衡水一本通--数学

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ᓄ2á៉ḄᦪÂᵨ6ḄpqᨬA.z{ឋὃᓫឋ:3142g6,ூæ1௃(2021èéêëÇÒì)HIíᦪ“=_02b=0/(x)>°,ᓽf(x)ᙠ(0,+00)ᓫ⌴/(2)᜻Ꮤឋ:24/397

22ூB1௃D.ᦪ/(X)FGHᙠRḄ᜻.ᦪ/(1)=1,Jx<0=10g(—x)+m,ᑣ'ᦪ஻?=42A.-1B.0C.1D.2ூUᫀ௃CூW᪆௃/(x)FGHᙠRḄ᜻.ᦪ/£1)=1,Zx<0/(x)=log(ߟx)+m,42f[ߟ>|=log[+m=-2+m=-1,/.m=ᦑ⌱C.I)ூ!"#௃a⚪c⌕ὃ>.ᦪ᜻ᏔឋḄeᵨfgh.ᦪ:ijᦪḄklmn.ᦪ᜻ᏔឋḄGHᓽopqrὃ⚪s.ூB2௃(2021tuvwxyz{|xὃ}).ᦪᙠ(-8,+8)ᓫ⌴Z᜻.ᦪ.D/(1)=1,ᑣ-147(x-2)41ḄᐝḄ:F().A.[-2,2]B.[-U]C.[0,4]D.[1,3]ூUᫀ௃DூW᪆௃ᵫ.ᦪ/(x)᜻.ᦪ/(—1)=/(1)=1+1«/(2)41ᓽ/(1)42)47(—1),/(x)ᙠ(-8,+8)ᓫ⌴ᡠᓽ14xW3,ᦑ⌱D.ὃ>ᕜ|ឋூB1௃(2021z{)GHᙠRḄ.ᦪ/(x)/(2+x)=f(x),f(2-x)=f(x),Jxe[0,l]/(x)=f,ᑣ.ᦪf(x)Ḅg(x)=NḄḄ¡"¢ᦪ()A.3B.4C.5D.6ூUᫀ௃AூW᪆௃ᵫ⚪¤hf(x)Ḅᕜ|2,ᐵqx=1¦§Z/(2-(x+2))=/(—x)=/(x+2)=/(x),/./(x)Ꮤ.ᦪᓽof(x)ஹg(x)Ḅ᝞ª:25/397

23ᓽ/(X)g(x)¡q(0,0),(l,D{",ᦑ⌱A.YIூ!"#௃(1)/(஻?+x)=/(x)ᨵ/(¬Ḅᕜ|m®(2)/(஻¯)=/(¬ᨵ/(ᐵq°=2ὃ>ᨬ:ூB1±²ha>0,³.ᦪf(x)=238*'+2°16,a±)Ḅᨬᜧ:M,ᨬ<:N,·¸M+N=()2018x+lA.2016B.2018C.4032D.4034ூUᫀ௃DூW᪆௃ᵫ⚪¤f(x)=26*'+2016=2018——1—.¹y=201ᓽ+Iᙠ»-a,a±Fᓫ⌴Ḅᡠ2018x+l2018x+lf(x)=2018—2(“+±ᙠLa,a±Fᓫ⌴ḄᡠM=*a),N=fi-a),ᡠM+N=f(a)+f(22a)=4036---------_---------=4034.2018a+l2018a+lூB2௃(2021z{).ᦪ/(x)=lnx+ln(2-x)Ḅᨬᜧ:.ூUᫀ௃0ூW᪆௃ᵫ/(%)=lnx+ln(2-Â)=ln»-(x-l)?+1±,Z0bog(x)}Ḅᨬᜧ:.ூUᫀ௃1,-[log2X,02h(x)=3—xF-x+3,x>2o.ᦪᑣA(X)max=h(2)=1.26/397

24ὃ>¦§ឋ:ூB1௃(2021GÓÔÕÖy᪥z{ᨴὃ).ᦪf(x)=Ù_Ḅ3AA.ᐵqÚ"¦§B.ᐵqxÛ¦§C.ᐵqyÛ¦§D.ᐵqÜÝy=x¦§ூUᫀ௃CூW᪆௃.ᦪ/(X)=Ä{=3'+3rḄGHÞR7Zf(-x)=y+3-*=/(x),ᦑß.ᦪᏔ.ᦪyᐵqyÛ¦§ᦑ⌱c.ூ!"#௃.ᦪxràḄá⦧ᐵã(D.ᦪäX)ᐵqXÛ¦§ᑣᨵ/(x)=-/(x)®(2).ᦪfMᐵqyÛ¦§ᑣᨵ-(3).ᦪ/(x)ᐵqÚ"¦§ᑣᨵ/(%)=-஺(Â)®(4).ᦪᐵqÜÝy=x¦§ᑣ/a)ᐸç.ᦪFè¢.ᦪ.ὃ>ᓫឋ᜻Ꮤឋᕜ|ឋéᔠê⚪ூB1௃ூ2019ìzὃíî௃³/a),g(x)FGHᙠRḄð¢ᕜ|.ᦪ/(x)Ḅᕜ|4,g(x)Ḅᕜ|__________Z:(x+2),0/(x)=Jl-(x—l)2g(x)=T,10.D.2ᙠñò(0,9±ᐵqxḄkó/(x)=g(x)ᨵ8¢èḄ'ᦪ᪷ᑣkḄ:F▲.ூUᫀ௃ô»ᓧ±ூW᪆௃ö÷.ᦪfix),g(x)Ḅ᝞ᵫoh.ᦪya)=Ji—஺—1)2Ḅ-2Oo-X^O^-o—^27/397

258(þ)=1(1<¯42,3<þ44,5<46,7<%48)Ḅÿᨵ2ᓽᙠ(0,9ᐵxḄ2/(X)=g(x)ᨵ2Ḅᦪ᪷⌕"ᐵxḄ/(©=g(x)ᨵ8Ḅᦪ᪷ᑣ/(%)=4_(1)2,xe(0,2+g(x)=ᦇ(x+2),xe(0,lḄ/0ᨵ2Ḅᵫ(1,0)ᑮ3456y+2Z=0Ḅ9:;<=)᝕1=,?=@=AB>0)+14•.•F(62,0),(1,1)G4ḄH᳛&=11334L%/஺1)+/2)ᑣᑡypজ/(X)/01aᐵ34x=2022¡ঝ/(2022)=0¡ঞy=/পᙠ஺1%2஺¤";¦aᦪ¡ট/()>4).ᐸ32AkḄᦪ()A.1B.2C.3D.4ூᫀ௃Aூ?᪆௃u;/(x);᜻aᦪᡠ±/(—x)=—/(x),ᡠ±/(x+2)=—/(x)=/(-%),ᡠ±³;x=l,u;/(x+2)=—/(x),ᡠ±/(x+4)=—஻x+2)="x),ᡠ±ᕜ¶;4,ᡠ±³x=l+4ᦇ஺eZ),ᦑx=2022¸ᔠᡠ±জAk¡/(2022)=/(4x505+2)=/(2)=-/(0),u;/(x)sᙠRḄ᜻aᦪᡠ±,40)=0,ᡠ±/(2022)=0,ᡠ±ঝAk¡u;VX1,º2ew஺1Xº2ᨵ)+xJ(X2)>XJ(X|)+xj(x),228/397

26ᡠ±;(6(1)6/(*2))>2(/(xJ—/(&))ᓽ(¾6¿2)(/(À)6/(¿2))>°ᡠ±“X)ᙠw0,1;Âaᦪᡠ±/(X)ᙠw4%,41+1(ÃZ);Âaᦪ,ᡠ±y=/(x)ᙠw2020,2021;Âaᦪᡠ±ঞAk;(3ஹᡠ±ᡠ±টAkᓽAkḄᦪ;I\)I7ᦑ⌱A.ூWXY௃[⚪ὃ^Ê0aᦪḄᕜ¶ËᓫÍឋឋḄLᔠÎᵨ?[⚪Ḅᐵtsᐜᵫaᦪ;᜻aᦪpᔠf(x+2)=-f(x),=ᑮ/(x+2)=-/(x)=/(-x)Ë/(x+4)=-/(x+2)=/(x),ÑÒ=ᑮaᦪḄឋËᕜ¶ឋ᪷ÓᩩÕ=m(Ö6஽)w/(ᓛ)6/(஽)>0,=ᑮaᦪḄᓫÍឋ.ØaᦪÙḄᨬÛ⚪ூᐺx௃rf(x)=x2-2ax-lᙠw0,2ḄᨬᜧSËᨬÞS.ூ?᪆௃f(x)=(x—a)2—1—a2,³;x=a.(1)ßa<0ᵫ/জf(X)max=f(2)=3—4a.(2)ß02,ᵫ/ট4f(x)ᙠw2,4s¦aᦪ...f(x)min=f(4)=18-8a.ß2Wa£lf(x)min=f(a)=2—a?.29/397

276—4a,a<2,••f(x)in6F2—a2,24.ফMØaᦪḄᨬᜧ(Þ)Srÿᦪ.ூ2ᦪy=-x2—2ax(02<""f(x)ᙠa,a+14@ᦪ".*.g(a)=f(a)=a2—4a—4.a2-2a-7,a2.ூ8C௃(1)/(E=F+H+°3I0)ᙠ23"2,J4Ḅᨬ"☢ᑖ᪆஺>0ḄᔜOPQজS#$%“=__ᓃᙠ23m,Jᑁ"ᑣᨬ8&Y(Z_)"ᨬᜧ&Y(஻?),/(஻)]Ḅ^ᜧὅ;2a2aঝSbc஻?"ᑣ/(X)ᙠ23Jᑁ&@ᦪ"ᑣᨬᜧ&f(n)7ᨬ8&f(in);2aঝSᑣf(x)ᙠ23*"?,஻eᑁ&?ᦪ"ᑣᨬ8&/("),ᨬᜧ&Y(m).2af⚪04ᦪhiᦪjkὃ1.(mὃᐰo1ᔁᳮᦪ6)ᦪ/")=r-2/ḄsᙠtᜐḄᑗ!wx&()A.y=-2x-1B.y=-2x+\C.y=2x-3D.y=2x+lூyᫀ௃B30/397

28ூ᪆௃f(x)=x4-2x\.\/z(x)=4?-6x2,/r(l)=-2,"ᡠᑗ!Ḅwx&y+1=-2(x-1),ᓽy=—2x+1,ᦑ⌱B.x,x<02.(2019ὃ)஺E£R,ᦪ/(x)=<11,Sᦪ)=/(X)-ax-஻ាbb(a+l)d+ax,132ᨵ3t"ᑣA.a<-\,b<0B.a<-\,b>0C.d>-\,b<0D.a>-\,b>0ூyᫀ௃Cூ᪆௃;x<0<0,y=f(J,-ᑁb)ᙠ[0,+8)4ᓫ®⌴@"ᑣ°/•(1)-ax-bᨬIᨵ0,ᓽG>-1<"¶y>0x£(a+l,+00),<ᦪ.J_L/J__I-y»yᓫ®⌴@"¶yvox£[0,4+1),<ᦪᓫ®⌴?"ᑣᦪᨬ¡ᨵ2/-\\Jt.᪷¼⚪´"ᦪy=/(x)-OY-bាᨵ3t=ᦪy=/(x)--À-Áᙠ(-8,0)4ᨵbt"ᙠ[0,+8)4ᨵ2t"᝞Q<0(-b>0,b<0,1-a>0,b>—1(a+1)3,Ãi]>-\,X0.ᦑ⌱ai-aF(a+l)3-L(a+l)(a+l)2-b<06'32c.[x2-2ax+2a,x<1,3.(2019ÆmὃᜩÈᳮᦪ)aeR,:ᦪ/(x)=ீSᐵËxḄ²Ì/(x)20ᙠ[x-aInx,x>1.R4ឤᡂÐ"ᑣaḄ&A.[0,1]B.[0,2]C.[0,e]D.[l,e]ூyᫀ௃Cூ᪆௃;x=l<"/(1)=l—2a+2a=1>0ឤᡂТ;x<1<"/(x)=r-2ax+2a>0<=>ᑣg(x)b■…-(…2(Jx)12aNfឤᡂÐ,¶g(x)=£+x—1X-11-X1—X1—X31/397

29=—h—x+1b2ஹ4Ö×2|I------i--21=0,;l-xn-1-,ᓽÙ=o<ÌÚ".•.2a2g(x)=o,τl-X1I(1-X)-11-XmaxIJ0.;Üு1<"f(x)=x-alnx>0,ᓽ——ឤᡂÐ"¶஻(x)=——,ᑣ'(x)=------>;x>eInxInÙ(Inx)"<"h'(x)>0,ᦪh(x)ᓫ®⌴@";0<Ù

302.ᜐᳮ8ᑗᨵᐵḄ;ᦪ<⚪>?᪷AஹᑗஹᑗḄCDᐵEᑡ;ᦪḄF4560;ᦪ஺পᑗᜐḄᦪᑗḄ!᳛஺(2)ᑗᙠᑗI஺(3)ᑗᙠI஺1ஹN)ᦪᓫLOPḄQR(1)N)ᦪf(x)Ḅ)6U஺(2)Vಘ஺(3)0'X"/(x)>0,0]ᙠ)6UᑁḄ_ᑖaᓫL⌴cOP஺(4)0'X"/(x)<0,0]ᙠ)6UᑁḄ_ᑖaᓫL⌴fOP஺ᦪ82.ᦪywᙠOP3iI⌴cᑣ/(x)K),(x)>0ᙠভiIᡂm”7WᙠᦪᓫLឋ(“iIᓫL⌴c”Ḅᐙᑖ's⌕ᩩv஺3ஹ᪷AᦪᓫLឋ;ᦪḄ(wxy(1)ᑭᵨ]ᔠPḄᒹ|ᐵEᜐᳮ}y=/U)ᙠ(஺)IᓫLᑣOP(i*ᓫLOPḄ]஺(2)y(x)acᦪḄᐙ⌕ᩩv5ḄX63b)ᨵV(x)K)ᙠ3,ᑗᑁḄ(OPIV(X)'ឤa*5"ḄX'ḕᶍᔲᑣ0஺4ஹᑜᑖᦪḄᓫLOP⌕ᙠᦪ)6Uᑁ⌕N)ᦪa஺ḄᦪḄP஺5ஹDᦪa0Ḅ'¡ᡠᙠOPḄᓫLឋ᝞¤x)=x3,/a)=3x2N0(f(x)=0ᙠx=0§ᑮ)©)ᙠRIcᦪ஺1ஹᦪ᩽¬<⚪Ḅ?®¯°±0⚪²ᶍ(1)³´ᑨᦪ᩽¬Ḅ¶·஺ᐜ¸ᦪa0Ḅ¹ᑨᦪa0ḄḄºஹ»¼½Ḅᦪ¾஺(2)¿³ᦪ᩽¬஺f(x)-->/(x)=0Ḅ᪷((>ᑡ⊤ÁÂ/(x)ᙠ/(x)=0Ḅ᪷Ḅᦪ8ᦪ▬ļ½Ḅ¾((>ÅÆ஺᩽¬ஹᨬ¬(3)¿³᩽¬;ᦪ஺Çᦪf(x)ᙠ(ÈÉ)ᜐ§Ê᩽¬ᑣ/(Ë)=0,ᙠ̺ஹ»¼½Ḅᦪ¬¾Í஺2ஹᦪ./U)ᙠÎOPÏa,ᑗᑁḄᨬᜧ¬ᨬ¬Ḅxy}ÇᡠÑḄÎOPmᑗ'|ᨵ;ᦪᑣ◤ᦪÓr)F/a)=oᙠOPmᑗᑁḄ᪷¹Ö×ØᦪXÙḄ᪷Ḅᦪ¬ÚÌᦪ¬8J(a),¤iÛÜᐸᨬᜧḄ(Dᨬᜧ¬ᨬḄ(Dᨬ¬஺ÇᡠÑḄÎOPÞᑗ|ᨵ;ᦪᑣ◤ᦪ/(X)>&;ᦪᑖ¯ᑨᦪḄᓫLឋß2Êᑮᦪᐔ0Ḅᨬ¬஺33/397

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32A.y=fx+JB.y=2xc.y=-D.-JX424424ூᫀ௃Bee'(x—1)/22ூ᪆௃ᵫ⚪/(2)=_,ff(x}=ᑣ(2)=_ᡠ"ᑗ$%&'(—3=3஺+2)2x2424ᓽy=—x.ᦑ⌱B.4ூ/012௃3⚪4⌕ὃ78ᦪḄ;<=>ὃ7?@$1AB%&ḄCᵨEFGẠ⚪.ὃ78ᦪIJᦪᓫLឋNூO1௃(2021•RᓭTU+V)WXJᦪ/(x)Ḅ8Jᦪ'/'(x),YZ[=xeR,f'(x)-f(x)<0,/(2)=e2,^/஺)<+,ᑣ/Ḅ_`b'()A.(0,2)B.(2,+oo)C.(0,e2)D.(e2,+oo)ூᫀ௃Bூᑖ᪆௃᪀⌼Jᦪg(f)=")—l'nJᦪg஺)ᓫL⌴pqrsBstFg(0a>bD.b>c>aூᫀ௃Bூᑖ᪆௃JᦪḄ8ᦪ᪷8ᦪḄ¡ᑮ/(X)ᙠ(1,+00)ᓃᓫL⌴¤xᔠJᦪḄᓫLឋᓽw¦§ᑮᫀ.35/397

