUKm36]^᪛ᩈḄᩞ¬Oᐸ᪷¿ÀÁ☢ÙÚᡂTÛ6-&ï=á6ð&y=1209m\ᑣÆ᪍ÈÉÊ᪛ᩈḄÞᩞ¬Å1209m320.(1)?+?=1(2)(0,-2)ூ᪆௃ூᑖ᪆௃(1)ñÐ+Íᐭ©»ḄÝKÖᓽ-q(2)©»olÝK6OòᙊCḄÝKὶ|6ᑖõö÷øù᳛ᔲüᙠ6ᓽ-&.(1)0ᫀ216⚓6ᐳ21⚓

22!©òᙊEḄÝK>W+஻y2=i,J/'O,_2(,8'|,-14஻=1ᑣ19,6&ÿ«=7>+஻=13414ᡠᙊEḄ^+ߟ=1.43232J0,-2,S-,-l,ᡠZB:y+2=§x,22জ)*+PL-2Ḅ./0᳛23ᙠ5./6=1.7ᐭ6+ᓃ=1,34:;஻1,<5N1,->57ᐭN8y=gx-2,:;7A+3,B5ᵫA=A;ᑮ“2#+5,>.H;"N:᜛=2->x-2,*+0,-2.ঝ)*+P஺5-2Ḅ./0᳛3ᙠ5MAx-y-O+2=0,25P,\R,S.+2)=0ὶV5;(3•+4)x2-6Z(2+k)x+3k(k+4)=06k(2+k)-8(2+%)X1+x2c+3k2+43`+4:;3A(4+^)4(4+442b2)[\]2aa=3k+43`+4de+fg=h**y=ytk+3,l,“3ᨴ+6-nl.ὶVj,:;:H;opHN-.y-y=eb:x-R,2q(0,-2),7ᐭ᦮ᳮ;2a+x)-6(y+a)+Xa+g-3yM_12=C,2iq*7ᐭ,;244+12%2+96+48A-24&-48-48A+24᮱_36/2-48=0,}ᯠᡂV55:;./"N*+0,-2.ூ+௃H+ஹ⚪Ḅᨵᫀ17⚓5ᐳ21⚓

23জᱯᐭ<5H5ebᐵ¡ঝ.¢£ᳮஹ¤¥5¦ᙠ¤¥£ᳮḄ*[§¨5A;ᑮ.21.(l)_V=2x(2)(-8,-1)ூª᪆௃ூᑖ᪆௃(1)ᐜ¥ᑗ+,eH¯¥0᳛ᓽ:(2)H¯5±஺ᑖ²³´5±6ᑖ(-1,0),(0,+8)µᑖẆ·(1)/(x)Ḅ¸¹(-1,+8)ºa=1pJ(x)=ln(l+x)+Tf(0)=0,ᡠᑗ+(0,0)/(x)=-+¾,/(0)=2,ᡠe1+xeᑗ/0᳛2ᡠÀ/N=/(x)ᙠ+(0J(0))ᜐḄᑗ/᜛=2xফZ7Y/(x)=ln(l+x)4--eÄX)Å=¥+Ç])l+xeஹ(l+x)evMg(x)=eஹ+a(1-M)1°)a>0,ºxe(-1,0),g(x)=eஹ+a(1)>0,ᓽ/'(x)>0ᡠ/(x)ᙠ(-1,0)ᓫÌ⌴ÎJ(x)0ᡠg(x)ᙠ(0,+«>)ᓫÌ⌴Îᡠg(x)>g(0)=1+Ö0,ᓽf'(x)>0ᡠ/(x)ᙠ(0,+oo)ᓫÌ⌴ÎJ(x)>/(0)=0ᦑ/(x)ᙠ(0,+8)ÑᨵÒ+52ᔠ⚪Ô3°)(1)ºX€(0,+8),ᑣg'(x)=e*-2ax>0,ᡠg(x)ᙠ(0,+oo)ᓫÌ⌴Îg(0)=1+Q0ᫀ18⚓5ᐳ21⚓

24ᡠ3ᙠme(0,1)5Ú;g(m)=05ᓽf\m)=0ºxe(0,஻?)5r(x)<0J,(x)ᓫÌ⌴ݺÞ6(,+8),/(ß)>0,/(6)ᓫÌ⌴Îᡠºxe(0,MJ(x)Qᡠg'(x)ᙠ(TO)ᓫÌ⌴Î,1g(-l)=-+2<0,g(0)=l>0fleᡠ3ᙠ⊟(-1,0),Ú;g'(")=0ºX€(-1,஻),g'(x)<0,g(x)ᓫÌ⌴ݺxe(n,0),g'(x)>0,g(x)ᓫÌ⌴Î,g(x)0eᡠ3ᙠfe(-)5Ú;g(0=0,ᓽf\t)=0ºxe(-lj)J(x)ᓫÌ⌴Î5ºxe(r,0),/(x)ᓫÌ⌴Ýᨵx—--coA/(0)=0,ᡠºxe(f,0),஻x)>0ᡠ/")ᙠ(-1,/)ᨵáÒ+,“,0)bÒ+ᓽ/পᙠ(-1,0)ᨵáÒ+ᡠëᔠ⚪Ôᡠ)“X)ᙠìí(-1,0),(0,+8)ᔜាᨵÒ+5H஺Ḅðò(9,-1)ᫀ19⚓5ᐳ21⚓

25ூ+௃+ó⚪Ḅᐵôõ±஺Ḅòö÷ᔠᳮᑖ²5ᔲùú¦ᵨ5ᔲü◤⌕ÿ
ᓽ⌕☢.22.(1)yf3x+y+2m=0195(2)---<«?<—''122ூ"᪆௃ூᑖ᪆௃(1)᪷'᩽ᙶ᪗+,-ᙶ᪗Ḅ/ᓄ12ᜐᳮᓽ5(2)ὶ7/+CḄ:;ᵨᣚᐗ?ᜐᳮ᪷'@AaḄCDFG"HḄFᓽ.(1)IJ/Kpsin(0+§K+H=0,ᡠT;p-sin6+-(K056+%=0XIJp-sin6»=y,0-cos6»=x,ᡠTᓄ^Jgy+`a+b=0᦮ᳮd/Ḅ,-ᙶ᪗:KVJx+y+2m=0(2)ὶ7/+஺Ḅ:ᓽhx=JJcos2%,y=2sinfjᐭJJx+y+2஻?=0md3cos2f+2sinf+2b=0,ᡠT3(l-2sin")+2sin/+2b=0,ᓄ^J
6sin?f+2sinf+3+2b=0,⌕qI+Cᨵ1ᐳt,ᑣ2/n=6sin2/-2sin/-3ᨵ",vᫀx20⚓ᐳ21⚓

26zsin/=4,ᑣz/(஻)=6/-2஺-3,(-IWaWl),~J஺=:ᔣ6ᡠT/3)M=/(T)=6+2-3=5,ᡠT--<2w<56,195mḄCDFJ---0,h>0,c>0,ᑣ->o>0஺>0333____ᡠTJ+;6£|ᓽ()g,ᡠT"cj,mᓽa=b=c=gefgh.(2)KIJa>0,b>0,c>0,ᡠTb+c2y[bc»Q+cN2Vac,a+h>2y[ah,333ᡠT,0-b?b+c2\[bc2\/abca+c2>fac2y1abca+b333¢iL-_abcaab5c2a2-A24e21-----1-----1-----<--+--¥------—------b+ca+ca+b2>Jabclyfabclyjabc2y/abc2y/ihc஺=6=c¦C§.vᫀx21⚓ᐳ21⚓