2021-2022学年湖北省宜昌高三（上）月考数学试卷（10月份）（附答案详解）

《2021-2022学年湖北省宜昌高三（上）月考数学试卷（10月份）（附答案详解）》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

202L2022
ᓅḕᩲ᪥()ᨴὃᦪᔁ(10ᨴ)1.ᔠ஻={1,2,3,456},4={“€2|2%<6},8={124,6},ᑣ40((.8)=()1/A.{2}B.{3,5}C.[1,4,6}D.{2,3,5}2.“log3a<167'93>┐Ḅ()A.ᐙᑖ?@⌕ᩩCB.@⌕?ᐙᑖᩩCC.ᐙ⌕ᩩCD.N?ᐙᑖO?@⌕ᩩC3.Eᦪ/(%)=£GḄHIᜧK9()4.Eᦪy=/(x)ᙠST[0,+8)ᓫW⌴YZ[/■(]^)=/(x),ᑣ()A./(In2)>r(loge)>/(lo|)B.f(ln2)>/(lo|)>/(loge)2gigi2C./(loge)>/(ln2)>/(loi)D.f(log*)>/(loge)>/(ln2)2gl2202J5.ᙊ┵Ḅ⚔ijk☢ᙊᕜnᙠᳫ஺Ḅᳫ☢Zᙊ┵Ḅqrst3,u☢vwHḄ☢xt3ᐔZᑣᳫOḄ⊤☢x|}()AOB.~C.D.O8282

16.rl(a>0,b>0)Ḅ⚔iᱥry2=2Px(p>0)ḄᯖiḄt4,rḄ⚔i[rḄrᱥrḄrḄiᙶ᪗(-2,2),ᑣrḄᯖt()A.V3B.2V3C.V5D.27.Eᦪf(x)=Asin(3x+0)+1,(Z>0,3>0,|3|<Ḅᨬᜧt2,ᐸH¡¢£¤¥¦§¨©TḄtᡈ[/(%)ḄHᐵ}r7=¬¥¦Zᑣᑡᑨ°±²Ḅ9()A.Eᦪy=f(x)ᙠ[]£,³ᓫW⌴´o3B.Eᦪy=/Q)ḄHᐵ}i(-±0)¥¦C.Eᦪy=/(%)ḄHᐵ}r·=-¸¹¦D.⌕ºᑮy=sin2x+1ḄHZ¼◤¾f(x)HᔣÀg¤ᓫÁ—2%2+2.x,xW1i-1%>1ZÄ¥ÅÆ·GRZf(x)-|x-2/c|-|x-1|<0xZឤᡂÌZᑣÍᦪ&ḄÏÑ9()A.(-°°^]U[1,4-00)B.(-8,ÖEZ+8)C.(-8iØ+8)D.(_8,l]U[2,+8)9.ᔣÛÜÝ=(1,1),¾ᔣÛᡈÞßi஺⌮á┐âã90஺ºᑮᔣÛäZ¾ᔣÛå5Þßi஺æá┐âã135°ºᑮᔣÛçZè!1()A.OA+OB+OC=0B.\^C\=\CA\C.OAOB=0D.CA-AB=-210.ᦪᑡêᓽìḄí஻⚗jtZ[ïðḄ=1,a=2,a+i=4%-3ñ]1Zᑣ2n☢òó±²Ḅ9()A.ᦪᑡê4+i-ᓽìt|ôᦪᑡB.ᦪᑡêḄ+1-3ᓽìt|õᦪᑡC.a=3n-1+1D.S=Tnn11.☢ö÷±²Ḅ9()A.Q>0,b>0,[Q+b=l,ᑣlog2஺+logzbW—2B.Eᦪ/(%)=ÄOV/Vb,[f(a)=f(b),ᑣa+2bḄᨬú92ûC.ü+ý=l(x>0,y>0),ᑣ3x+yḄᨬút2+2ûD./+y2—%—y—xy+2=O(x>0,y>0),ᑣxyḄᨬúti12.þᙊM:^+\=l(a>b>0)ḄஹᯖᑖFi(—8,0),F(V3,0),22Ḅ!"#$ᙊ&'(A*8+*Pᙠ#$ᙊ.*/|48|21,ᑣ4ᑡ6789Ḅ:()A.<ᙠP,=>N&P%=90°B.EFAF1PF2GῪIJKḄᨵ2MN2⚓*ᐳ19⚓