33e*1e'(x-l)(e*ஹூ᪆௃ᵫ⚪=Jᦪ/(©)=_++++©,w/(%)=--------+x-l=(x-l)|—I+1x2f)xe(1,+8)¯°(x)>0,/(%)ᙠ(1,+8)ᓫL⌴¤,²'1<2°3<2,Iog25>k>g24=2,ᡠ"2°-3<2wXᙠé1ᜐḄ8ᦪᓽ'ᙠê1ᜐḄᑗ$A᳛.᪷8JᦪÓÔwXNxG(-00,-3)¯f(x)<0,ᙠxd(-3,1)¯f'(x)>0••Jᦪy=f(x)ᙠ(-8,-3)ᓫL⌴pᙠ(-3,1)ᓫL⌴¤ᦑঞãäᑣ-3ÁJᦪy=f(x)Ḅ᩽`1ᦑজãä•.•ᙠ(-3,1)ᓫL⌴¤rÁJᦪy=f(x)Ḅᨬ`1ᦑঝrãä•.•Jᦪy=f(x)ᙠx=0ᜐḄ8ᦪᜧF0,ᑗ$ḄA᳛ᜧFâᦑটrãä.ᦑ⌱C.ὃ1Nᑭᵨ8ᦪẆºí$é1ᑗ$A᳛JᦪḄᓫLឋI8ᦪḄᐵJᦪ᩽`Ḅᑨç.I7(x)ூO2௃(2021•îᓭïðñὶὃ)ZFãᦪk,ç>JᦪNg(x)=ீ^ZJᦪ(k,f(x)>k36/397

34/(x)=ln2x-x+2,ᨵg(x)=/(x)ឤᡂöᑣ()A.ᦇḄᨬᜧ`'l+ln2B.2Ḅᨬ`'1+In2C.%Ḅᨬᜧ`'In2D.4Ḅᨬ`'In2ூᫀ௃Bூᑖ᪆௃ᑭᵨ8ᦪnJᦪ/(X)Ḅᨬᜧ`ᵫJᦪg(x)Ḅç>xᔠg(x)=/(x)ឤᡂöwX஻>)4᝕ᵫùwnúḄ_`buvwnᔠ〉Ḅ⌱⚗.I7(x)J(x)«kூ᪆௃ZFãᦪk,ç>Jᦪ:g"…,Yg(X)=/(x)ឤᡂöᑣf(x)0,ᦪ/()ᓫ⌴>1f(x)<0,ᦪ/(x)ᓫ⌴.ᡠ"/(

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889m>0;f(x)Ḅᓫ6⌴ZWX©g'Bᓫ6⌴VWX©Qm'+^).(2)½m=²ijf(x)=,lnx----x.~Vx”xi^[2,2e2]¿ᨵg(x1)Nf(X2)ᡂÇÈ~Vx£[2,2e2j¿2e222e2ᨵg(x)n,>f(x),ᵫপᙠ[2,2e2]±f(x)ḄᨬᜧE©f(e2)Â,g'(x)=l+a>0(a>0),xG[2,2e2],"inmax2x2ᦪg(x)ᙠফ2e?]xZ"ᦪg(x)=g(2)=2--,ᵫ2—%kLa<3,§a>0,ᡠOa£(0,3],ᓽmin222CᦪaḄDEx(0,3].opMᐰ·ஹᙠ¸¹ឤᡂ⚪ḄI.ᙠX1EA,ÑKX2^Bjf(X])Ng(X2)ᡂᑣf(X)maxNg(X)max.2.ÑKX1WA,ᙠX2ÒB,jf(Xl)Ng(X2)ᡂ,ᑣf(x)in>g(x)minm3.ÑKX]WA,X2ÒB,jf(Xi)Ng(X2),ᑣf(x)miÓg(x)max.4.ᙠX]£A,X2ÒB,jf(X])Wg(X2)ᑣf(X)minWg(X)max.Ô⚪09ÕÖ×ØÙὃ1.ூÛὃᐰÜIூᔁᳮᦪ7௃᝞|x<¥á☢ÕḄãä|å¥á☢ÕæᩩèḄ<¥éᙠêä|ë~ìḄ©Mᙠíä|ë~ìḄ©Nᑣîéᙠïä|ë~ìḄ©()NA.EBF.C.GD.Hூñᫀ௃Aூóôõ௃᪷÷ãä|øá☢ÕÕ|uᓽLMᙠïä|ë~ìḄ.ூF᪆௃᪷÷ãä|øá☢ÕÕ|u89/397

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133ᵫjW+&1=>3ó2+4;/+6my—9=0,ôᯠAு0Þy+y=-&n,yy-9122123m+43ö+4[x=my+lcS=%+SX2—÷ߟùW+;—©ú■J"',_____«_6l+1_6t_6ᔣ7=g1t]3]᧕Sᙠre[1,+8ᓫ⌴S|G'^,|.Iூ௃ᙊḄ!ᔠ#⚪%⌕'()প'(+,-ᵨ⚪/0Ḅ123ᩩ56778ஹᙊḄᩩ5:ফ<ᓄᨵᐵᙊὶABC2ᐗEFGHIḄJKLMNO᪷QᦪSTḄᐵQஹUVஹW᳛ஹYZ[Ḅ☢]^#⚪.ὃஹW⚪v___X22FFFvூd1௃e2021.gᓭiYEjkᙊC:f+o=\]a>b>0Ḅqஹrᯖᑖuvτ,2w2x/zᙊC{M,N~e/Nᔠ6MN,aFiF2MḄᕜVᑖuv128.e1ᙊCḄGH:]2Yᙠᔲᙠ2T,BMM77VḄW᳛S]v8ᙠCᡠᨵᩩ5ḄTḄᙶ᪗:ᙠ6ᳮᵫ.[4஺=12ூ᪆௃eI/ᙊCḄᯖ¡v2cec>0,ᵫ⚪(¤B¥12஺+2c=8[a=3______22B¥,,ᡠ¦…=2/¨©ᙊ஺ḄGHv—+j=L\c=198e2¨v/wBeL0¯FNᔠᡠ¦//ḄGHvx=my+l,x=my+1------------ὶAGH<²2'],µ¶x¸᦮ᳮBe8஻/+9»+16¼-64=0,I--+---I98132/397

134\6m/N(x,y)ᑣ¥'6422t»=-_______I*12*84+9-72m2+9ᡠ¦$+஽="?(M+%)+2=8/+9᳝/=(/"X+1)(,Ṻ2+1)=ó,ô+õ()[+%)+18m³+9y.y2/T«,0)ᑣ÷MW77VḄW᳛ᑖuv%Eᜩ=7úv=û1264kk-y.y_yy_8õ+92x2ᑣTMTN(x-0(x-/)ߟüüߟ/(ü+ü)+þ272õᓝ9f8ߟ121212TLf8M+98M+9-64-(8r-72)m2+9-18r+9?2'ᡠ¦Ä8—72=0,ᓽ416Ät=-3%VmeR,k-k-Ä/=3%\/mGR.k•k--_.TMTN77TMTNTT¨©ᡠᨵᩩ5ḄTḄᙶ᪗ve—3,0e3,0.ூ௃ÉÊ)8#⚪ËÌ)e1/ÍᐭEFÏGH᦮ᳮᡂ2ᐗEFGH:e2ÑÒ8ᳮᑡC~᪷Ô~᪷]:e3ᑏC8ḄᐵQ᦮ÖÍᐭ~᪷Ô~᪷])e4᦮ᳮe3ᡠB⊤ÒØÙᐸឤᡂAḄᩩ5.ூd2௃ᙠZᙶ᪗Qxoy0ÏC)¥Þ=ß+஺e஺à0zM,N~,4eIÄá=0%ᑖu஺ᙠMNᜐḄᑗGH:eIDyᔲᙠP,BÄk®¯°7±ᨵNOPM=NOPN?6ᳮᵫ.1%ூ᪆௃eIᵫ⚪/¤BM6a,Ne—æa,ᡈMe—2ᡈèNQé,஺.)y'=2ᦑy=2e224ᙠx=2&ᜐḄìᦪví஺ᙠe2ᐗ,aᜐḄᑗGHvy—a=4஺஺22.஺4-y—a=0.ᦑᓽ133/397

135>=ᙠx=—2j2aᜐḄᦪ—0ᙠ2,஻ᜐḄᑗ!"#y—஺=&'+2()ᓽ44ax+>>+a=0.ᦑᡠ.ᑗ!"#4ax-y-a=0<^Jax+y+a=0.II0ᙠ1ᔠ⚪4Ḅ5)67᝞9:;PO,b1ᔠ⚪4Ḅ5)N/,%)B!PM,PNḄC᳛ᑖFᦇ)%.Hy=I+஺JᐭCḄ"#᦮ᳮO4(-4a=0.x+ᐝ=4%,xᐝ--4a./.121212Q+ᦇ———+——---=-----———------....-RS=-aT)ᨵ&|+ᦇ)=°)ᑣZ!Ḅ[Mx\]2a2C^_Z!PNḄ[C^`⊡)ᦑ/OPM=NOPN,ᡠbPO,—a1ᔠ⚪4.ὃHW⚪ூd1௃2021•hijklmᦻop5AᙠᙊC:x—/Y+y2=]6v)0,P0?£,!yABḄᚖZ|ᑖ!_AC}~5D.1.5஺Ḅ"#]2Y5ḄZ!/C᳛0ᙠ)Z!/_5஺Ḅ}~M,N5.67:Z!_PNḄC᳛.ூ᪆௃1ᵫC:x—6Y+y2=i6O)ᙊC5,0)r=4)5Dᙠ!yABḄᚖZ|ᑖ!v))|D4|=|DB|,..\DB\+\DC|=|OA|+1OC|=|AC|=r=4>|BC|=2)ᵫᙊḄO5஺Ḅb8,0)஺0ᯖ5)2a=4Ḅᙊ.222x2V2&6/=2,c=&2,b=a-c=2ᦑᡠ.5DḄ"#+——=1-42^y=kx-\2;/:=I1,Mx,y,Nx,y,ᵫᡭ¡¢£yO2ᦇ2+if—4¥2=0,I122+=11424%2¦ᯠA=-4¨2+82G+l=/+8>0,+ᐝ=,xx=-.12122«+12/+1x¬0,ᓃ®0,;Z!PM_PNḄC᳛ᑖFᓃ)hᑣ134/397

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140(2.0)-(cosa+2»sina)=2cosa+4<6,ᦑ,Ḅᨬᜧ>q6.rdsᵫ⚪¨-"=(2,0),©P(x,y),-lSt(x+2,y)=2x+4W6,ᦑ•Ḅᨬᜧ>q6.ூ*7௃᝞I"ᙊ஺x᳛qᳮḄ±ᙊTsF+)2=l(a>஻>0)ᑗµVM(0,1)2a2b2y|·VM¸¹ᩩ»ᚖḄO½/,¹O¹NOᑖ¿ÀµVA,CB,2஺(ᙳÂÃᔠ).ÅPq±ᙊEX:V"ÆVᑮ¹OḄᑖ¿q4,d,ᑣÇ)2+d3Ḅᨬᜧ>D()A.4B.5C.—3ூBᫀ௃C,ூF᪆௃᧕-±ᙊC(y=l"ᙊ஺Ḅijqf+y=l,{P(X,y),Ëq/"/,ᑣḄijq+0012124,L.2Ì+-116—4+(yo-l)2.Ëq%=1,ᡠaÍ+&=4-4*+(Ï:1)2=—*3)+"Ëq:ÐÑÒ1"ᡠaÏ=43:ÓÔ"Õ+d2^ᨬᜧ>Ö"×VØC.I233[*8]᝞I",-ÚᱥO/="VA(20"j,ÚᱥOEḄV(x,y)[·V8JOAPḄᚖO"ᚖ1qVQ.জ9OAPZ᳛Ḅ>Þ.ঝ9IPAHPQIḄᨬᜧ>.,1ᱏ--ூF᪆௃জ{OAPḄZ᳛qA,k=—^=x--.,12X-\--2Ëq-18,ᡠaOAPZ᳛Ḅ>ÞD(:I,1).22:+4Z+3ঝὶãOAPBQḄijF^V஺Ḅçᙶ᪗D3=2+]äᑗ:å:=0,k~1k+\2ËqPA|=1+a=\l+R(k+l)"|PQI=ஹ'+Q(X0-x)=-Jl^+1ᡠa|4|.|஺|=:ê-1)6+1)3.©ë1)=:ì:1)(&+1)3.Ëq(%)=—(4k—2)(%+1)2,©íî)=0,^ï•ᡈñ=:12139/397

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202(4)ẆþÿḄ᩽ᙶ᪗⌕ᙶ᪗ᓄ.ᩩ“”“ᑮ᩽ᙶ᪗”!"#ᐭ᩽ᙶ᪗%&'()⚪Ḅ+,-ᩭ/ᜧḄ1.(5)56/89M)(xo"=)">?@a,y)@/DEFG"ᑣ/ḄIᦪ,-x=xo+tcosa,ᦪ@஺@Iᦪ).y=yo+fsinaaSM"%U1DḄVW"XYḄIᦪᑖ[@h,t,ᑣ\||^=13᜜1.b2=1/2-61=,&+g2Gh"2.bSkMM2Ḅl@M3"M"%"mXYḄIᦪᑖ[@n"o᜜ᑣp=JG42CS/DḄkḄl@M>(xo"t)"ᑣ/|+u=0"f"2<0.x⏨zᙠ|ᵨIᦪḄ~F!"⌕FIᦪ☢Ḅ%ᦪYU>?Ḅ"ᔲᑣIᦪᐹᜓ~.1.XḄ+প|ax+b|Wc,|ax+bc(c>0)Ḅ+z|ax+b|Wco-cWax+bWc,|ax+b|2c=ax+b2cᡈax+bW-c,ᯠ᪷¡a,bḄ¢+ᓽ¤.(2)|x-a|+|x-b|2c(c>0)|x-a|+|x-b|Wc(c>0)Ḅ+zজᑭᵨXḄ~F+"§¨ᦪ©ªᔠ¬®ঝᑭᵨ“°ᑖk“+"§¨ᑖ±²³¬Ḅ.a.´µWX¶·Ḅ¸ᦪ@°"¹ºYḄ᪷®b.&»¼᪷ᢥ¾¿ᑮᜧ᣸ᑡ"ÂÃᦪÄᑖ@SÅWmÆ®C.ᵫᡠᑖmÆÉᣵX¶·ËSÅW"+»¼"º+Ä®d.¢ᔜW+ÄḄ¹ÄÎUÏḄ+Ä.ঞÑ9᪀ÓÔᦪ"ᑭᵨÔᦪÕÖ+"§¨Ôᦪ¬.2.+,XḄIᦪØ)⚪ÙᵨÚÛVÜz(1)&Iᦪᑖ±²³"&ᐸᓄ@ᑖkÔᦪ+,®(2)ÞßàXḄ~F"ᐜºIᦪḄX⊤ãḄᨬᡈ¢Ø"å᪷¡⚪æ⌕"+IᦪḄ¢Ø.ᵫà|x—a|+|x—b||x—a|G|x—b|ᑖ[⊤èᦪéDxXYḄêUa,bXYḄḄììí"îïX©᝞|x—a|+|x-b|%(c>0)ᡈ|x-a|-|xGbRc(c>0)Ḅ"ᑭᵨXḄ~F+òó.(3)YôõÚÛᓄzf(x)>aឤᡂøof(x)>a®f(x)aᨵ+minmax197/397

203=f(x)>a®f(x)ீaᨵ+=f(x)aû+=f(x)aឤᡂof(x)min>a.4.ᑭᵨᔠ!Ḅ#ᵨ$ᵨḄᨵ&(l)a2>0*(2)|a|>0*(3)a2+b2>2ab*/Ḅ0112ᨵ(a+b)224ab2(4^-^>ab(a>0,b>0),/Ḅ0112ᨵa+->2(a>0),-+->2(ab>0),^+-<-2(ab<0).abSᑖ᪆Ḅ9⚗&ᵨᑖ᪆⌕<“⌮?”┯BᙢDE“⌮F”ᑖ᪆ḄGHI◤⌕K?ᐙᑖᩩNᓽPQRᐙ⌕ᩩNSTRUᑖ᪆ḄVWR⌮ᔣVWYZᙠ⚪]^#ᵨ“⌕”ஹ"a◤'’d᪵Ḅfg“ᐵij6ஹlmno|bnaibYa|+|b|.p⌕Ḅqrs&(1)ᑭᵨlmḄuvwᣵlmyz{ᓄE}~.(2)ᑭᵨq|no|b||W|a±ba|+|b|.(3){ᓄEᦪ⚪ᦪ1ᔠ.7ஹXḄᦪᡈPᑭᵨlm?᪆1᝞f(x)=k+a|+k+ḄᦪḄᨬm᪆1᝞/(%)=%+J+|ḄᦪḄᨬmᨬᜧmᔲᑣwlzᑭᵨᑖᦪḄ¡?ᨬm.ᑭᵨ¢£?ᨬm⌕ᐸ¥Ḅᱯ§¨©umEª᪗.ὃḄ:ூ1௃(2021•°±ᔺ³o´(ᳮ))¶·ᦪ/(x)=|x+l|.(1)/(x)<4-|2x—l|198/397

204(2)¶·m+n=l(zn>0,»>0),»o1?¼x^a-f(x')/Jo2.mnூ᪆௃প/(x)<4¾2x-|l¿À<4¾2x-|l,44x<-lÁᓄE—(x+l)<4+(2x—1),ᓽ%>—2,—14ÃV1*221414x>_ÁᓄEx+1<4-2x+1,ᓽÆ_<:•<È<*2323(441ÉPÊÁḄËEÌo<%<>IÍ3jফ&|È+஺|o/(1)=k+4o,+“«¾+஻)o(x+1)¾o1|V-1<67<3,..-20,/?>0),/._+_=+=2—+_>4,mnmntnn_—2N2,/.ix—f(x)S+_—2.mnmn]ூ2௃(2021•ÖᓭØÙo´(ᦻ))¶·a>bு0,ᦪ,f(x)=Â+b(a—b)(1)»஺=1,b=L,?/(x)>2ḄË*2(2)?&/(x)+|x-a2|>4.ூ᪆௃(1)ᵫ4=1,PÊ/(x)=k+4,ᑣ/(x)>2Þx+|4>2,ᡠx+4>2ᡈx+4<—2,Ê&ஹுo2ᡈà<-6,ᦑ/(â)>2ḄËE{xx>—2ᡈx<—6}.(2)ᵫ⚪ᓽ,o44,YEX+~77T-+¾o஻-¾XH~——(X-Cl~J=6/d-----b(a-b)rIb(a-b)I]Ib(a-b)b+a-b\a2YEaு஻ு0ᡠa-஻>0,ᡠâ(஻o/?)<199/397

2052]!_>a2+4>2+ᡠa+/?("8)2b(a-b)a/=4êI4"~~cCᓽ”=J2஺=ᵯzᡂ,[b=a-b2ᡠX47-----+¾o0J2H7-----24,ᦑ/(í+¾o/t4ᡂ.b(a-b)ìτb(a—b)ஹ1ூïð௃ᐵiïïð&ñ⚪⌕òᑮᑭᵨlmqʨ/(%)+ὡ-஺2Ia'+b(a-b)1d᪵öXQêb+(a-3=஺ᓽPᵨ÷ñøwb{ᓄEaö஺Ḅùᦪúᑭᵨ÷ñᓽP.[3]üa,"cᙳE]ᦪêa+b+c=1,:1a2b1c2(I)ab+be+car(II)o+o+—>13bcaூ᪆௃(I)tz2+Z?2>2ah,h2+c2>2bc,c+er>2caa1+b1+(r>abbecaᵫ⚪(a+஻+c)2=1,ᓽ஺2+Z?2+02+2ab+2bc+2ca=1.ᡠ+ca)<1,HPab+beca_<^.3zy-2i/l02“11)!b>2a,!+c>2b,!>2c,..!+!+!+(a+b+c)N2(a+b+c),++abcabca/h2c2++N++a2622cBP------abc,..-i--41.bcabcaὃ)*+,-./Ḅ123ூ51௃(2021.789ᓭ!;(ᦻ))=ᦪ஻?=ᱝ+1A*!4|(1)1-.//(x)>0F(2)GᐵIxḄJK/(L)+3A-4|-2஻22+3/”=0NᨵPᦪ᪷RSPᦪ஻?ḄT,V.[OT](1)Wx24XR/(x)=2x+l-(x-4)=x+5>0,x>-5,ᡠxN4FW—Kx<4XRf(x)=2.x+1+x—4=3x—3>0,x>l,ᡠ1<%<4F200/397

206Wx<-2,XR/(x)=-x-5>0,^<-5Rᡠx<-5.2_`Ra-./Ḅ1bc(-d-5)(1,+8)F(2)JK“X)+3|x—4-2M+3h=0NᨵPᦪ᪷Rᓽ/(x)+3|x—4|=24!3஻?NᨵPᦪ᪷,ig(x)="X)+$=|2x+1+m*-4=|2x+l|+|2x-8|>|2JC+1-(2x-8)|=9,WqrW(2x+l)(2x—8)40XRᓽ!X.sᡂuRᓽ8஺),vc[9,+8),23G8(%)=2஻/!3᪷NᨵPᦪ᪷Rᑣ2h2!3᪷<9,ᓽ2᪷2_3y!9<0,ᡠPᦪ஻RḄT,Vc!!ீ᪷<3.2ூ{|௃J2{|3Iஹ*+,-./Ḅ123(1)ᑭᵨ*+,-./ḄS1RᦪᔠḄF(2)ᑭI“{ᑖ2”*+,S1RᑖF(3)᪀⌼=ᦪRᑭᵨ=ᦪS1R=ᦪJK.2ஹ-./ឤᡂu⚪¡ᓄᡂ=ᦪᨬ,ᩭᜐᳮ.ூ52௃(2021•ᑁℳªᨴὃ)¬=ᦪ/(^)=A+4—5.(1)®¯+F(2)¬a>0,G-.//(x)+2°!1|<0Ḅ1bc(᪷,஻)Rq஻—y=2,SaḄ,.ூ1᪆௃(1)®¯3/(²!|³+a—51=1%+஺|!|x+a-5|-5.ᵫ*+,´µ-./3|³+஺|—|x+a—5¶|(x+a)—(%+a—5)|=5,J/(x)-|x+a-5¶5-5=0,ᓽ/(x)1F*প…i<5,ᑣ¾gপ¿Àᨵ3[g(஻)=3஻+a-2=5n=201/397

207ÂÃ"4জWg(-஺)=2+2஺25XRᨵ!஺1ὃ)-./ឤᡂu⚪3ூ51௃(2021.▷àà7!;(ᦻ))á=ᦪ/(x)=f+l,g(x)=|x—a|—|2x-l|,>L2I7(1)Wa=_XR1-./g(f)ீãF22(2)+äåRX&R,G-.//(å)Lg(%)ឤᡂuRSPᦪaḄT,V.2ூ1᪆௃পW“JXRga)=ixã12æ1=!|%ã11,2211271717-./g(f)<_,ᓽ_ç2!_|_,222221è>4ᡈÃ<-3(ê)Rᵫf>4,1x<—2ᡈx>2.ᡠ-./8(/)<-ãḄ1bë(-0),-2)(2,+ì.2(2)ᵫ⚪,í◤ïðব¾nNg(%)ᓽ•1m202/397

208x+a-\,x<112J(x)=d+],F./(ô᝞=1Rö⚪,WaN—X,g(x)=R-3x4-67+1,—a[ᵫ!ç=ᦪឋ×RgQ)ᙠ[y஺R1'`ᓫù⌴ûRᙠ?R/ᑭa,+8)ᓃᓫù⌴ýRF.g(x)g(l)=a.l.1(J)Rþ=22i3i3ᵫ/(X)2g(x)Rl2a--RᓽᡠPᦪ”ḄT,Vë3minmax2222ூ{|௃{|3ÿ⚪ὃḄឤᡂᨵ⚪ᢥ᝞ᑣᓄᙢᦪy=/(x),xe[a,0,y=g(x),xe[c,d]প0\/஽€ᓃ5ᨵ/(xJফ03XG[C,J],ᨵ/(xjvg(B)ᡂ,ᦑ“DEF2ব0HIJ,3XG[C,J],ᨵ஻X|)2x+1,x-|1>2x+1,yz21{x-1>2x+l,|x<-2(}~)y<1{l-x>2x+l,|x<0,ᡠx<0,Ḅ[1%<0}.(2)ᵫ/(x)Ng(x),|-1|-2,☢ᑖyx=0{ឤᡂfeAF203/397

2093yx<0{ᓄ᦮ᳮ|(1/)x43,ᓽ1—ឤᡂᑣ1—/NO,ᡠY1Fx3y05F.x<4{/(x)>l,°x>5{/(x)>l,7./(x)=l,=min(2)ᵫ(1)+¹2+ᙳ=1*,•X]+1+¹2+1+¹3+1=4,22222尤2XXXX二223-42rZ\^+X++++XX-++1X+LH\%+++)/++>-X+X+X-1X—+I123\1237\I23)r24m7]1_S_L^a>y°»y¢=¼2=ᓃ=l½.A++l+Xj1+%21+z343t¾¿௃ᐵÀ¾¾¿|IÁ+1+z2+1+z3+1=4,᪀⌼¡¢Ḅ.ூ]2௃a,b,c,dÄᦪ°஻+¯=4,^2+Æ=16,±Èac+bd<8.±Èᵫ¡¢|(஺஺+Ê/)2r஺2+¯)(62+

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211ᡠ(ä4-1ᡈᡈýz21,-3(x-l)+x+l>2-3U-l)-x-l>2i-l)-x-l>2,II13(z|x4—lᡈ-13,ᓽx<0ᡈx>3,ᡠÿ
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/(z2/7{+|Ḅ}`'S|ḄBCE.f-3,x<-lூ᪆௃প/ಘ1,—1WxW2,[3,x>2x<—1'/(x)2lY71WXW2'ᵫ/(x)ei>'2X—121,>x>2'ᵫ“x)21>x>2.ᡠ0/(x)21Ḅ%X'0-(2)/()2f—+|>X41|72-x2+x,\|X+1|-|X-2|-X2+X^|X|+1+|X|-2-X2+|X|+|^|206/397

2123s(5~lx=7'|x+l|-72|-{2+x=_.ᦑḄBCE-oo,.211114I4.ὃ᩽ᙶ᪗,ூp1௃(2021•<⛸7(ᳮ))ᙠ☢¡¢ᙶ᪗£x஺)'+'¤¥CḄMᦪJx=2coscz(a1Iy=2+2sina2Mᦪ).0¦G஺᩽G'ᑐ¨Ḅ©ª¨᩽¨«.᩽ᙶ᪗£'¤¥GḄ᩽ᙶ᪗ᱏVl+3sin20(1)S¤¥GḄ®Y(2)¯AL¤¥G<Ḅ°G'BL¤¥G<Ḅ°G'S|AB|ḄᨬᜧC.22ூ᪆௃(1)ᱏ_/,==_I——r7:'•,-P(cos26li-4sin2^=4,Jl+3sirr஺Jcos7ᑖ4sirr஺ᓽx2+4y2=4,'2y=1.——(2)ᵫ¤¥GḄMᦪrᐸ®£+(y-2)2=4,´L0C(0,2)ᙊ¶'2ª·Ḅᙊ'•••AL¤¥G<Ḅ°G'8L¤¥C2<Ḅ°G'A4mx=¸஺|,¹+2,¯B(2cos0sin,ᑣBC)J4cos?ᓡ(sinᓡ2»—=J-Bsin?¼4sin48=<3)in/?F'sin(3=—,pCI=128—74½,/.\AB\=2ᢤ+2.3IImax733IImax3ூGH௃ᐵÀGH,ᙠÁÂÃP'ᐵÀLᵫᙊḄឋÄÅ|45|ḄᨬᜧCiᓄSBCLX+2,ÆÇᔠGᑮ¡¥ḄÊËÌ0Í©ÎsᦪḄឋÄSÏ|AÐḄᨬᜧC.ூp2௃ᙠ¡¢ᙶ᪗£xOy+'0ᙶ᪗¦G᩽G'x¨Ḅ©ª¨᩽¨«.᩽ᙶ᪗£'¤¥GḄ᩽ᙶ᪗/xos&=4.(1)M¤¥C1<Ḅ°G'Gpᙠ¥bOM<'TU|0M||0P|=16,SGPḄÑÒGḄ᩽ᙶ᪗;(2)¯ᓰAḄ᩽ᙶ᪗'GBᙠ¤¥C<'SOAB☢ÕḄᨬᜧC•.........................(2,-)2Ö207/397

213ூ×ᫀ௃পÙx-2Ú2+y2=4Ùx#0ÚYফ2+Ýூ᪆௃Þ⚪ᑖ᪆,Ù1Ú¯ÏPḄ᩽ᙶ᪗'ᯠáᑭᵨ⚪ã>Ï᩽ᙶ᪗'ᨬáiᓄ¡¢ᙶ᪗Ùx-2Ú*+y2=4Ùx*0ÚYÙ2ÚᑭᵨÙ1Ú+ḄÇä'¯ÏGḄ᩽ᙶ᪗'ᯠáÇᔠ☢ÕÌ>ᑮ☢ÕḄå¢sᦪ'Çᔠå¢sᦪḄឋÄX>ÖOAB☢ÕḄᨬᜧC2+g஺Þ⚪᪆,Ù1ு¯èḄ᩽ᙶ᪗Ù0'8ÚÙ᜛ு0Ú,MḄ᩽ᙶ᪗Ù᜜6ÚÙ2{0Ú,ᵫ⚪¯r\OP\=p,|OM|=p=஺1111cosQᵫ\0M\-\0P\=16>GḄ᩽ᙶ᪗0=4COS6Ùp»ÚoÙ2Ú¯GBḄ᩽ᙶ᪗Ù4,ἔáõ0Ú,ᵫ⚪¯r஺4|=3'/2=4cosa,5LÖQ4B☢ÕS=_i^YA^psinZAOB=4cosa-sinfa-|]iJ=2sm\2a-M^-\ÔIYT42+^-0g—£'SB>ᨬᜧC2+5ᡠ0Ö04?☢ÕḄᨬᜧC2+Â.12ὃMᦪ,fx=2+2cos஺ூp1௃Ù2021.ûüûý7ÙᦻÚÚᙠÿᙶ᪗xQyCḄᦪீ,c.%ᦪ,1=l+2sm஺#ᙶ᪗$%᩽%X()*(᩽(+,᩽ᙶ᪗-/Ḅ᩽ᙶ᪗pco12IY41314-/Ḅ-ᙶ᪗5CḄ67832-/9C:;MN>%?%PḄᙶ᪗30,-2,4|PMF+|PNFḄCூE᪆௃31CH3x—22+3y—12=4,-/Hx-y-2=0.208/397

214”ᦪL/ḄᦪMᐭ3x—22+3>-12=4,32?/HPQ+,R=஻+஻=«+/2U2”50-18=32,YZ?+/”==32.\x-pcosOூ%\௃-ᙶ᪗]᩽ᙶ᪗Ḅᐵ_`ᑭᵨcdீ.ᑐf᩽ᙶ᪗]ᓄ-ᙶ᪗Ḅhy=஻sine(729/T=8r+y~,tὅvw#x᩽ᙶ᪗yz{|}~/cos஺in஺#]ᓄUᐵ_`ᑭᵨcdJvtan&_lOx☢%ᙠᙊ┵yᓄᡃw#ᵨUYᦪᩭ⊤%ᙶ᪗fᑭᵨ•ᐗᦪ49%ᨵᐵḄᨬC⚪.ὃᦪ9᩽ᙶ᪗ᓄHL=r+1—1ூ1௃32021•⛸¡¢3ᳮᙠ-ᙶ᪗X஺CḄᦪ.P3fᦪ#ᙶy=t--ஹt᪗$%஺᩽%x(Ḅ¦§*(᩽(+,᩽ᙶ᪗.314஺Ḅ᩽ᙶ᪗8TT32-OP:ᑖSeR9C:;%M,N,4¬MNḄ.63=,+-1ூE᪆௃31ᵫCḄᦪ'±3ᦪ²CḄ673x+l2—>2=4,wᓄy=t--x2+2x-y2=0,ᦑᐸ᩽ᙶ᪗cos232/KOS᜛/sii?&3.jr32LQ·ᐭ/cos?¸2¹sa/sin2=3,²/+23P-6=Õ6•e*/?+/?=-2⌲7ῗ=-6,½"N|=|/?-/?=|J3᜛±+᜛2J—4/Á=6-ூ%\௃ᐵ_%%\H4E᩽ᙶ᪗ÂḄÃᐵÄÅᐵ_ᙠ;ᳮE᩽ᙶ᪗ÂḄ᩽Æ᩽ḄÇÈÉÊᵨ᩽Æ209/397

215ᡈ᩽⊤ᡠ4Ḅ|.IY—flx=2+2cos]oூ2௃ᙠ-ᙶ᪗xOy-/Ḅᦪ`τ~3tᦪCḄᦪ`U'+ljy=2sine39ᦪ#஺᩽%x(Ḅ¦§*(᩽(+,᩽ᙶ᪗.314-/5CḄ᩽ᙶ᪗87T7E32ÐÑÒ஺ÓHe=a3ᐸ0+V=4,᩽ᙶ᪗ᱏ4cos஺./ᐔ1132à⚪ÉHae30

216ூ`᪆௃51+cc+£=1,ᦑCḄ9ᦪ"#fx=4cosa5a9ᦪ+169y=3sina/Ḅ;<"#$x+y-6=0.52+i஺@P54cosa,3sina+Pᑮ/Ḅopd,ᑣar4cosa+3sina—6|15sin5a+஺+—+ுwxy6zᖾট2ᦑS=|sin5aiy+=l}~ᓽsing',£osg4,_AIIP2V55}'ᓃ=]ᦑᙠC@CᙠP,EMBPḄ☢S9=3,PḄᙶ᪗5“.ூ4௃52021•᪥ὶὃ+☢/ᙶ᪗xOy0CḄ9ᦪ"#X^T+Trw-l+.1iC59ᦪ->=I1+f4cos0ᙶ᪗0᩽xḄ᩽᩽ᙶ᪗CḄ᩽ᙶ᪗"#ᱏ.sin2651+MGḄ᩽ᙶ᪗"#GḄ/ᙶ᪗"#=n52+¡¢AḄ᩽ᙶ᪗51,0+,l:0=apeRYCB,ᐸ0¤¥AḄn1C50,-+2M,N3Lnil,-τAM1AN]=w,MaḄ~§\OB\2\JTூUᫀ௃(1)p=------------(ªª)/=4x$(2)a=sinft-cos6L4®,1fxi%x+y=l(xw—1).ூ`᪆௃(1)J=>JL®y=2-2[1+z[t+lIAp0cf)•__________(b0),*.*p=_____=>/xin20=4cos6=>psin20=4/ros^,y2=4x.sinᑖcos஺·sin2015¹ᨵ+B,ᡠ|08-----!-----(2)/$&akpeR)1G$P=-----------sinft-cos஺sina+cosa211/397

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218ூ2௃J!Kᦪ/MXO=|2%—4+5%,ᐸVWᦪa>0.M1Oa=3\“xON5x+lḄ#M2Oa/MxOீ஺Ḅ#dxlxW-1f,\aḄg.ூhᫀ௃M1O/MXON5x+1Ḅ#dx|j41ᡈxN2fM2O஺=3ூ᪆௃প஺=3/MxOZ5x+l&ᓄ|2x-3|»l,ᵫo&pqW1ᡈxN2,ᦑ“xOZ5x+lḄ#dj1x41ᡈxN2fফMstuvgḄwxὃ⇋Oᵫ/M{O=0,^2-\a<-5^XX|}''JoᓄJxN2ᡈJ2,p12ᡈI2,aIa12%-Q+5X«0[_M2j-QO+5xW0———a>0,ᡠḄ#dx|-2f,ᵫ⚪&p%“=-1,ᦑa=3.33%Msᓄwxὃ⇋Oᵫ/(x)<0,V2x-\a<-5x,oᓄ5%<2x-a<-5x,ap|f5x0,\2x-a<-5x\x0,ᡠa=3.5¡¢uvgḄa4£uvgVxḄᦪ1Mᡈ&ᓄ1O,&⌱ᵨ+,ᡈ¦§\¨©ª.axḄᦪᐰ1,ᑣ⌱ᵨ¬5ᑖ®¯°\±²-³5gḄ´µ.213/397