2C.Q4FJF2=60஺*ᑣSA&PFZ=?D.|PF/-|PF2|ḄSTVߟ2W,2XY13.Z[ᦪzEF(l+2i)z=3—4i(i]ᦪᓫ_)*ᑣ|z|ḄT.14.ᙠ(`-2/
Ḅabcd*e⚗Ḅgᦪ(ᵨᦪijk).15.!/lx—y-2=0"ᙊ&ᑗ(M(3,l),/ᙊnᙠoᱥ!y?=qrḄs!.*ᑣᙊḄ᪗suv.Q16.ᙠwxKABCOd*yz4D஻BC,^DAB=60°,AD=2BC=2,48=*}:!~4஺.Ḅ*/=/1*ᐗ•=I*ᑣ;1=__.Q:!~CO.Ḅ4*ᑣ•ḄᨬT.17.yzABCd*JcḄxᑖa,b,c,3bcosC+2csinCsin^=0.(1)JC(2)Qc=2X*S^=V3,a+bḄT.ABC(3)Qc=2W,a=|,sin(24+g).18.yzᦪᑡḄ஻⚗*/=±(1)ᦪᑡaḄ⚗c;nফZ%=%Ḅn⚗%.19.᝞*ᙠw┵P-ABCDd*wxKABCD:JK*ABLAD,AB//CD,PC1JKffiABCD,AB=2AD=2CD=4,PC=2a,E:P8Ḅd.()l☢EAC_1_☢PBC(0)¢a=l£*!PD"AEᡠᡂJḄ8¦Tl()Q§☢JP-AC-EḄ¨¦T©*!PA"☢EACᡠᡂJḄ8¦T.20.2021ª«¬Ẇ¯q°±e²³ᢗᐭ¶·*b¸├º»¼*½¾¿*├º⌲ᨴÂÃ*4⊤2021ª1ᨴÅᑮ7ᨴÅ*├ºy(ᓫ_lWÇ)"ᨴÅxÈÉḄᐵg.ᨴÅX1234567├ºy611213466101196(1)ËÌᦣ*³᪷ÏᦣᑨÑy=ax+b"y=cdYcdᙳᜧ(ÔḄÕᦪ)ÖqM〉ᔠj├ºy"ᨴÅxḄÙÚuvÛÜ(ÝÌᑨÑᓽß*àá6âᳮᵫ)å

3y(2)᪷Ï(1)ḄᑨÑæçè⊤dḄᦪÏ*yᐵ(xḄÙÚuv*³⚜ê2021ª8ᨴÅḄ├º(3)ὃ⇋├ºஹe²í±èîï⌲ð4ñGòó*⚜êô2021ª1ᨴÅᑮ12ᨴÅ(xḄSTõXöj1ᑮ12),÷WÇ#e²ḄᑭùP=10-஺.஺5/+஺Sᐗ*2021ªúᨴÅ#e²Ḅᑭù஺ᨬᜧ.ûὃᦪÏl77100.54yVi=li=l62.141.54253550.123.47ᐸd%=lg%,V=^Vt=1ûὃcl(qýᦪÏ(%,᝕),(u,v)*•••,(UV),ᐸÙÚ!U=ÿ+2”Ḅ
᳛22n/nḄᨬᑖ8=ἠᙶa=v-pu.SiliWf-nu2ᔆ21.!"#ᙊC5+\=l(a>b>0)Ḅ%ஹ'ᯖ)ᑖ*F,+)FIḄ.//21C23M,N4)5“78Ḅᕜ:8,;.//ᚖ.3x=>|MN|=3.(@)B#ᙊCḄ᪗DEFG(H)I#ᙊCḄ'⚔)A,./AM,ANᑖ2./x=-43P,஺4);APQF1Ḅ☢MN5OMN☢MḄ5P>B.//ḄEF.22.!"Rᦪ/(%)=Inx—ax2+(2—a)x,aER.(H)!"V=1f(%)Ḅ᩽X)BY/y=f(Z)ᙠ)(1,/(I))ᜐḄᑗ/EFG(@)^_Rᦪg(x)=/(%)+axḄᓫaឋG(@);aef3gh1%£(L+8)(%I

4|ᫀ~᪆1.ூ|ᫀ௃Bூ~᪆௃ூᑖ᪆௃⚪ὃᔠḄᑡḄ2⊡ḄὃO3Ạ⚪.7BᔠA,ᯠ2⊡Ḅᓽ7.ூ~|௃~•••U={1,2,3,456},A={2,3,4,5},B={1,2,4,6},CuB={3,5},AD(CuB)=[3,5}.ᦑ⌱B.2.ூ|ᫀ௃Aூ~᪆௃~ᵫlog3a>¤ᡂ¦ᓽᐙᑖឋᡂ¦;a=l,b=-l>¨©:>£,¬log3aḄᐙᑖ®⌕ᩩ±ᦑ⌱A.᪷³´Ḅឋµᑭᵨᐙᑖᩩ±®⌕ᩩ±Ḅᑨ¹ᓽ7.⚪º⌕ὃᐙᑖᩩ±®⌕ᩩ±Ḅᑨ¹ᑭᵨ´Ḅឋµᐙᑖᩩ±®⌕ᩩ±ḄN~»⚪Ḅᐵ½NẠ⚪.3.ூ|ᫀ௃Bூ~᪆௃~x)=¾´=c¿À=—f(x),ᑣ/Q)N᜻Rᦪ᣸◀A,D,;x=ᐔᑣ/'(ᐔ)<0,᣸◀C,ᦑ⌱B.᪷³Rᦪ᜻ᏔឋḄᑨ¹RᦪḄ᜻ᏔឋfÈឋᑭᵨ᣸◀ᑨ¹ᓽ7.⚪º⌕ὃRᦪÉÊḄËᑨ¹ᑭᵨRᦪ᜻ᏔឋfÈឋḄឋµᑭᵨ᣸◀N~»⚪Ḅᐵ½NẠ⚪.4.ூ|ᫀ௃Dூ~᪆௃ூᑖ᪆௃⚪º⌕ὃᑭᵨRᦪḄᓫaឋÌ᜻ᏔឋÍÎRᦪXᜧÐÑÒᓄÔÕḄÖᵨ3Ạ⚪.