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22014A.-B.-C.2D.925ூᫀ௃Cூ8᪆௃•♦•/(O)=2°+l=2,.•./(/(()))=/(2)=22+2a=4+2a.?ᵫ/(/(0))=4aÇ4+2஺=4஺=>஺=2.ᦑ⌱஺.1,x>0,l,xºᨵᳮᦪhᵫ/ÌÍ4.Ê/(Ë)=<0,x=°g(x)=<0,xºÎᳮᦪ‘""g3)Ḅpº-1,x<0,A.1B.0c.—1D.ᑍூᫀ௃Bூ8᪆௃•.5Îᳮᦪ(ᐔ)=0ᑣ(0)=0,ᦑ⌱B.7UC,ஹcos_,0l)4D._5ூᫀ௃B215/397

221ூ8᪆௃ᵫ?2"T—2ு_2ê/(«)=m3,ᦑ/(a)=-log(a+1)=-3,a+\=2?=8,ᡠ=a=7.ᦑ23/(஺-7)=/(0)=2m'm2=mù.ᦑ⌱B.,2x,x>02.[ᦪ/(%)úmû.Â=ᑣ%ᦪaḄp}?x+l,x<0A.-3B.-1C.1D.3ூᫀ௃Aூ8᪆௃a>0ᵫ/(a)+/(l)=0Ç2"+2=0,Î8ü஺<0ᵫ/(a)+/(l)=0Ç஺+1+2=0,8Ç஺=-3,ᦑ⌱A.ᑖÃᦪḄQ%ÊyÊW⚪v(-X2,x>01.(2021.ᓅýþÿ.)ᦪ/)=ீᑣᦪ“X)Ḅ()[2",x<0A.[0,1)B.(-8,0]C.(-00,0)(0,1)D.(--1)ூ'ᫀ௃Dூ*᪆௃ᵫ-.ᦪḄឋ0123ᦪy=-fᙠ7[0,+8)ᓫ:⌴<1=x=0,ᦪ>3ᨬ@1ᨬ@y=0,ᓽ(-8,0]BᵫᢣᦪᦪḄឋ0123ᦪy=2,ᙠ7(-8,0)ᓫ:⌴D1EF(0,1).GHIὺlW(x)Ḅ("M).ᦑ⌱D.P2.᝞RSᑖUᦪḄRV1ᑣWᦪḄXY,ூ'ᫀ௃[—112][-1,1)ூ*᪆௃ᵫRV2[1\SUḄXY1-1,0),[0,1)B\-UḄXY[0,2],[-1,0J.ᡠ_%14W1-I,I)f—x+6,xW2,P3.ᦪḄ=ீ(a>0hawl)Ḅk[4,+oo),ᑣlᦪ஺Ḅ>ok[3+log“x,x>2,ூ'ᫀ௃(1,2]216/397

222f—x+6,pW2ூ*᪆௃q/(x)=,ᡠ_=xW2F1f(x)>4Brᦪ/(x)Ḅ[4,+oo),ᡠ_[3+log“x,x>2•,*31o(1,2].[3+log஻224ᑖÃᦪḄ6ËW⚪v(1)ᵫvXRw᪷y*᪆vzXᦪḄRV[2',x>0P1.(2021.{|ᐸ~(ᦻ))ᦪ=ீI,ḄR()RT,X<0ூ'ᫀ௃Bூ*᪆௃᪷y⚪1=X20F1y=T,ᢣᦪᦪ1ᓫ:⌴D1hᙠx=0Fᦪᨵᨬ@1B=x<0F,nry=2-"1-1ᢣᦪᦪ1ᓫ:⌴<1hᦪy>i.ᦑ⌱B.(2)ᵫRXvw᪷yRVᦪḄ*᪆vP1.᝞Rᡠ1ᦪf(x)ḄRVkᢚUABC,ᐸAஹBஹCḄᙶ᪗ᑖ(0,4)ஹ(2,0)ஹ(6,4),ᦪf(x)Ḅ*᪆v.—2x+4,0WxW2,ூ'ᫀ௃f(x)=X—2,2VxW6.ூ*᪆௃UABᡠtḄᦪ*᪆vy=kx+b,x=0,[x=2,,ᐭ13y—4ly=O4=b,fb=4,.,.y=-2x+4(0WxW2)0=2k+b.lk=-2.2x+4,0WxW2,ᳮ1UBCᡠtḄᦪ*᪆vy=x-2(213217/397

223*᪆w=x=0F1y=/(l)=3,ᓽy=/(l—x)ḄRVª«(0,3),᣸◀AB==-2F1®=§3)=-1,ᓽy/1—x)ḄRVª«(S2,-1),᣸◀BB=Xw—1F1¯°J=iogf<0,ᓽ,=±_³ḄRVª3M4«(_L1,logi஺1᣸◀C,ᦑ⌱D.3j3ᑖÃᦪDHW⚪v(4^77-M)kᕜ2Ḅᕜᦪ1ᦪg(x)ḄÇ«ᓽ×y=/(x)Øy=HḄÙ«ḄÚᙶ᪗ÛR᝞Ü1ᵫR2[1=᝕=0F1g(x)ḄÇ«—111,3,5.ßk᜻ᦪ1EFᒹÑ2019,=ᦇ=1F1g(x)ḄÇ«0,2,4,…1ßkᏔᦪ1EFᒹÑ2021,=ä=åF1g(x)ḄÇ«Sæ11—*12<Ø7…,EFᒹÑ2019-è1qEg(x)ḄÇ«SXÏᒹÑ2020+è.ᦑ⌱D.222ூᐵê«ë௃*⚪ḄᐵêᙠìᑭᵨᑖUᦪஹᦪḄᕜឋ_ïᦪḄÇ«ḄᭆñòóÛR1ᑭᵨᦪôõᔠòó*.218/397

224\a,a-h<1,P2.lᦪ஺"1XY÷øù“”w஺ᶧ=ீ/(x)=(42)<8)(x-£),ûwR.ᦪy=/(x)-cḄRxüាᨵþÿᐳᑣᦪcḄ()A.(-oo,-2u|^-l,J)B.(-oo,-2஺11,ூᫀ௃Bூ᪆௃ᵫ⚪f—2—(x—ᓽ—lீxK!"/$)=&_2()᮱—2—(x—,)>1,ᓽx<—1232——ᡈx>5"f(x)^x-x⌕01ᦪy=/(x)_cḄ234X5ាᨵ89ᐳ:;<=/(x)-c=Oᨵ89>?@Ḅᦪ᪷ᓽBᓽ1ᦪy=/(x)Ḅ234CDy=cᨵ89>EḄFᓽBGH1ᦪy=/(x)Ḅ234CDy=c,>IJHᫀB.fx2+2ax+a,xWO,K3.Ma>0,1ᦪ/(x)=ீ,ᐵPxḄ<=/(x)=oxាᨵ29QRḄᦪᑣST-+lax-2a,x>0.aḄ.ூᫀ௃(4,8)ூ᪆௃)xW0"ᵫd+2ar+a=ax,J஺=-x2-ax()W>0",f-x2-ar,x0ᵫ,+2ax-2a=ar,^2a=-x2+ax.Xg(x)=<[-x24-ar,x>0YHCDy=a,y=2a,1ᦪg(x)Ḅ2Z᝞2ᡠ]g(x)Ḅᨬᜧ`y-g(x)272—a+a=bᵫ2ZB/(x)=axាᨵ29QRḄᦪᑣ4242a@fgᔠὃj1ᦪᓫlឋn>@fopqᑖrstuv.K1.(2021•ᐶyz{!|}~|(ᳮ))yᙠKḄ1ᦪ/(x)f(x+2)=l/(x),)xe0,2)2219/397

225L-2?,0@f/(s)-g20I'-k21[-2τ2,l0Jx>஺ᡈx<-2,ᵫ3r+6xVOJ2cx<0,ᵫ3x2+6x=0,x=0ᡈx=-2,•,.1ᦪg(x)=^+3(+»ᙠ(-o஺,-2),(0,+oo)ᓫl⌴½.ᙠ(2,0)ᓫl⌴¾.•.»G[-4,-2),gmin=g(-4)=¿—16.•>@ff(s)-g(?)>0,-8>m-16,ᦑᦪÂ8,ᦑ⌱C.ூᐵÄÅ௃Vse[-4,-2),3re[-4,-2),>@ff(s)-g20ᡂ¡,Æᓄ`ÈÉÊË*,Í᪷Î᪆fnÏᦪÐH1ᦪḄᨬ»Ð.ÑP~᫏⚪.cos^x,x£[0,1]K2.M/U)`Ꮤ1ᦪ)xN0"f{x}=jc,Jஹᑣ>@f/(x—DW2ḄÛ`2x-\,x6G+oo)2124731121-17LA.*1-3-3-4B.f--43f434134713c1LrL34L」-T3434220/397

226ூ᪆௃)0Wx"X/(x)=cos^xW1JWWÜ)x>l"X/(x)=2x-1223222131313113J:0A.(-oo,0]B.(-oo,l]C.[-2,1]D.[-2,0]ூᫀ௃Dூ᪆௃/á=ᶭ12"W0•.ᵫJ«å0æᵫçÉln(x+l),x>0x~-2x>axln(x+1)>arx~-2x>axBJaNx-2,ᑣa2-2,᣸◀A,B,)a=l"᧕ëln(x+l)0ឤᡂ¡ᦑa=l>〉ᔠ᣸◀C,ᦑ⌱D.ᑖÃᦪDÌïᵫ1ᦪðḄñᙠòóÐôᦪḄᡈõ⚪ᐵÄᑭᵨ1ᦪ<=uvᡈᦪ÷gᔠuv᪀ùᐵPôᦪḄ<=ᡈ>@fÐ.stôᦪஹᦪ÷gᔠúrõ⚪Ḅû⌕<ü.(xIOIIK1.(|ὃᜩþᔁ9)ᦪ/(x)=ீᦪg(x)=/()—W?_2x|eR)ាᨵ4,\-x,X௃ᵫg(0)=0,@ᔠ4BC⚪EᓄGy=lJ-2|K/1*)=——ᨵ3NOP4ᑖ\x\R=0,R<0,Z>0UVWX4ᦪY@ᔠZ[ᓽ]^ᑮ8ᫀ./(x)ூ`᪆௃bcᑮg(0)=0,ᡠe⌕gg(x)ាᨵ44h◤jk|l-2|=mmាᨵ3n᪷\x\221/397

227ᓽ]4pq)=6,ᓽkr-25stuvᨵ3NOP.f(x)w%=0x4yx=2,᝞u1,y=2Ke{=|■ᨵ2NOP4N~⚪c;\x\/(X)wk<0x4᝞u2,yx>=|—2|K/z(x)=|4ᨵ3NOP4~⚪cwA>0x4᝞u3,wm=2Ky=fᑗx4ὶjk^JC2—+2=04p=()^428=0,`^ᦇ=2(()4ᡠeᦇ>20.4kḄ'(*G(—00,0),+00),ᦑ⌱D.ூ`௃⚪Ḅᱯ+ᦪuvᐸᙠḄᮣᵨ4⚪ὃ¡¢ᦪKjkḄ£ᵨ4ὃ¡ᦪY@ᔠஹᑖ¥Z[ஹEᓄKᓄ¦tᦪ§;¨j©4ὃ¡ᦪ§ªஹ«¬¨vஹᦪ§®t§¯°±.`⚪ᐵ³+´µ¶rᦪuv4£ᵨᦪuvᐸឋ¸`¹C⚪.222/397

228[ex,x<0,º2.ᦪ/(x)=ீg(x)=f(x)+x+a.g(x)»ᙠ24ᑣ஺Ḅ'(*+[Inx,x>0A.[—1,0)B.C.[-1,+oo)D.[l,+oo)ூ8ᫀ௃Cூ`᪆௃ᦪg(x)=/(x)+x+஺»ᙠ24ᓽᐵÁxḄjk/஺)=Â஺ᨵ2NOḄn᪷4ᓽᦪ/(x)ḄuvK«Ãy=-x—aᨵ2P4¶r«Ãy=-x—஺KᦪḄuv4᝞uᡠÅ4ᵫu]4஺W1,`^a21,ᦑ⌱c.12—ixi,x<2ºஹÈᦪ/(x)=ீ11ᦪg(x)=b-”2-x),ᐸÏbeR,ᦪy=/(x)_g(x)ា[(X-2Í'X>2ᨵ44ÉÊḄ'(*+A.4,+oo)B.(-oo,1)77C.(0.)D.J2)4444ூ8ᫀ௃Dூ`᪆௃ᵫ"“)2-|x|,x<2,2—12—x|,x>0^/(2-)=(x-2)2,x>2,2Ô4x<0+X2,x<0ᡠey=/(x)+/(2-x)=j4-|x|-f-x|,02d+x+2,Ô<0ᓽy=/(X)+/(2-{=<2,02ាᨵ4t×Ájk/(x)+/(2—X)—Ø=0ᨵ4NOḄ`4ᓽᦪy=bKᦪy=/(X)+/(2x)Ḅu7vḄ4Ùᐳ4ᵫuv].

229τ1)º1.(2021ᜩê☟ìí•ïUᨴὃ)/(%)j(4—ax+2,(x«l)+RḄᓫó⌴õᦪ4ᑣnᦪaḄ'(*G()A.(l,+8)B.[4,8)C.(4,8)D.(1,8)ூ8ᫀ௃B(f,x>1a>1aூ`᪆௃ᵫ⚪c4ᦪ/(x)=ᙠRᓫó⌴õ4]^.4->04`^4Wa<8,ᓽx+2,x<12a'>4--+2.2nᦪaḄ'(*G4,8).ᦑ⌱B.º2.ᦪö)+ᕜøG4ḄᏔᦪ4wxe0,2x4©=xT,ᑣNtáMU)>0ᙠ—1,3Ḅ`ûG()A.(1,3)B.(-1,1)C.(-1,0)U(l,3)D.(-1,0)U(0,1)ூ8ᫀ௃Cூ`᪆௃f(x)Ḅuv᝞u.wxC(-|,0)x4ᵫxf(x)>0^xG(-l,0)wxG(0,1)x4ᵫxf(x)<0^xG஺wXW(1,3)x4ᵫxf(x)>0^XW(1,3).ᦑxG(-l,0)U(l,3).º3.ᦪ/(x)+ÜÝᙠRḄᏔᦪ4üᙠíý0,w)ᓫó⌴õ.nᦪ“~/(logM+f(k)gM42/(l)ᑣaḄ'(*+2A.[1,2]B.[J]C.",21D.(0,2]22ூ8ᫀ௃Cூ`᪆௃æGᦪ“X)+ÜÝᙠKḄᏔᦪ4ülog/u-log"4ᡠe/(loga)+/(log=/(loga)+/(-loga)=2/(loga)<2/(1),ᓽf(log?஺)Vf(1),æGᦪᙠíý22222[0,+8)ᓫ-ó⌴õ4ᡠe/(|loga|)

230
2',ᦑ⌱C.iᑖÃᦪḄᕜÓឋஹ᜻ᏔឋW⚪1.(2021••!)#$%&ᙠR)Ḅ*ᦪ/(-.//(x+l)=/(451),67xe[-Ll]=
f(x)=7ᐸ?aeR,஺>066".E+=ᑣb=Q.{lo^,o+1)=/(151),ᑣf(x)=/(x+2),ᡠQ
*ᦪ“X)ᕜftzx+l,-106XY1.[log஻\,012-2-2112-2.2.l)U

231/(x)=1ÍÎ-6,6Ï)ḄÐᦪ᪷ÒxV.ூHᫀ௃-6ூ᪆௃iVr(-x)=—/ಘ6X-=/(2-X),ᡠQ/"(%)=/(2-x)=-/(x-2)=-/(2-(x-2))=-/(4-x)=/(x-4),ᓽs/•(Ö=/(4-4)ᡠQ*ᦪ/'(X)ḄᕜV4.70/ᦪ«x)=—x+3,g(x)=log2X,ᑣ/ᦪ/z(x)=min{y(x),b,a>b.g(x)}Ḅᨬᜧ=>.226/397

232ூ@ᫀ௃1ூC᪆௃E⚪&h[x)=log-A஺I04W2K/?a)=log2%>/ᦪIx>2Kh(x)=3—x>.—x+3,x>2./ᦪᑣh(X)max=h(2)=1.ᑖÃᦪᓫÏឋW⚪!1.QRᐔH(2-)x+l(x()12a'(X'l)XL©B.P3A.L2JC.(1,2)D.(1,+8)ூ@ᫀ௃A2—஻>0,ூC᪆௃E⚪&f(x)>ᙠRḄ/ᦪ$>ᨵ„>1,Ck%a<2,ᦑ⌱A.2(2-a)X1+1[2n,xW1!ஹo/ᦪ/(©=<ᑣWX/(x)W2ḄxḄ_=a>[l-logx,x>12A.[-1,2]B.[0,2]C.fl,+8)D.[0,+oo)ூ@ᫀ௃DூC᪆௃IrK2sW2,CkQ0,ᡠOWxWltIx>lKl-logz^W2,Ckx1ᡠx>1,uvRw20.xyzCᑖ|/ᦪᓫឋ~⚪K◤⌕ὃ⇋|/ᦪY>/ᦪᡈ/ᦪᐸὃ⇋|/ᦪḄᑖx᝞>/ᦪᑣ/ᦪḄᨬᜧ=⌕$$/ᦪḄᨬ=/ᦪḄᨬ=⌕ᜧ$$/ᦪḄᨬᜧ=.ூᓣ௃uᔠ☢ḄCᑖ|/ᦪ/ᦪ~⚪ᑮᦪஹ¡¢tᑖ|/ᦪ✌ᐜ>/ᦪ¥>¦§/ᦪ¨>§/ᦪtᑖ|/ᦪḄᜐᳮ¡¢:ᑖ|/ᦪᑖ|ẆtC⚪®¯°±²³´µᙠ¶¦|·¸¶§C᪆¹º᪵¼⌕ᑖ|½¾ஹ¿Cᓽ⌕ÁÂᑖ½¾ᙠC⚪ÃÄ®ḄÅᵨ.227/397

233Ç⚪16ÈÉ/ᦪ®ÊᨵËᦪ~⚪ÌÍÎÏÐÑὃ#$ÈÉ/ᦪḄὃÒÈÉ/ᦪ®ḄËᦪ~⚪¦Ó>ÑὃὃÒḄÔx~⚪¦.ÑὃὃÒËᦪḄÕÖ⌕ᨵzQR×ᔠØḄᒹÊᐵÛ¿ËᦪtQR/ᦪḄឋÜ¿ËᦪtQR/ᦪḄÝxᡈ¡Äஹ¨¹ᨵ'ᦪC¿ËᦪQR/ᦪÞßᱯá¿Ëᦪ.┐#ÑὃὃÒḄÕÖãäåæ᦮ᳮᢕéÈÉ/ᦪḄÞßêឋÜë“ᦪ”ê“¡☢ãäᐰ☢Ûðñòᨵó$〉ÅÑὃḄ⌕¿õ_ÑὃÑᑖ.ஹᔠᐵuÕÆÖᦪW⚪QR×ᔠØḄᐵÛ¿ËᦪḄa>ÕÖ⚪¦ö~⚪ÕÕê/ᦪ÷øᔠᐸC¢ùÕ>úó$ᦪû᪀ý¨¹þÿᡈᵨᦪḄឋ.1.ὃᐰIᔁᳮᦪ2ᔠA={x4-4W0},B={x|2x+a<0},*408=3-2-1},ᑣa=YA.-4B.-2C.2D.4ூ2ᫀ௃Bூ5678௃ᵫ⚪;✌ᐜ>ᔠA,H,ᯠ@AᔠBḄAC>ᑮᐵF஺ḄHIJHIᓽLMNOᦪaḄP.ூ᪆௃RSTUVV—4W0L>YA={x\-2Y8=1][*4Z"].ᵫFAnB={x|-2Ya=-2.ᦑ⌱B.If2ூghi௃j⚪ḄᱯlmnopẠJj⚪ὃrsZᐗRSTUVḄuஹwxᦪḄZᐗZSTUVḄuJὃrᑭᵨᔠḄBz{xᦪḄPJὃrᦪ|Aᔠ5}Jὃrᦪ~z{}U~.⚪ᐵmMZᐗRSTUVJᵨᦪ|AᔠuxᦪḄP.2.ᔠ4={+2,2"+"},3WA,ᑣ᪷ḄPf.ூ2ᫀ௃2ூ᪆௃f3£A,ᡠ+2=3ᡈ2஻+஻?=3.᪷+2=3,ᓽm=lJ2m2+m=3,ᔠAᨵoᐗ3,ᡠm=1Tᔠ⚪;J2"+m=3J>஻?=—3ᡈ=]J᪹=—3J¡+2=43ᔠ⚪;.ᡠ/??=—-.22223.ᔠ£=3Z20x55},B={x|m+l

234ூ᪆௃VBCA,2m-l>m+1f,জ8=0,ᑣ2m—17.7஻<2.ঝ8/J®/¯+1°Z2,>2Jᔠ⚪;ḄOᦪ¯Ḅ¦P¨f(-8,3].5,a~b4.ᔠ4=1aJ,B=[ha+h,Z1},An8={2,-1},ᑣa=,b=.fூ2ᫀ௃a=l,b=2´=2,J,ூ᪆௃ᵫACIB={2,-1},>aᡈaa—b=-1a—b=2.l,A={5,2,-1},B={2,3,-1),ᔠ⚪;;C2,A={5,-1,2},B={-1,0,—1),Tᔠ⚪;.b=-1×ஹDᦪḄ᜻ᏔឋᨵᐵḄÆÖᦪW⚪ᦪḄ᜻ᏔឋxᦪJ¹ºmᵨ᜻ᏔᦪḄN»J᪀½ឤUVJᡈ¿ÀFᦪÁḄÂÃឋ⚪.5.ᦪ/஺)=-------------f᜻ᦪJᑣ஺=(2x+l)(x-a)123(A)—(B)-(C)-(D)l234ூ2ᫀ௃Aூ᪆»Å"^f᜻ᦪ’È=஺’>ᔩ;.61ὃËÌᔁ8]N»ᙠRÏḄ᜻ᦪf(x)ᙠ(-8,0)ᓫÑ⌴ÓJ*"2)=0,®IÔÕ^(x-DNOḄxḄ¦P¨m()A.[3,+࠷)B.[-3,-1][0,1]C.[ߟ1,0][1,+8)D.[ߟ1,0][1,3]ூ2ᫀ௃Dூ5678௃✌ᐜ᪷Ùᦪ᜻ᏔឋÚᓫÑឋJ>ᑮᦪf(x)ᙠÛÜÝÏḄÞJß᪷ÙàáᦪḄâãᜧFUFåJᑖçèᓄfÂêëìTUVJᨬ@î>AC.ூ᪆௃fN»ᙠRÏḄ᜻ᦪᙠ(-8,0)ÏᓫÑ⌴ÓJï/(2)=0,229/397

235ᡠ/(X)ᙠ(0,+8)ÏðmᓫÑ⌴ÓJ*/(—2)=0,/(0)=0,ᡠxe(-oo,-2)u(0,2)J/(x)ு0,xw(—2,0)(2,+8)J/(%)<0,[x<00ᡠᵫ4'(x—1)NOL>YZᡈJᡈ]Z()J1K0ò-1»2,04ó-142ò-14-2Zô“Zö>—1WxWOᡈ14x43,ᡠÔÕ4(x—1”0ḄxḄ¦P¨m[ߟ1,0][1,3],ᦑ⌱D.ூghi௃j⚪ḄᱯlmnoᦪឋḄᵨJj⚪ὃrsᦪḄ᜻ᏔឋஹᓫÑឋJὃr÷TUVḄuJὃrᑖçøùஹᦪ|AᔠஹèᓄÚᓄúU5}HuJὃrᦪ~z{ஹ}ஹᦪ~½ûU~.7.(2021üýὶÿ)
ᦪ>=/(ḄR,/(x)+/(—x)=0%>20ᨵ"“*/)<0,x+y=2020ᨵ஻+/(2020)>஻y)ឤᡂᑣxḄ"#%()x-xl2A.(0,+¥)B.(-¥,0)C.(1,+¥)D.(—8,1)ூ'ᫀ௃Bூ*᪆௃᪷-“x)+“r)=0.=ᡠ0“X)1ᙠR3Ḅ᜻ᦪᑣᨵ/(0)=0.5ᵫx>x20ᨵ"“)7"/)<0.>="ᙠ஺,+¥3ᓫ<⌴>.5y=஻x)1᜻ᦪᑣᨵ/(x)ᙠ(-¥,0)3Aᓫ<⌴>.ᑣ/(x)ᙠR3>ᦪᡠ0/(2020)<0.x<0y-2020-x>2020.ᡠ0/y
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Dx=0,y=2020,E/x
+/B2020C=/B2020C=/y
,ᦑ“xC+/B2020
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GᡂDxு0y=2020-x<2020,ᡠ0/(y)>/(2020)y(,))>/(2020)+/(x),IᩩKLMᦑXḄ"#%(-¥,0).ᦑ⌱B.ூᐵPQQR௃E⚪ὃUᦪ᜻ᏔឋḄXᵨZᓫ<ឋḄXᵨ*⚪ḄᐵP1᪷-/(x)+/(-X)=0.f(-x)=-/(x),ᡠ0/(x)1ᙠR3Ḅ᜻ᦪᑣᨵ/(0)=0.5ᵫ[>஽]0ᨵ/(%)-/(W)—7^——<0.y=/(x)ᙠ(0,+¥)3ᓫ<⌴>.5y=/(x)1᜻ᦪᑣᨵ/(X)ᙠ(7¥,0)3A12ᓫ<⌴>.ᑣ/(X)ᙠR3>ᦪᡠ0/(2020)<0.ᯠ_ᑖabc*ᓽe.230/397

236*⚪ᐵP1fgXᵨᦪḄឋhiᓄGklmᩭc*.o8.p1ᙠR3ḄᏔᦪf(x+2)=f(2-x)xG[-2,0]/(%)=(71q(-2,6)ᙠrsᑁᐵuxḄvwxf(x)-loga(x+2)=0(a>0x1)ᨵyᨵ4zG{Ḅ᪷ᑣ|ᦪaḄ%1()c~A.τ,1τB.(1,4)C.(I,8)D.(8,+oo)4ூ'ᫀ௃Dூ*᪆௃uḄX€R7ᨵ/"(X-2)=/(2+JC),/(.r+4)=/([2<-(.r+2)]=/[(.r+2)-21]=/(x),ᦪ17zᕜᦪT=4,5.2,0]/(x)=(ᙶ)-1,ᦪ/(x)1ᙠR3ḄᏔᦪqᙠrs(-2,6)ᑁᐵuxḄvw/(X)—log”(x+2)=0ាᨵ4zG{Ḅ|ᦪ*ᑣᦪy=/(x)Iy=log“(x+2)(a>1)ᙠrs(-2,6)3ᨵzG{ḄQ᝞ᡠD5/(72)=/(2)=/(6)=1,ᑣᦪy=log“(x+2),ᵫ⚪e.x=6Ḅᦪ#u1,ᓽlog஻88,.laḄ%1(8,+8),ᦑ⌱D.ஹDᦪḄᓫÏឋᨵᐵḄÆÖᦪW⚪
ᦪḄᓫ<ឋcᦪ1Xᵨᦪஹ>ᦪḄ᪀Gkl(m)ᡈXᵨᑖᦪiᓄᡂcᦪḄᨬ#⚪.o9.(2021ᓅ⊝⊝¡¢£¤ᐸ¦§¨(ᦻ))
ᦪ/(x)ª«Dজ0«<®2,ᨵ'&)7,ಘ<0Dঝᦪy=/(x+2)Ḅ³ᐵuQ(72,0)´.q|ᦪa,6ª«x-x{2/(/+2347/(7/72a),ᑣḄ"#%()(21a+bAµ111Rµ111C.µ1/D.[2,4]182j(421[2J]ூ'ᫀ௃B231/397

237ூ*᪆௃ᵫ0·¸<¹2,»"ᵨ)—"“)<0,e./(ᙠ[0,+8)3ᓫ<⌴>¿ᵫᦪx-x12y=f(x+2)Ḅ³ᐵuQ(-2,0)´.ᦪy=/(x)Ḅ³ᐵuÂQ´e.ᦪy=/(x)᜻ᦪ¿ᦑ"X)ᙠR3ᓫ<⌴>.u1./(஺2+2H4/Ç2+2஺)../+2È/+2”ÊË7"+2a—28W03—஺)|>7(2-ᑗ<0.ᑣa/1/Ò"Ób=y,ᑣ⚪kÔu|(y-x)W-(2-x)*0y.Q(X,y)ª«rÕ]᝞▢ØÙᑖ,ᵫãឋäᑜæe(x,y)I(0,0)çãḄl᜻ᦪ.q/(1)=-1,ᑣª«71êë(.72)ê1Ḅ஺Ḅ"#%1A.[-2,2]B.[-1,1]C.[0,4]D.[1,3]ூ'ᫀ௃Dூ*᪆௃ᵫᦪ/(x)᜻ᦪ.ë(71)=7/(1)=1,Gkl71ᡠ0.12஺—22—1,ᓽ1W&W3.o11.qᦪ2*+1'x'°ᙠ(8,+8]ᓫ<⌴ᑣnḄ"#%1.ூ'ᫀ௃(0,3]232/397

238ூ*᪆௃¿ᦪñ=B2ò+1'X'°ᙠµ8,+8,ᓫ<⌴..ᦪó=!^+11-1ᙠrs—8,0C3ᦪ..B_öD¿BDö=2*.00,xe(l,+oo).X+1X+1233/397

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iÈḄ᪷ᑣ᪷Ḅ=?.ூDᫀ௃(3,ᵪ)234/397

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242A.(-1,2)B.(-4,3)C.(-2,1)D.(-3,4)ூ9ᫀ௃Aூ<᪆௃(m?-m)4*-2y஺ᙠxC(-oo,-1]ឤᡂ±m?-m<^_=1ᙠxe(-oo,-1]ឤᡂ±ᵫÖf(x)ᙠxG(-oo,-1]ᓫR⌴U,Vx<-1,Ú.f(x)>2,.'.tn2-m<2./.-l(æVxeRឤᨵ/'(x)<2,ᡠCF'a)=/'(x)—2<0ឤᡂ±ᡠC+(x)=/(x)—2x—1ᙠRPᓫU.í+(1)=/(1)-2-1=0,ᡠCF(x)>0Ḅ<è((-8î]7ᦑ⌱B.ூïð5}௃ᑭᵨᓫRឋ<£®¯µ¶ᵨÖòপᑖó.ᦪô£®¯Ú(2)õᔠ.ᦪô£®¯Ú(3)ö.ᦪô£®¯Ú(4)<᪆¯÷õᩖḄ£®¯.Jxl+2,x<120..ᦪf(x)=f.úa€R,-ᐵÖxḄ£®¯f(x)N|x+a|ᙠRPឤᡂ±þÿḄ
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243/ᦪḄBᔠDᵨF⚪GGHI/ᦪḄឋKILᦪḄDᵨMN“ឤᡂQF⚪“RᐵTUVᵨWᓄNᓄYZ[ஹᦪ]^ᔠZ[ᮣ`ᜐᳮ.xlnx-2x,x>0,c21.de/ᦪ/(g)=i[jXW0Ḅ*klᨵnoᨵpq-rḄsᐵtuvy=-lḄwxsᙠ2"2'>="-1Ḅ*klᑣzᦪlḄ
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A.(0,1]|_,+8)B.(0,1][3,+8)C.((){+00)D.(0,£[3,-too)ூᫀ௃B238/397

245ூ!᪆௃60ீ¢W1'ߟ21,/ᦪ¨=/(%)=(©ஹ—1)2,ᙠª0,1«lᓫ⌴¯/ᦪy=g(x)=%5+஻2,mᙠª0,1«lᓫ⌴²³´/(0)=1,g(0)=¢/(l)=(m-l)2,g(l)=l+Rᡠ·/(0)>g(0),1/প1'n0<-<1,/ᦪm1119y=/(x)=(mx-1ᙠª0,Àlᓫ⌴¯ᙠª_/«lᓫ⌴²º'/(0)3.⌱B.ூÆZÇᓣ௃Bᔠl☢ḄᔜÊËÌ!ÍÎÏÐÑ/ᦪÒḄÓᦪF⚪⌕sᨵ?wÎÏÐÑ/ᦪ*+NឋKḄÔÕÖ×½ᦪ]^ᔠZ[ஹᑖËÙÚZ[ஹWᓄNᓄYZ[ÑᦪÛZ[5ÜḄVᵨ½ÝTÞwßàáâὃË⚪Ḅä^YåæçDwèé.ᑖ᪆ê·ëìÎÏÐÑ/ᦪÒḄÓᦪF⚪HI/ᦪÊËíஹ⚪Ìí⚪îḄï᧕-³ºᙠñòÒ-óôâõöD÷øᔜÊ⚪ÌḄᜓὃúÕ÷øâὃûüḄýþ-ÿᐙ
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ᓭ“=44"bn4?1-c=«4ஹᑣ°,ÝcḄᜧᐵA.a>c>bB.a>b>cC.b>c>aDb>ct>cூ#ᫀ௃Aூ'᪆௃)*+ᦪ-=14ᙠR0*1+ᦪ23ᡠ5‘47<’4᝾2ᓽc<஺2)*+ᦪ4ᙠಘ77?ಘ…70,+80*D+ᦪ24>3>0,ᡠ5Gᓽc>6,ᡠ5a>c>b,ᦑ⌱A.77?প31428-N3.2021OPQRSTUᦪ஻=_e2,b=-e37c=_e17e*Yᯠ[ᦪḄ\ᦪᑣa2b,cḄᜧ237ᐵ*A.a247C.2a<2cD.2"+2y2ூ#ᫀ௃Dூ'᪆௃+ᦪ)=|2V-1]Ḅ2᝞2:acbcc,f(a)>f(c)>f(b),uᔠT2஺a<0,c>0,/.0<2a2(-1,..2a+2c<2,ᦑ⌱D.-1|1.2[ᦪ+ᦪḄᜧ¡⚪[ᦪḄᜧj2⌕£a¤ᑖ[ᦪ\ᦪᔲ§¨2ᵨ[ᦪ+ᦪḄᓫpឋ2©ᵨ[ᦪ+ᦪḄᓫpឋ,⌕£a[ᦪ+ᦪḄªᵨ2©ª£a«¬0,1¨Ḅᵨ.N5.a=log6,/?=log10,c=log14,ᑣ357A.c>b>aB.h>c>aC.a>c>hD.a>h>cூ#ᫀ௃Dூ'᪆௃a=log6=1+log2,b=log10=1+log2,c=log14=1+log2,335577ᵫ°TD±².11'³´a-log,6=1+log2=1H------,b=log10=1+log2=1H------355log3log,52c=log14=1+log,2=1+-1—,ᵫlog,3c>bB.a>b>cC.c>b>aD.b>c>a241/397

248ூ#ᫀ௃A2332333233233ூ'᪆௃_<,InÃJInJ.ᓽa>c,ln_c>b.ᦑ⌱A.1.3Å+ᦪஹᢣᦪ+ᦪஹ[ᦪ+ᦪḄÇᔠÈÉʨ+ᦪËᦪ»ÌÍᦟᩞº⌕ᑁÑ2ªᵨgÒ2ÓÔÕÖËὃ×⚪Ø2ÙÚ+ᦪឋÛḄªᵨᜧ¡⚪2ÜÜÝÞ+ᦪஹᢣᦪ+ᦪஹ[ᦪ+ᦪ¨Çᔠᙠß2ὃàὃáḄÇᔠªᵨTâ'ã¡⚪Ḅäå.N1.(2021g¹æ᪥ὶὃ)STa=4°6,å=log0,c=ln2,ᑣ()A.c405=2J=log30ᡠ5a>2,0,/(x)*D+ᦪ.ᡠ5/(x)2/(0)=0,ᓽe*—x—120,ðñðx=0jò¨ó2ᡠ5e*>x+l(x*0)..229911ᦑÄ=eloo>_----_|_1=---->----=a,ᓽ.10010010111_yg(x)=lnx-x+l,g'(x)ô-1=2bg'(x)=0,'¶õ=1.XXXe(o,l),g'(x)ு0,g(x)*D+ᦪxe(l,+oo),g'(x)<0,g(x)*1+ᦪ.ᡠ5g(x)