5ᵫ⚪hrf(x)ᏔRᦪ×ᙠØÙ0,+8)ᓫa⌴ÛᯠÜᔠᓫaឋÌ᜻Ꮤឋᓽ7ÍÎRᦪXᜧ.ூ~|௃~ᵫ⚪hrᏔRᦪ×ᙠØÙ0,+00)ᓫa⌴Û/(logi)=ff)0g3'),.0.log3>loge>ln2>0,2222JWW/(log3)>/(loge)>/(ln2),22ᓽf(log*)>f(log2e)>/(ln2)2Jᦑ⌱D.5.ூ|ᫀ௃Aூ~᪆௃~ᙊ┵Ḅ⚔)Þ☢ᙊᕜoᙠᳫ஺☢àᙊ┵Ḅá☢âãÉḄ☢M3ᐔä/:3,Iᙊ┵Þ☢åær,//;'ᑣnrx3=3ᐔrr=l,1,•••ᙊ┵Ḅçh==2>/2,o,_2BèIᙊ┵᜜êᳫḄåæR,7rR2=(2V2-R)2+ë~rì=í•.ᳫ஺Ḅ⊤☢M4ᐔX(ᯅ)2=£■ᐔ.ᦑ⌱A.ᑭᵨ!"ᩩ±Bᙊ┵ḄÞ☢åæcñBrᙊ┵ḄçᑭᵨòóᳮB~ᳫḄåæ,ᓽ7B~ᳫḄ⊤☢M.⚪ὃõöÐḄ᜜êᳫḄ⊤☢MḄBὃ÷øùúÔûOÌ.üÕýḄᦪ÷þÿ
᫏⚪.6.ூᫀ௃Dூ᪆௃ூᑖ᪆௃⚪ὃᱥḄឋ⚪◤⌕ᳮ!᫏⚪.ᱥḄ"#$=-'()*+,⚔./012Ḅ345#y=-^(x-a),6.(82,2)9ᐭ;p=4,<2a=2b+ab,ᵫḄ>⚔.ᱥḄᯖ.Ḅ@A#4,;mb,c,BCD;ᫀ.ூ௃EᱥḄ"#4=-F()*+,⚔./012Ḅ345#y=G#+Ḅ,⚔.</012Ḅ3ᱥḄ"ḄH.ᙶ᪗(-2,2),K6⚓ᐳ19⚓

6ᡠO8E=_2,M2=——(—2—;p=4,<2a=2b+abfG#Ḅ>⚔.ᱥḄᯖ.Ḅ@A#4,ᡠOḄ>⚔.#(82,0),ᡠOa=2,9ᐭ2Q=2b+ab,;b=1,ᡠOc=Va24-b2=V5,ᡠOḄᯖ@#2c=2V5,ᦑ⌱ED.7.ூᫀ௃Cூ᪆௃E•.,dᦪ/(%)=i4sin(cox+9)+1(4>0co>0,\(p\<])Ḅᨬᜧr#A+1=2,,•A=1.ᐸuvwxyz{|}~Ḅ@A#;.=9.•.3=2,,."()Ḅuvᐵ!3X={|•.2+pfc6Z,k=0,D;9=$ᦑf(%)=sin(2x+)+1.ᙠ2x+r[0dᦪ/(%)ᨵᓫឋᦑA┯635x=-g;/Q)=l,D;/(x)Ḅuvᐵ!.{|ᦑB┯o6¡=—¢;/(#=0,#ᨬ£rD;/(%)Ḅuvᐵ!3¤=-¥{|ᦑC§¨©f(x)uvᔣ,1«gzᓫ¬D;y=sin(2x-+1Ḅuvᦑ஺┯ᦑ⌱EC.ᵫdᦪḄᨬᜧr¯4,ᵫᕜ±¯3,ᵫuvḄ{|ឋ¯9ḄrD;dᦪḄ᪆²³ᑭᵨdᦪy=Xsin(wx+9)Ḅuv·ᣚ¹ºஹ§¼dᦪḄuv½ឋ;¯¾¿.⚪À⌕ὃᵫdᦪy=Asin^x+@)ḄÂᑖuv᪆²ᵫdᦪḄᨬᜧr¯A,ᵫᕜ±¯3,ᵫuvḄ{|ឋ¯ÃḄrdᦪy=4sin(3x+“)Ḅuv·ᣚ¹º§¼dᦪḄuv½ឋ!᫏⚪.8.ூᫀ௃Bூ᪆௃ூᑖ᪆௃⚪ὃᑖÆdᦪÇÈᵨὃᦪɾᔠḄË4ÌὃuvḄ1«¹ºὃᑖÍοḄᦪÏËὃÈÐÑÒ!ÓÔ⚪.