249ᡠ523)*,ᡠ5஺ுc,3)*Tnx>—x+l(x=1),ᡠ5100100100100,101,100100,1……c=In___=-In___>-___+1=___=a7niᓽc>a,Ç0஺>c>a,ᦑ⌱B.100101101101ூᐵrsst௃É⚪ú⌕ὃàᑭᵨ}ᦪẆ+ᦪḄᓫpឋᩭ'ãᜧ¡⚪2'ãÉ⚪Ḅᐵr*᪀⌼+ᦪ“X)=e*-x-lüg(x)=lnx_x+l,ýþÿ⚪.1.4ᔠᦪḄ᜻Ꮤឋஹᓫឋᜧ1nx1./(X)ᙠ(8,0)#(0,+8)%ḄᏔᦪ&'(x«0,+8)+&/(.r)=—./<2=á(_âc=/21ᑣ-ãcḄᜧᐵ5()IyIIyIIII2J<2)೐A.a>b>cB.c>b>aC.h>c>aD.c>a>bூ7ᫀ௃D;<᪆>?@/(x)@Ꮤᦪ&ᡠBa=;b=;2)I2)I2/(xe(l,e)+&/(x)^llnxl^111A,.((x)=1"",\X\XX2?@xe(l,e),ᡠB00,ᡠBy=/(x)ᙠxe(l,e)%ᓫ⌴O&2eᐔ(e\(7i\f2ஹQ_321(2Y'127?@><2<22,ᡠBc>a,ᡠBc>a>/?,ᦑ⌱D.ln~T2Tூᐵ`ab௃c⚪ὃe᪷gᦪᓫឋᜧ&<⚪Ḅᐵ`ᑭᵨjᦪᑨlmn(oᙠxe(l,e)Ḅᓫឋpqᑨl.2.ᙠR%Ḅᦪ/(s)=t'*-1(v@wᦪ)@Ꮤᦪ&xa=log3,Z?=/(log5),c=/(2})ᑣa,b,cḄᜧᐵ5@052A.a

250C.c0,T=-11X(-9)x(-7)=-693<0,237>-1lx(-9)x(-7)x(-5)=3465>0,7=3465x(-3)=-10395<0,T=-10395X(-1)=10395>0,[(n>6+&T=aaaaaaa>0,'6ni23456nl,+i=444+i=஻=2஻—1121,ᓽTNT,ᡠB(“26+&ᦪᑡTᓫ⌴O&ᡠBᦪᑡTT—aaa஻+௃«+i஻nnn12nᨬᜧ⚗&ᦪᑡ1ᨵᨬ⚗7=70395,ᦑ⌱c.2.ᦪᑡ4Ḅ¡@d,¬w⚗®@S“&ᑣ“d>0”“5+5>25>>Ḅ465A.ᐙᑖ³⌕ᩩ¶B.⌕³ᐙᑖᩩ¶C.ᐙᑖ⌕ᩩ¶D.·³ᐙᑖQ³⌕ᩩ¶ூ7ᫀ௃Cூ<᪆௃V(S-S)-(S-S)=a-a=d,(d>0,S&+S6>2¹(S’+S',>2S§,d>0.ᡠB6554b5“0”“S+S>2s5”ᐙᑖ⌕ᩩ¶&⌱C.46244/397

2513.ᙠᦪᑡ4“&«i>0,d>0,¬஻⚗®@S”ᦪᑡdÁÂ"="|,"=m&¬"⚗®@T”ᑣ¿ÀA.SQ*஺B.S4<஻C.S4=74D.SA^TAூ7ᫀ௃Aூ<᪆௃ÄÅÆᦪᑡ5Ḅ¡@q,ᑣᵫ⚪q>l,ᦪᑡbnÀᓫ⌴O&[&=È+ᵪ¿Ê+63À=஻|+஺4—஻ËÌ=S¿1—qÀ+al~q^=~~^¿᝞஻ÏÀ=^~~^¿sÊÀ>0,ᡠBSQA.qqqĩųÐÑa=7n-4,ᑣᦪᑡmḄ¡q=3"=2,ᡠB5=54,7="#—À=45,ÒᯠS>T,nn444401—q⌱A.1.6ÔÕᦪḄᜧ⚪tana+tanp+3tanatanB=3,ᑣa,0Ḅᜧᐵ5¿À1.┦Õa,஺ÁÂsina—cosa=’A//-6A.a<<0B.p<^aC.;0,ᡠB[tana+tanp+3tanatanp=3,ᡠB=a>tan¿a+pÀ=tana+tanP=3,ᡠBa+p-ᡠB-.ᦑ⌱B.=,[a>p<OM>MP,ᦑᨵsina0¿ᐸï¿xÀᦪf¿xÀḄjᦪÀ,22245/397

252ᑣðᑡ³ñᡂóḄ¿ÀA-஻0À>ô©ÀB.¶ᶌ2஻9D.ô(-$0,ᦑᦪᙠú%@Oᦪ&ᵫF¿OÀF9ு,ᓽ4349>/᣸◀B⌱⚗.ᵫ0<?ᓽ/'OX2/%,᣸◀C,⌱⚗.ᵫ'(ᡀ*fᓝᓽ-0-%c>bB.c>b>aC.c>a>bD.a>b>cூXᫀ௃Aூ[᪆௃?@ᦪ<(x)=sinᐝf(A)=log,x,(x)=logx,£(x)=3ஹᑣ"a/(x)bc(x)def2n5QḄgᙶ᪗bakb%defQḄgᙶ᪗cacᜐbo஺defQḄgᙶ᪗ᙠrsᙶ᪗tu,vwx,xx,x,xḄde᝞dᡠ{.ᵫd|}a>c>b,ᦑ⌱A.ூᐵQQ௃⚪ὃ@ᦪPQᜧ⚪Ḅᐵa@ᦪPQᓄT@ᦪḄfQᙠrsᙶ᪗tw@ᦪḄdefQḄgᙶ᪗.246/397

2532.1@ᦪbᔠᙠḄu|ḄᱯQ᪀⌼@ᦪ¡¢£@ᦪḄᨬ¥¦§@ᦪḄᨬᜧ¥ᡈᨬ¥ᡂª«ᑣa¬aᡂªḄ®¢|Ḅᓄᑮ£@ᦪḄᨬ¥°ᩭ.,ஹ2x31.(202178²³ᨴὃ)µ}@ᦪ/(x)=ln(x+l)----------x+2(1)%x>0«/(x)>0¶(2)%…+0,ᓽ/(᜜ᙠº»¼ᑁT¾@ᦪᓽ|¿.(X+1)(X+2)2(2)᪷Á(1)¿Âk=%uj•0«f\x)=-='>0,ᦑ/(x)T¾@ᦪ/(x)>/(0)=0.x+1(k+2)~(x+l)(x+2)-(2)ᵫ(1)}%ln(x+l)>2xÂ1«ᨵ2"<]n஺+Jn_Z_<]n3x+2------------12Î+1n஻1II~+2I)YI„2,22,32τ஻+1ᦑ_<111_,_

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2551ᵫট4=2"-2,1_2"<1.11^11<<1121]__8^2"1_ᐭফ]=2------T~----------<----------h2-122-1d஺2^zn஻-1n-22"-"32'-'s<2^+l++1Y21-£_4f1>.rJ—^஺,'eX-444ᓛ_/'(x)<0,'-2kêëGZ),/2kxீ2kç~(keZ^).<<444(34jr\**(᝕eZ)⌴¨.ᡠ@ᦪy=/(x)ᙠ2■8,2¢/8(▕Z)⌴¥,2kᱝ<44472k4I7(3஻3^জ©be2kî—«eN)2k7r+¯81<0,f(2k^2/r)=e2k^-l>0,8“|®22k2>ூᡠ@/(X)=0ᨵ±ᨵ8/;(³2k^+~2kᐔঝ©2,€wN)/(2¶=e—1^0,2ZTZ4~—4-1>0,4(:/2ᦇm81௄81<0,ᦑ©/(x)=0º/;2஻[jr(ZeN),/(x)=0ᨵ½ᨵ8/.©Z?£2Z□■8Ẇn42k2I¾ᔠজঝ'h¿)(஻Z2)ᙠ8ஹ▲ÀÁÂ஻=0,ᦑ᧕Äᦪy=/(Å)ᙠ(0,ᵨ249/397

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2581$rᦪᑡ&NḄs⚗toফlᦪᑡLvNḄgᐔ⚗i]rx\^2aM.4,71=1,2$ᵫ1$b¢=L,rஹ,¥u”ᑣᦪᑡL----NḄg2⚓i”2n+1,n>2SneN'/5+/+•.•n=l4=©=᜼.•.n=l,7o=A¬4<1111■'+--+----+,,,+--------------..T4x55x77x9(2n+l)(2n+3)n=—+—+—a+•■•+—5ߟaifl22a30n0n.i111111111ஹ31=47S+2X[(S-7)+(7-9)+"'+(2^M_2^T3)]=20+2X(12n+3)=20-4n+6•.•ᙠᐔe,n>Lne%•••4n+6N0,.•.ᯅ£²•••”-1N-♦³´ᯅBµ¶\·¸Ḅx¹ᵨḄ»¼\1$½¾¼\2$ᑖ᪆¼ÀÁᔠ¼Ãᑭᵨᑖ᪆¼ᑖ᪆ÅᑭᵨÁᔠ¼ᑖ᪆o3$ÆǼÈ⌕sÊᑖËᑖÌḄ᡽ᜧᡈÇஹ⚗ᦪḄR]ÀÐÑÒÓÔᑮxḄÖḄ.ூ×ØÙᓣ௃Áᔠ☢ḄÜݸÞ
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262ூ᪆௃ᵫ⚪3x—1<0,1,ᵫx2+(a+\)x+a1,ᑣᑣ(x+l)a+a)40Ḅ6$D.஺,.1I,ᑣD.a,-lI9QIᦑ“>1.STᨵVaḄWXZ$[-1,+»“]-τ,ᦑ⌱B.L3)ூ`abc௃d⚪ὃfghiḄ.ᐗkl&'(Ḅmn⚪oᐜqrs(tᓝvwx#(ᑖ᪷{•ᐗkl&'(ᡠ~ḄḄ᪷Ḅᜧᑖᑏ6.᝞3&ᓝvwxᑖ◤⌕ᐜ~ᑨ(Ḅᜧᐵᑨ(ᜧ'ᵨ᪷(~Ḅ᪷ᑏ6.2.&'(8/.(8sina)x+cos2aN0~xcRឤᡂ*ᑣ஺ḄWXZ$.7T5§ூᫀ௃D0,_ID—ಘ66ூ᪆௃&'(8x2-(8sincr)x+cos2d>0~xឤᡂ*ᑣᨵA=(8sin^2-4x8cos2(z=64sin2o-32cos2a^07ᓽsin2aW1.0ឤᡂ*ᑣ¼ᦪ¾ḄWXZ¿.ூᫀ௃(-8,2+22)ூ᪆௃À3x=t,ᑣ¶x£(0,+8)À(1,+«>),ÂÃ஺=1—mt+m+l(tW(l,+00)),ᑣᵫ⚪y(r)=t2-mt+m+l(te(1,+8))Ḅ²ÈឤᙠxÊḄTo/=(.w)2-4Ḅ+D<0ᡈ256/397

263Ì0,.W1,m<2+222/(!)=1—/n+m+120,4.Îᦪ/(x)=x2-1,~-xe[2,+8ஹ//(B-1)+4/(º)ឤᡂ*ᑣ¼ᦪ"2IL3)IwJḄWXZ¿.ூᫀ௃mW—ÐᡈºÑÒ■22X22223ூ᪆௃Ô{⚪D.1.4Õ(/_1)<(A-1)-1+4(--1)ᙠxwJ+8)Tឤsᡂ*ᓽm213233325-4w2<--+1ᙠxw+oo)Tឤᡂ*.¶x=Îᦪy=--+1WᨬX.ᡠ×222:2Xx3m~x'x2»4º2«-5.ᓽ(3º2+1)(4"?2-3)20,Û4.Üᡈº2Ý.m23225.µ³ÎᦪÃḄk%2—2×.1+ma£R.প3஺=2,àÎᦪy=KO(x>0)ḄᨬX?xফ~-Ḅx£D0,2I,&'(ᡂ*à஺ḄWXZ.V(1)Ô⚪^=v?-4v+l=l-.#$>0,ᡠ×x+^2.¶åæ¶X@yx+4xXXXXXᓽx=l'çᡂ*.ᡠ×y>-2.ᡠ׶x=l)FḄᨬX$-2.X(2)#$4*).஺=᮱.2×.1,ᡠ×⌕%“~-ḄxCD0,2J,&'(f(x)&ᡂ*”í⌕“î.2ax—lW0ᙠD0,2Iឤᡂ*”.&ïg(x)=r-2ax—l,j?(0)W0,Do—o—i^0.ᑣí⌕g(x)W0ᙠD0,2ITឤᡂ*ᓽo.ᡠ×ñ,ᓽò(2)W0,14.4a-lW0,33+«)1Ì.ᑣaḄWXZ$LiJ.43.ᐸôÎᦪV~ឤᡂ*Ḅn⚪õᵨᑮ×±°Vপa2/(X)ឤᡂ*oaN/(x)max(2)a

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266ூF௃ᑭᵨᑖW^Xᦪឤ()ᡂ#$G᪷fᑣJ¡W^:(I)VxeD,/«/(x)<»m>/(x)ymax(3)3XED,/n/n/(x)<=>/n>/(x)$.n)n§2.¨©2x+஻?+ª>oa~ᑗx£(l,+oo)ឤᡂ#$ᑣᦪmḄ®(°).X—1ூ/ᫀ௃(-10,4-00)ூ^᪆௃᪗+,஻+6>0Gᓄ³2஺-1)+´>~ᑗ~2,X—1X—1Vx>l,.,.2(x-l)+—>22x-]•¶=8,i·¸ix=3l®¹.X—1X—1;2x+"7+->0a~ᑗx£(l,+¼ឤᡂ#$—/H—2<8,^5¾>~10.x-l§3.x2—2%+52À~3aabcᦪxឤᡂ#$ᑣᦪaḄ®(°³()A.[-1,4]B.(-8,-2]U[5,+8)C.(~8,-1]U[4,+oo)D.[-2,5]ூ/ᫀ௃Aூ^᪆௃x2—2x+5=(x—1Ã+4Ḅᨬ'(³4,ᡠfx2—2x+5$a2—3஻abcᦪxឤᡂ#$Ä◤a2—3a^4,^5~10aa.×ஹᑖÖᦪᡠÆḄÇÈឤÉÊᦪËÌᐗᑖAÎ$ÏKÐ⚪Ñᓄ³WÌᐗXᦪḄᨬ($JKW6ᦪ°.ᑭᵨᑖᦪᩭÓÔ/(Õ4)20(XGD./I³ᦪ)ឤᡂ#×ᦪØ®(°ḄÙÚÛÜ(1)ÝᦪËᑖ$ᓽᓄ³g«)2/(x)(ᡈ80)ß“))ឤᡂ#ḄÉy(2)W/(x)ᙠxe஺Ḅᨬᜧ(ᡈᨬ')(y(3)^ga)"(X)max(ᡈgR)"(x)).5©J®(min°.〉ᵨ⚪ä(1)ᦪËᑖy(2)XᦪḄᨬ(᧕W6.§1.(2021æçḕé×êë×᪥íîᨴὃ(ᦻ))¨©Xᦪ/(_)="2+2(a-l)x,g(x)=2lnx+2,aVx«0,+oo),஻x)2g(x)ឤᡂ#$ᑣ᦮ᦪaḄᨬ'(³()259/397

267A.1B.2C.3D.4ூ/ᫀ௃Bூ^᪆௃/(%)2g(x)ᓽ³f2+2(஺-1)x221n%+2,a(x2+2x)>2

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269ᵫ(3a+b)(z+6=10+^+210+2]£=16,£=ᓽ.=aI'ᓽᨵm=16,ᑣmḄᨬᜧ16,ᦑbᫀ16.'éÖᣚr——ëìíé3&'(ឤᡂ+,⚪ᙠᑖ23ᦪ⍗ᑮMḄᡈὅᓽo᧕ᑖ2D3ᦪ47ᦪḄᨬᓾ6D:rὃ⇋4ᣚ¡¢£¤“¦§¨”ᓽª«¬iḄ¨ᐗ43ᦪ4Ḅ“ᙢ¯”°ᣚZ±4²³£´µ¶%ឤᡂ+,⚪··r¸¹&º⌕Ḅᑖ»Mᡈo,⚪¼½ஹ¿ᓄÁᑮ‘'ÃÄÅÆᶧÈÉÊᨩÌÍZ᩟”ḄD᜻ᑴÑḄᦔÓ.O1.TU0WmW4ḄÖ×m,&'(x2+mx>4x+m—3ឤᡂ+ᑣxḄaFÙ.ூbᫀ௃(-8,-1)0(3,+8)ூ-᪆௃&'(rᓄm(x—l)+x2—4x+3>0ᙠ00X2—4x+3>0{“ààáo={/"tᓽx3./(4)>°x2-l>0ᡈ“O2.st7ᦪ/(x)=x2+ä-1,uTUÖ×xw[ç஻?+1],\ᨵ/(é)<0ᡂ+ᑣ`ᦪêḄaFÙ.ூbᫀ௃(—¥°)ff(m)=2m2-1<05ூ-᪆௃ᵫ⚪×rIì(x)<0TU[ᓅ"+1]iឤᡂ+ᓽ:{IஹcIcà-I♦<ᵨ<0.[f(m+1)=2m"+3m<02O3.TÖ×/ne[—1,1],7ᦪ,/U)=]2+(m—4)x+4—2mḄឤᜧU<6xḄaF.ூbᫀ௃(-8,1)U(3,+oo)ூ-᪆௃ᵫf(x)=x2+(m—4)x+4—2/n=(x—2)஻z+ᐗ2—4X+4,jg(/w)=(x—2)᪷+9ߟ4x+4,ᑣù,⚪úᓄᐵUmḄZ½7ᦪ,⚪.ᵫ⚪×tᙠ[-1,1]ig(m)ḄឤᜧU0,\-Ix3.L(1)=(x—2)+f—4x+4>0,ᦑxḄaFÙ(Z8,1)U(3,+8):TÖ×Ḅme[—j,I],7ᦪf(x)ḄឤᜧU<.Ùஹᦪîïᔠuᡠþ&'(ÿᔠᳮḄᓄ/(%)>g(x)(ᡈ/(X)?@AB?CஹDᣩ.F1.Hᐵ6xḄJ4Lr<3x—4(஻>0,Sa/1)56UVḄx>2ឤᡂZᑣ஺Ḅ\]_`()261/397

270a0,bD.I2C.[2,+8)D.(2,+8)ூiᫀ௃Baaூm᪆௃J4aa<3x—4o6஺plzᙠ|}~☢+ᙶ᪗44"ᦪḄ$%᝞$জᡠᵫ$ᩩx00A.[0,+oo)B.[0,e]C.[0,1]D.[e,+oo)ூiᫀ௃Bூm᪆௃ᵫ⚪V'("ᦪ¨=7(ᔩª¨=<«—1Ḅ$%᝞$ᡠ.HJf(x)¬ax-1ឤᡂZᨵ0

271fl2X2,00m/x>0ᡈx<-2,ᵫ3/+6x<0m/}2ீ3<0,ᵫ3.F+6x=0,x=0ᡈx=-2,.•"ᦪg(x)=V+3X2+"?,ᙠ(—8,-2),(0,+8)Îᓫí⌴ïᙠ(}2,0)Îᓫí⌴ð.1.3ZG[-4,-2),g×min=g(—4)=ò—16,•J/(S)-g(r)>0,/.-8>m-16,ᦑ¤ᦪóᜐ8,ᦑ⌱C.ூᐵõ²²ö௃H¡÷-4,-2),3/e[-4,-2),J/ব-g×20ᡂZùᓄú஺*û(஺*ü᪷þm᪆JÿᦪᦪḄᨬ᫏⚪.Úஹñᐗòᓄ.(2021)஺beR,e'2ax+'()*Ḅ+wRឤᡂ.ᑣahḄᨬᜧ2()1eA.-B.1C.2D.-e2ூ9ᫀ௃Dூ᪆௃=a<0,ᑣ>=B+8ᓫE⌴Gy="ᓫE⌴JKLMNO᮱QB+ᓃ(xeRឤᡂ.ᦑU஺QD.=a=0ᑣV?=0.=aு0,ᵫe'da+b\]N'-ar,ᑣa`be'-aᦪ/(x)=ae'-a-,.,.c(x)=a/-/="(e*-a),e/'(x)=0\a=0,ô|x=Ina,263/397

272fx0,ᦪ/(x)⌴Jijfk=l"hᦪ,(X)mᨬ/(X)Ḅᨬ2.ag(a)=ᶭ-/ᔊ஺(4>0),g'(n)=tz(l-2/n«)(a>0),ᵫg'(a)=0\a=J",1ef00,fa>&hg'(a)<0,.•.fa=rhsUm\ᨬᜧg(/)=«u•e>.abḄᨬᜧ2—ᦑ⌱D.2ூxyrz௃K{|ឤᡂ.}⚪~জᑖᦪ஺2/(%)ឤᡂ.(஺2/(1)ᓽ)ᡈ(ᐝ)ឤᡂ.(஺4/(ᓽ)iঝᦪᔠ(y=/(x)ᙠcg(x)ᓽ)iঞᨬ/(x)M20ᡈ1n0ឤᡂ.iটᦪ᣸◀Kᔠ⚪*Ḅᦪ⌱ᔠ⚪*Ḅᦪ.2./(+)¡¢ᙠḄ᜻ᦪO/প=1,=¥஻§-1,1,¥+"0h¨©ª1>0,=m+n/(x)4f2-2m+i(ᡠᨵḄឤᡂ.ᦪfḄm.ூ9ᫀ௃2ᡈ2ᡈ=0ூ᪆௃®⚪K{|ᨵ¯°±B²ᐗ´ᣚḄ¶ᶍᐜ²¹º¯°±᧕\/(X)¡¢ᙠḄJᦪᡠB/(X)ᙠ-111ᨬᜧf(l)=l}⚪´ᓄ2½-2ᡂ+121(ᡠᨵḄae-1,1ឤᡂ.¾}⚪Ḅᑮ´ᓄ.À2",”Â1,1,஻+"Ã0h¨"3>0ᡠBᦪ/(ÄᙠÅ-1,1JᦪᡠB/(x)ᙠ-1,1m+nᨬᜧ."1)=1,f(x)4J-2Æ+u(ᡠᨵḄឤᡂ.ᓽ½-2S+1N1(ᡠᨵḄa4—1Çuឤᡂ.t2-2at>0(ᡠᨵḄae—1,1ឤᡂ.eg(a)=-/+2a/,È◤MN|˺\Ì-2ᡈd2ᡈf=0.gপ40ÛஹôᵨᦪẆ÷ឤᡂÝW⚪ÍÎᦪÏÐK{|ᡈẆÒK{|ឤᡂ.}⚪ḄÓ®ÔÕBᦪÖK{|2ÓẠᓫEឋ2ÙÚᨬ(᩽)2ÜÝᑭᵨ´ᓄàᓄáÔâãᦪᔠஹᑖå{æçèéêëÒì~¾K{|}⚪´ᓄ2ᑨîᦪḄᓫEឋஹᦪḄᨬᑭᵨᨬ\ïðᐸᑖåì~ᵨᑮḄᦪòÔâ.ᑖᦪஹ᪀⌼ᦪ~ᵨ.264/397

2731.(2021õö÷ᐶᨴὃ)e2ûᯠ(ᦪḄýᦪ஺'2ᦪOK{|lnx+(2e—a—l)x+8+lW0Ḅxw(0,+8)ឤᡂ.ᑣᨬᜧaḄ()a+1A.2eB.2e-lC.3eD.3e-lூ'ᫀ௃Dூᑖ᪆௃ᐜ᪀⌼/ᦪf(x)=lnx+(2e-a-l)x+b+l,12-(x),456728(9:400,ᡠX/(x)ᙠ(0,+Z[⌴]^_ᔠᩩbᦑa>2e-l"஺)=஺26,g(/)="~ᑣga)_/2eE(’2e)2ᙠrsয[⌴u,R^,(3e)=0,ᡠXg(f)ᙠ(2e,3e)[⌴](3e,+s)[⌴uᡠXg(f)ீg(3e),|[2<ᨬᜧ}a+l=3e,a+1ᡠXa=3e-l,ᦑ⌱D.ூᐵ௃⚪Ḅᐵ᪀⌼/ᦪᑭᵨGᦪ12/ᦪḄᨬ.2./ᦪJ(x)=ax+

274x,xe[l,e].(1)஺=1,17U)Ḅᨬᜧ.(2)yu)woឤᡂ1ᦪ஻Ḅ.1—8,—~ூ'ᫀ௃e+1Ie_.Ix+1ூM᪆௃(1)a=Lᑣf(x)=x+lnx,f(x)=\+-=*xxxe[l,e],ᡠXf(x)>0,ᡠXf(x)ᙠ[Le][]/ᦪ,ᡠX஺¡=¢)=+1.(2)f(x)W0ᓽax+lnxW0x£[l,e]ឤᡂᡠX,“¤¥e].xlg(x)=——,x£[l,e],ᑣg'(x)=——1XX2265/397

275XG¨1,e©,ᡠXg'(x)WO,ᡠXg(x)ᙠ¨Le©[⌴uᡠXg(x)min=g(e)=-—ᡠXax4-1(2)^¶·fGJ>ᦈ1ᙠ46E,21©[ឤᡂ1ºᦪ஻Ḅ.ூ'ᫀ௃(1)»M᪆(2)(0,e-l).ூM᪆௃(1)ᵫ⚪⌕´ex>x+l,¾◤´/'(x)=”%—120,1G0,xe(-8,0)f(x)=ex-1<0,•V(x)ᙠxe(0,+8)]/ᦪᙠ:te(-8,0)u/ᦪᓽfಘᙠx=0ᨬÇ/-(0)=0,fix)>/(0)=0,ᓽf(ᑐ)=ex-%-1>0,/.ex>x+1.(2)^¶·/(Éுᑁ-1ᙠÌ6Í2©[ឤᡂᓽe*-x-l>ax-lᙠx[ឤᡂÏᓽᙠxGÐ2©[ឤᡂlg(x)re<2©,XÑ19(É=?ᙠ46£,2©[ḄᨬÇ0'(Ó=eÔxeR,4/(É£°,xe¨L2©©g'(x)>0,...Ö€Ø,1©©g(x)ᓫÚ⌴uxe¨L2©©g(x)ᓫÚ⌴].,.ÛÉᙠÜ=1ᜐ<ᨬÇ·1)=e—1,.•.ºᦪ஺Ḅ(0,e—1).ூÞßàᓣ௃[âãᒈ᪆8ᦪåæὃèឤᡂé⚪Ḅêë⚪ìíMîMïðñ⚪ò⌕óô·ãḄᱯö⌱÷ᔠ〉ḄùîXúûüÉý.(1)þÿ
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278A.10B.11C.12D.13ூᫀ௃Cூ᪆௃ᦪᑡaa=2,S=28,ᦑa+44=2,4^|+04^=28«ᓽ2a+34=14,"54121#4=10,J=-2,ᦑ=஻xl0+)næn-l)x(-2)=-n2+iln=-n(»-11),z?eN,.1S-2஻(஻211)<0#n>\\,4஻eN*ᦑ”Ḅᨬ9:;ফᦑ⌱C.n>2.?@ᦪᑡa,,Aᦪᑡ/=8,4=4,ᑣD஻⚗FS“ᨬᜧḄA()A.SB.⎃ᡈS5C.§5ᡈ§6D.§63ூᫀ௃B.ூ᪆௃ᵫ?@d-4-4=4-8=-4,a,=%+(n-3)d=8+(஻-3)x(-4)=20-4J,ᵫO=20—4஻N0#஻<5,ᡠR⁐>0U=0/<0,ᡠR&=S5AS஻Ḅᨬᜧ:.ᦑ⌱B.>3.(2021•XYZ[\])?@ᦪᑡ%ḄD஻⚗F;S“4U_3,S5430,ᑣ4Ḅᨬ9:A()A.-1B.0C.1D.2ூᫀ௃B,ஹ[a,=a.+J>3ூ᪆௃bᦪᑡaḄc;d,ᵫᩩfj'iF(;+423,ᵫjkḄឋmn«^5a+10J<30'no௃a+2446ெ5iI,#4=2(q+4)-(q+24)22x3-6=0,ᦑ⌱B.×ஹᦪᑡDᦪ'ḄïᔠḄᨬyW⚪পtᦪᑡ/ḄD“⚗FS”Ḅᨬ:u⌕Awxyz)জẆ}ᦪᑡ;=/(஻)Ḅ⚗Ḅ~ᑨS,Ḅᨬ:ঝẆ}s“Ḅ⚗ckts“Ḅᨬ:.ফtᦪᑡḄᨬ:u⌕ᨵwx)জᦪὃ⇋ᑭᵨᦪy=/(x)Ḅឋmtᦪᑡa=/(஻)Ḅᨬ:ঝᑭᵨᦪᑡᦣḄᱯὃᡈ1%4+:ᯠᑨᦪᑡaḄᨬ:~.njஹீn~ak-\[ak-ak-\(3)ᦪᑡjk¡ᔠḄᨬ:£⚪¥¥¦§¨ᦪḄឋm(᝞ª«ᦪஹ“¬ᦪ”ஹᢣᦪᦪ)ᡈ®¯jk.268/397

279>1.?@ᦪᑡ஻°±஺=15,%2%=2,ᑣḄᨬ9:;()n1nn27A.7B.2715-1C.9D.24ூᫀ௃Dூ᪆௃ᵫ⚪µ@a,^-a,=2n,o-cz,=2-l,a-«=2-2,a“-a,i=2(஻-1),¹Rº“»232/\2(H-1)(1+஻-1)2LL,ICkÀÁ#஺~a~2(1+2+3+n-1)==n~-n,ᡠRa=n2-n+15,w12”,4'=஻+15_I,1g(x)=x+15_]()=_15=)-15[]^()xe03x<0——_gx\——2ÇÈnnxxxÇxc[4,+00),g'(x)ு0,g(3)=3+5-1=7,g(4)Ê+˪]=27,ᦑᨬ஻⍦:27,ᦑᫀ;D.444>2.(2021•ÍÎYÏÐÑÒÏÐÑÓÔÓᨴὃ(ᳮ))?@ᦪᑡa°±a=1,fl,,+l+1=1.Øa஻+i-S஻+1NOឤᡂÜᑣÝᦪ()A.ᨬ9:A2e-1B,ᨬᜧ:Aᔠ-1C.ᨬᜧ:AeD.ᨬ9:Aeூᫀ௃Cூᑖ᪆௃ßàH-a“=a,+áln(“e+l),᪀⌼ᦪ/(ä)=x-ln(x+l),ᑭᵨåᦪ@æn#O”>a>a=l,nt¹a—ta+]20ឤᡂÜᓄ;/«+1=2%+i+1.ஹ2])ឤᡂÜ᪀⌼ᦪg(x);4QN2),ᑭw+inaIn(a+1)(""+iInxnn+lᵨåᦪ@ætêg(x)Ḅᨬ9:ᓽn#.ூ᪆௃ᵫëᵨ-=1#%+1+1=ì#ê=í—1="1,a„=ln(a„+1),ᡠR+11V*a-a=a-ln(a+1),1/(x)=x—ln(x+l),ᑣ/(x)=l-=(x>-l),/J+1nn+171+1x+1x+1Ç-l0,ᡠRf(x)ᙠ(21,0)º⌴òᙠ(0,+00)º⌴óᡠRÇô=0È/(õö#ᨬ9:/(0)=0,ᡠR/(õ20,ᡠRᔣ)20,ᡠRa>a,>a=1,ø;a„-to„+l>0ឤᡂÜᡠRta„

280.1úëûü—1)ឤᡂÜ,1gপᑣ᝞"lxlnx-x--=lnx-1=2Inýþnn+1ÿing'(x)<0lnx-1<0,0cx0lnx-l>0,x>e,ᡠg(x)ᙠ2,e)⌴ᙠ(e,+8)⌴ᡠx=eg(x)ᨬg(e)=e,ᡠMe,ᓽfḄᨬᜧe,ᦑ⌱c.ூ!௃#⚪ὃ&'()Ḅឤᡂ,-ᨵ/0⚪1ᢥ᝞45ᑣ7ᓄ9®^k>f(x)ᙠa,:ឤᡂ,ᑣk>/(x);max/(x)ᙠ3,ᑗឤᡂ,ᑣk/(x),;njnA(C)ᙠ3,ᑗᨵ/ᑣD4/(X)max;E3.F⚗(Hᦪᑡ4Kaoi=a+2a4)Lᡈᑣ£+;Ḅᨬ(()282016201A.1B.-C.PD.-ூQᫀ௃Cூ/᪆௃•UF⚗(Hᦪᑡব}Ka2oi8=a2(M6+2a2oi4a2()i4q4=a2(H4q2+2a2oi4TazoiQ஺,:q4=q2+2/1q2=2,.*.q=>/2,aa=4a^ajxqn+m_2=4aJ,qm+n2=4,m+n=6,mnᑣ+-=-(A+-)(m+n)=-(2+ஹ+>]^&=`]m+n=6ᓽm=n=3(a.mt16mlimnE4.(2021•cdeᐶgh)ij4,k…஺51,2,3,4,5Ḅmnop᣸ᑡ.ᑣrs:uvmn஻e{l,2,3,4,5},xᨵy+k++஺“4Ḅ᣸ᑡ4,a....%ᨵ()2A.49pB.50pC.31pD.72pூQᫀ௃Aூ/᪆௃|1+2+3+4+5=15ᡠ஻=54+k+k+/+/=15W54ᡠ423,a=5mn᣸ᑡᙳrs⚪n;ᐳᨵ&=24p14270/397