7¯y=/(x)—|x-1|,ᙠ3Õᙶ᪗Öׯdᦪy=/(%)-|x-1|½y=|x-2k|ḄuvᑖÍοB2ᓽD.ூ௃ᙠ3Õᙶ᪗Öׯdᦪy=/(x)-|x-1|½Ù=|x-2klḄuvজÛ2k=1ᓽÜÝÞß+(1,0)Ûx0,ᑣᨵx<1Ü/(%)-|x-2k\-|x-1|<0ឤᡂä,x>1ÜᵫuvD;f(%)-*82k\-\x-l\<0ឤᡂä;ঝÛ2k=~ᓽk=ÜÝÞß+90),Ûx>3y=|x-1|=x-pᵫ!x>1Ü/(x)<0,æ⌕ὃ⇋è0,ᑣᨵ:1ᡈ¤<1ÜᵫuvD;f(x)-|x-2/c|-|x-1|S0ឤᡂäᑣk=1,ìí{îïxeR,/(x)-\x-2k\-\x-l\<0ឤᡂäঞÛ2k>1ᡈ2k<%ᓽᡈÜᵫuv1«D;{îï¤6R,/(%)-\x-2k\-|x-1|<0ឤᡂäটÛ:<2k

8õD;Ḅr÷#k>:ᡈk

9ூh᪆௃hAO¢A,loga4-logb=log(aZ?)2V2ab=2A/2,£|¤£a=2bᓽQ=V2,b=¨ᡂ§ᦑB89,O¢C,3x+y=(2x+y)+(x+1)-1=[(2x+y)+(x+1)](©+~1=2+ª±12+±Z>2+2«EZTZ¬=2+2&,2x+yx+1~y2x+yx+1£|¤£5=®¯"=”ᡂ§ᦑc892x+yx+1O¢஺v%2+y2—%—y—%y4-22x2+2y2—2x—2y—2xy+42_(%-y)24-(%-l)2+(y-1)2+22>|=1,£|¤£=y=1ᡂ§.•+y22_y_+2H0,ᩩ±ᡂ§ᦑ஺┯,ᦑ⌱AABC.O¢AB,᪷COᦪ²ᦪḄឋ´µbYwḄឋ´ᑨTᓽX-O¢C,᪷CbYwḄឋ´ᑨTᓽXO¢஺᪷C0¶·ᑨTᓽX.Y⚪ὃ\]Oᦪ²ᦪḄឋ´ὃ\bYwឋ´Ḅ¸ᵨµᓄ»UP᫏⚪.12.ூeᫀ௃ACDூh᪆௃hA᪷C⚪¼Xc=V3,Ḅᨬ¾¿/1,ᡠMBminl=/=1,Àc2=a2-b2,ᡠa=2,c—V3,6=1,ᦑÁᙊ¶Ã/Ä+y?=1,£P/ÅÁᙊḄÆ⚔,tan/OPF?=V5,ᡠZOPF2=60஺,ÈN&P%=120஺ᡠÉᙠP,ËNFJF2=90஺ᦑA89-£P/ÅÁᙊḄÆÌ⚔ÍÎÏᵨÐÑ/wῪÓÔÀ./2-bWIPF2I42+Õ|Ö×2|=2ØᡠÍÎÙ×2|=|&×2|ḄPᨵ2ÜÝᳮÍÎ|P&|=|&×2|ḄPᨵßÜᦑ889-à4×/×2=60°,|P&|+|PF2l=4.|&×2|=2ØᵫâãGᳮ=|P&ä+\PF\2-2\PF\-\PF\COS^FPF,21212ᓽ|PF1|2+\PF\22|PFI|•\PF\=12,À|PF/2+Ù×2ä+2\PF,\\PF\=16,\PF\-222Xå10⚓ᐳ19⚓