281஺4,⌕a2H5,ᐸ᣸ᑡᙳrs⚪n;ᐳᨵ3x3x2x1=18p,=3/1ᡈ2,ᡠᨵḄ᝞49᣸ᑡ32145,rs⚪n;᣸ᑡ31245,rs⚪n;᣸ᑡ32154,rs⚪n9᣸ᑡ31254,rs⚪n;᣸ᑡ32415,rs⚪n;᣸ᑡ31425,rs⚪n;᣸ᑡ32451,'rs⚪n;᣸ᑡ31452,'rs⚪n;᣸ᑡ32514,'rs⚪n;᣸ᑡ31524,rs⚪n;᣸ᑡ32541,'rs⚪n;᣸ᑡ31542,'rs⚪n;ᐳ7prs⚪n.rs⚪nḄ᣸ᑡᐳᨵ24+18+7=49pᦑ⌱A.ூ!௃/⚪Ḅᐵ᪷⚪nᐜḄ¡ᑖ£¤,µᙠv஺1=3¶◤⌲p¹ºḄ,k஺4,¥1Qᫀ.ஹᦪᑡᨬᜧá⚗W⚪sE1.¦2021.ᓅ©ªP«¬ὃ(®ᦪᑡ¯a°Ḅ±"⚗³Sija=-5,a=-1.i»=3஻=1,2,…)ᑣᦪᑡ¼°Ḅ()A.ᨬ⚗4B.ᨬᜧ⚗aC.ᨬ⚗aD.ᨬᜧ⚗“ூQᫀ௃Cூ/᪆௃ᵫ⚪nÁ(®ᦪᑡ¯஺°Ḅ®d,|a=-5,a=-\,1d=±&Å^U2,"133-12LLttU/Êccrc4-Cl)஻(—51+2஻-7)?rnᡠa=-5+(n-l)x2=2z?-7,S=';=~-----=n--6n,nnSn2-6n32-6X342-6X4ᑣb=÷=_______,1=_________=9,b=_________=-87ᡠÕb,1᣸◀AஹD;"a“2n-732x3-742x4-74x2-6x77,(lx-6)(2%-7)-(x2-6x)x22(x2-7x+21)iS/(x)=-----e[l,+—)6+°o)Ûᑣ/(x)=ÜK-J'2x-722v7(2x-7)¦2x-7>à7ஹ7|á=(—7)2-4xlx21â0,ᡠ/'(x)ு0,ᡠ/(x)ᙠäåUæ(,+ooxᓫè⌴éᦪ,L512ᓽ஻=1,2,3ᦪᑡê°⌴ᦪᑡᦪᑡ¼°¼⌴ᦪᑡᐸKb-æ,b=9ë-9,b-S,b=oì,,E᝞஻=251Õ>b,ᡠB'FíCFí,îC.ூ!௃ᦪᑡ-éᦪஹ'()ᔠ0⚪Ḅ/ðᶍ:271/397

282¦1ijᦪᑡḄᩩó/ôéᦪ0⚪/ôõ£0⚪oö⌕ᑭᵨᦪᑡḄù⚗Â)±Ê⚗³Â)³¥ú(uv)ûᓄüýþÿᦪᑡᦪḄᦪᑡ᦮ᦪḄᦪᙠ⚪⌕ᱯឋ"2%2&ᦪᑡ'(Ḅ)ᔠ⚪+,-⚪.ᑣ⌕ᮣ1⌱3'(Ḅ,-45᝞785ஹ)ᔠ5ஹᑖ᪆5ஹ<=5'+>?ᦪḄ'(ឤᡂB⚪ᑣCᑖD?ᦪEᓄẆHᨬJ⚪ᩭ.M2.NOᦪᑡP᝞QḄR⚗T(““=%஻+1
91,YZᦪᑡ.ᨵ\ᨵᨬᜧ⚗^+ᨵ_`ᨬᜧ⚗aᨬᜧ⚗Ḅbc"+\ᨵde-ᳮᵫ.ூ᪆௃5j,..“"+1—a”=("+2)gf}+i—("+1)w“<9ai—a>0,ᓽ{+1>ᓽ"n+nw஻=9஻஻+1}=ᓽdn+\=Qnwn>9—ᓽ{+1<{Zᦪᑡ.ᨵᨬᜧ⚗9ஹ10⚗«=aio=iotiJ9.9*஺%n>2&,ᓽr%nflO'&9n+2“GN*,.•.஻=9ᡈ"=10,...Zᦪᑡ.ᨵᨬᜧ⚗9ஹ10⚗49=00=4x&19.ூᓣ௃ᦪᑡḄ)ᔠ⚪¡¢ᑮḄᦪ¤¥jᦪ4¦¥%᝞j_ᨬJᡈ§¨&ஹEᓄᓄ©¥%᝞j_aᡈªᵨ&ஹᱯᑮ¬¥%᝞j_R⚗T(&ஹᑖ®¥%᝞j'7ᦪᑡ_aᡈ&'.NOᦪᑡḄ¯n⚗a$“Ḅ±ᐵᩩ´_ᦪᑡR⚗T(Ḅ§¨µ¶·j%1&¸aEᓄ⚗¹ᓽᑭᵨa„=S-S,,_¸aEᓄnl⚗.%2&C¸ᩩ´ᦪᑡPs“QḄ⌴½T(ᐜ_`s.ᯠÀ⚪ᓽEᓄNOᦪᑡḄ¯n⚗as“_ᦪᑡR⚗T(.M3.%2021•ÂÃÄᐶÆ•Äᐶ.ÇÈÉÊ&NOTË2Ḅ'ËᦪᑡP6,Q,4%,Îᡂ'7ᦪᑡ•%1&_ᦪᑡP¹QḄR⚗T(;%2&+ᦪᑡP஺QḄ¯஻⚗aS,_ᦪÑJ'ÒḄᨬÓ⚗.ூÔᫀ%1&a=2n-ll"%2&ᨬÓ⚗7⚗.n272/397

283ூ᪆௃(1)ᵫ⚪Oja2=a-aᑣ(12+a=a-(a+8)ja=-9,ᓽa=a+(஻-l)d=2"-11.715]111n19+11-2nS10/2—/2(2)wp4=ll—2஻S-xn=lOn—n,ᑣ,==10-n»ᓽ஻=5n2nnw஻26a=2T?-1LS=S+1+2஻"x(஻-5)=n2-10஻+50,ÝÞj=ø+'-10,M“5c2nn50á/ஹ.inஹ,/ஹ50r-50â/(x)=x+-10,x>6,f'[x)=-=,w6Vx<5M,f'M<0,wx>%Q/(x)>0,ᓽᦪ/(x)ᙠ(6,5ª)åᓫç⌴èᙠ(s/I+8)åᓫç⌴éᓽ“=7(V=êᨬÓ⚗7⚗ëì——ஹ/minூᐵíîï௃¨⚪Ḅᐵíᙠðᐜ®஺“=2஻-11ḄñòóôõP|q|QḄR⚗T(øó`ù,ᨬÀᵫúᦪḄឋûü¢ýᦪ`ᦪᑡḄᓫçឋᵫþ`ᨬÓJ.ü⚪20nîḄGᨬyW⚪ÿ᪗ὃᦪ⚪Ḅᨬ⚪◤⌕ᵨᑮᣚஹ!"#ᳮ%%&◤⌕'()*+(,-ᦪ./01234ὃ5Ḅὃ6Ḅᨬ⚪7ᡂὃ9⚪Ḅ:;<=.?=@ᙠ!"#ᳮB-ᦪឋDஹ)*+ᔣFGHḄIᔠK/⌕,LᨵNOḄPQRSTUஹឤTU(WXḄYZTU[T\ᑭ^_.`a▭ᦟᩭefgᑖGHiᔠឋᜧ'(GH☢lL^mnoNpqᑖ᪆st◀vfw⚪x*yᨵ:#qz{⌕|LḄឤTU}~N&ᨵ|ᨵᡂ^⚪Ḅ+ᝅ⍗ᑮwḄ⚪xLᳮ.*ᦻ▤fw⚪wḄIḄ.ஹnîᑭᵨþnᐵuÆḄᐵ{⌕ᨵ1.¡¢ᜧ£¡¡¢¤¥£¡/2.:§ᜧ0஺ª¥18G),¢¯|ᜧ0஺ª¥180°/3.³A|:Ḅᑁᑣ஺

284┦¢¯|ᜧ90஺ª¥180*1/5.ᙠ½:ᜧ¡5ᜧᜧ5ᜧ¡.¾ᵨ¿fÀᐵ|^mBᨵᐵ⚪ḄᐵÁ.Â.ÃḄ¡஺+1,஺+2,ᐸᨬᜧÆÇ120஺ᑣaḄÈÊ|ËÌ3,5A.0Ò,^Ó;Wa<3,ᦑ⌱B.2a.a+1
2ÂË2021•ØÙᚁÛ•?ÜÝÞ[ᨴὃÌ#àá☢âã¡á☢Kä;ᑁzᦪ§¥180஺Ḅã¡.7Gᙠá☢âã¡ABCDZA=30°,ZB=135°,AB£AD=2,³C£Ì=r,ᑣIḄÈÊ|ËÌூ_ᫀ௃Dூ^᪆௃ᵫ!"#ᳮGBD2^AD2+AB2-2ADABcosA^3+4-6^\.ᓽᙠçA3஺tBDᨵ/DBA=90°,ᑣNOBC=45°,ᙠaDBCᵫ"#ᳮ------=-----,᦮ᳮÓf,ëᵫsin450sinC2sinCâã¡Ḅ#àGI5°

285ᨵᨬᜧᑣaᦪýḄÈÊ|.ூ_ᫀ௃3ᐔᑍbூ^᪆௃þ:A=ᡠ0<8<4,111ᳮsinBᡠᓃ=2sinB,c=2sinC,(ᑍᡠAb+c=2/tsinB+2sinC=2/lsin8+2si*4-ᢤcosBinBI=(22-sinB+ᐺCOSB-=2/lsinB+2τI2/kJ2=Q>ᓽQe=cosB"ᨵᨬᜧ&ᡠ'ù,22ᑣ'c=/2ú-)*2+2.sin/B+9*ᐸ2ta5f'⌕89+cᨵᨬᜧ&ᑣ8+஺⌕<=:22—Q2ᵫ@0<8<^ᡠ“<ᯠ"ᡠtane>l,ᓽᦈு1,,G£

286«tᱥᡠ8<33662ᡠ23sin(63ef3,23).ᓽ2b—cḄ=&Kt[3,23).ஹ
ᑭᵨ}(2021.°±²³ὃµ¶)ᙠA8C2=bᑣcosAḄ=&KL()tan3tanCtanAA□B.P,1)c.D.{2/A”[bjITJiL3Jூ¸ᫀ௃DூG᪆௃º'ḄᑁTA,B,CḄ_ᑖt஺h,c,ᑣᵫ¼½ᳮ(cosBcosC}sinAsin(B+C)sin2Aa2b2+c2-a2a2cosA=sinA------F-I=---------------=------=—7ᵫcᳮcosA=---------=,ᡠVsinBsinCJsinBsinCsin^sinCbe2bcbe3/=ᡝ+ᜩᡠZ?2+c2-----3À+c22cosAcl,ᡠcosAcᦑ⌱D.---------->3bc3ூᐵÂPPQ௃W⚪ὃÃÄᳮÅcᳮᐵÂLƼḄᑗqÈÉÊᳮஹcᳮ_T̺4-C2ᓄ᦮ᳮᡂcosA=--------7ÏÐᔠVWopqᓽrÒ=&K.3bc}.ᙠABC2ᑁTA,B,CḄ_ᑖLa,b,c,s[nB+j=f,a+c=2,ᑣABCᕜÔḄ=&KL()A.(2,3]B.[3,4)C.(4,5]D.[5,6)ூ¸ᫀ௃BூG᪆௃«tÕTBtSTUḄᑁTᡠ-B=~,ᡠB=~.Ö=/+/-2accosB=(a2"2223+c)2—3ac=4—3ac>4—?[2}2=1.¨a=c=l=p×ᡠØ1,ᡠ஺+c+᪹3஻+c=2>b,ᡠa+c+b<4,ᡠA8CᕜÔḄ=&KL[3,4).'
ᑭᵨ
ᨬ}(2021•ÛÜÝÞ³SNß(ᳮ))ᙠA8C2A=30°,_àḄ³t1,ᑣABC☢âḄᨬã&t()A.2—^/5B.2-ᨵC.2+äD.2+å276/397

287ூ¸ᫀ௃BூG᪆௃ºBC_àḄ³tAD,ᑣAD=\,AD1BC,᝞çᡠè:ABA஺ACsinBsinCᡠS=/ICxsinA=ABxAC=,ABC2~44sinBsinCTTS/Tºy=4sinBsinC,«tA=,ᑣB+C=,66S77I(STT57rᡠy=4sinBsinC=4sinBsiᳲ-B)=4sinêsiigcosB-cogsin.71=2sinBcosB+2"sin2B=sin28—ycos28+&=2sin(2B—1/,,í/í57r”,τínᑍ/7C47r«txr3£(0,_yᡠ23__(-_,_AE6333ᡠsin(2B-*w(r-,1],ᑣy=2sin(28-4+3w(0,2+31,ᡠy=2+x—fji)Imax3231cᡠABC☢âḄᨬã&t——=2-ᵫᦑ⌱B.%iaxூPQ௃G⚪ḄᐵÂLÆ⚪îᩩðsᓄty=4sin8sinC,᪷ò8ḄKÐᔠSTwᦪḄçóMឋõrGὃÃᑖ᪆ᳮGö÷r&Ḅ<øù2᫏⚪.}.ᙠABC2TA,B,CᡠḄ_ᑖta,b,c,ºStA8CḄ☢â4/1*rTCḄᜧãফrsinA+sinBḄᨬᜧ&.ூG᪆௃/1*ᵫ⚪ýabsinC=q2abeosC,ᡠtanC=3,«t0

288=sinA+—cosA+-sinA=3sin(A+-)<3.AABC!"#$%&',226ᡠsinA+sinBḄᨬᜧ,-3..2021./01234234!56!7ᦻᙠA3C5:"A,B,Cᡠ;Ḅ<ᑖ>-☢@SS,ᑣḄᨬᜧ,b1+4acூCᫀ௃F16_acsinB^.acsinBc3_=2_____________<________=sin8,/?2+4aca2^-c2-2accosB+4ac6ac-2accosB4(3-cosB)Gy=sin8ᑣ3y=sin8+ycosBᦑIJK3-cosBLyு0,ᦑ0a,b,c,a=csinB,ᑣtanAḄᨬᜧ,543A.1B.-C.-D.-432ூCᫀ௃Cூz᪆௃ᙠABC5ᵫ஺=csinBᳮ^sirtA=sinCsinB,sinB+C
=sinBsinC,ᓽsinBcosC+cosBsinC=sin3sinC,<◀sinBsinCd^—+—!—=1,tanCtanB278/397

289/.I>2.ᓽtanBtanC24,OPtanB=tanC=2&'ᡂT,tanBtanCtanB+tanC=tanBtanCtanBtanC4ᑣtan3tanC=4$;tanA%ᨬᜧ,_ᦑ⌱c3’-1iூXY௃⚪ὃᳮḄᵨz⚪Ḅᐵ«-ᑭᵨᩩ-----+—!—=1,ᑭᵨ&k®tanCtanBtanBtanC>4...(2021.²³´µ6!ᐸ·7¸(ᳮ))ᙠA5C5ᑁ"A,B,Cᡠ;Ḅ<ᑖ>b,c,OsinA-sinCb-c,.¼½+¾=,b=3,¿!1ABCḄᕜÁḄᨬᜧ,-.sinB+sinCaூCᫀ௃9ூz᪆௃;&kÂÃ"ᓄ0,c>0,ᡠ7I22(஻+cYᡠ(Q+C)-9<3xlI,ᓽa+cW6,OPa=c=3$(஻+c)=6,ᡠ(o+0+c)=9,ᓽABCḄᕜÁḄᨬᜧ,9.(a+cÒூᐵ«XXY௃z⚪ᐵ«-ᵫ&kᑮac<\I,ÂKÕM×ᐵᔆ4+cḄ&kÙK®a+cI9JḄÛÂKz...AABCᙠᑁ"A,B,CḄ;<ᑖ>a,b,c,஺=bcosC+csinB.(I)ýB>(II)ÜÝ=2,®ÞABC☢@Ḅᨬᜧ,.ூz᪆௃(I)Ç஺=bcosC+csinB,ᡠᵫᳮ^sinA=sinBcosC+sinCsinB,ᡠsin(B+C)=sinBcosC+sinCsinB,71B|JcosBsinC=sinCsinB,ÇsinCWO,ᡠtan3=1,z3!â(M)ᵫᳮ^᮱=஺2+ä—2accos—ᓽ4=/+c2—dZc,ᵫ&k^«2+?>2ac,O279/397

290P஺=஺$%&'ᡠ42(2—é)ac,zac<4+2êᡠÞABCḄ☢@acsin2W±x(4+ë)=6+1,ᡠÞA8C☢@Ḅᨬᜧ,ì+1.244ஹ
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291sinAaqinATTூ-᪆௃(1)V"XtanAYZ[ᳮA==',sin5=cosA,ᓽsin3=`+A),cosAbsinB27CIT7C71a3JLGbDJ-Ae(@,ᦑ8=+dᓽB-A=e(2)ᵫ(I)fC=^-(A+B)2227sᑍᐔ7171e(2A+5)=g,2A>0,hAe(0z)ijsinA+sinC=sinA+sin('-2A)1Qjr=sinA+cos2A=-2sin?A+sinA+l=-2(sinA-_)2+_,m01,0=J³+2?-2xlx2xcos¦J5-4cos22_________¢+0=^+-2-2xlx2xcos(^-0=«+4cos),ᑣ>281/397

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¯(eéঞëᵨJK᳛ḄìíÖᙊ┵G+Ḅìíᩭ¯aéট᪷"ᙊ┵G+Ḅðìí¯a.ஹ12Ḅ9kñòó⚪ḄὃÛôôõᦪஹ,-ஹᔣøஹù☢ûü@ýÎþᔠḼὃᑖ᪆⚪ஹ⚪ḄஹᨵḄ⌕.1.2021."#ᔠ%&.'()*ᦻ,,-ᑡ/012ᯖ4ᙠy789:;1<=ᚖ?Ḅ@,22rA.x2—y2——4B.——D=1C.—x—1D.x2—y2—lூIᫀ௃A22ூ᪆௃L/01ḄMNOP21-^1«>0,^>0,1ᑣᐸ:;1Oy=a2b1bXO:;1<=ᚖ?ᦑLW-|=-1ᓽa=b,ᦑ/01ḄMNOy2-x2=a2,ᦑ⌱A.h.h.'2.abcᱥ1y=ax2a>0,Ḅe1OLᔁhᙊCjxe32>y2=1=mᡠopqOᑣcᱥ1ḄMNO.ூIᫀ௃y=r"4ூ᪆௃cᱥ1y=a/஺>0,Ḅe1/,=—௃/0w2-y2=lḄyᩩ:;1ᑖ{Ov=1x,y=-1x,}o~422XA=-1»1,ᑣH8H1--1,=4,ᑣ1/2a2a2a2a4]342/397

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