10\PF\=^2ᡠSAPFFZ=3XIPF1I-IPFzlxsin/PF2=y,ᦑC89-\PF\-\PF\=|P&|-(2a-|PFi|)=2|PFJ-4,ᑖ᪆X|PFJ6[221,2+è],12•••\P^i|-|PF|e[2-V3,2+V3],ᦑ£)89.2ᦑ⌱AACD.✌ᐜIÁᙊ¶Ã£×/ÅÁᙊḄÆ⚔IíîÐ×2,ᓽXᑨT4N᪷CIPF2IḄðᑨTᑭᵨâãGᳮµÓÔ☢`uᑨTC᪷CÁᙊḄGHµIPaIᑨTDY⚪ὃ\ÁᙊḄÁᙊḄòóឋ´ὃ\QRKUP᫏⚪13.ூeᫀ௃V5ூh᪆௃hAᵫ(l+2i)z=3—4i,2=f.3-4i13-4i|5•1•|z|=lIT2il=iiT2q=^=^ᦑeᫀ/AV5.ôwõÔᑭᵨᖪḄ÷w¢÷Ḅᖪh.Y⚪ὃ\øᦪùᦪÔḄú◀QRὃ\øᦪ÷Ḅ·UbẠ⚪.14.ூeᫀ௃-80ூh᪆௃ூᑖ᪆௃Y⚪ü⌕ὃ\⚗GᳮḄ¸ᵨ⚗þÿḄ⚗⚗ᦪḄឋẠ⚪.ᐜ⚗Ḅ⚗xḄᢣᦪ5,rḄᓽ⚗Ḅᦪ.ூ!"௃15r-5!$⚗%-2/)5ḄḄ⚗'4+1=(-2)rCl-xߟ,(^=5,r=3,ᦑ-᮱⚗ᦪ'(-2>.Cf=-80,ᦑ"ᫀ'$-80.15.ூ"ᫀ௃(x-l)2+(y-3)2=8ூ!᪆௃!$1ᱥ3y2=-4xḄ43'x=1,ᡠ67ᙊḄᙊ9(l,b),:3/$x—y—2=0<ᙊ=ᑗ?M(3,l),$ᔠx1=-1,!b=3,ᙊḄᙊ9(1,3),ᙊḄAB'$,(3-1)2+(1-3)2=2vL

11ᡠ6ᙊḄCD'$஺-1)2+(y—3)2=8.ᦑ"ᫀ'$(X-1G+0-3)2=8.I1ᱥ3Ḅ43CDᯠK!ᙊḄᙊ9ᙶ᪗--->-->--->-->>-->1--->>11--->-->EF=EB+BF=AB-AE+BF=AB-1AD+—஻48+(|+$஻)i஺=(1j஻)AB+)kᡠ6l.l=[(1j஻)_+3஻a]++ߟ^21_——►1—,2=jn(1—fl)AB4--M)AB-AD+-jU(l+4)AD=-"(1-")+|,G-42)+4(1+஻)=,2-£oᔠpqᦪZr<ឋst஻=uv$42j3"+]wᨬyz.ᦑ"ᫀ':|.}~,at}ᐸᔣᵨ,a⊤[ᓽ!O⚪.O⚪ὃQᔣᙠ-ḄᵨὃQᔣḄ3ឋᦪὃQᔣᐳ312⚓ᐳ19⚓

12Ḅᩩ6pqᦪḄឋὃQᦪḄ᪶9-᫏⚪.17.ூ"ᫀ௃!$(1)ᵫ`¡ᳮ3bcosC+2csinCsinB=03sinBcosC+2sinCsinCsinB=0.b'sinB>0,ᡠ63cosc+2sin2c=0,ᓽ3cosc+2-2cos2c=0,!cosC=-1ᡈcosC=2(°)ᵫ஺'±²³ᑁ²"(2)b'SAABC—gabsinC=fab=¼ᡠ6ab=4,b'c=2A/3,ᵫ¾¡ᳮc2=+¿_2abcosC,ᓽ12=a24-624-ab=(a+6)2-ah=(a+h)2-4,ᡠ6Q+b=4Ä(3)ᵫ`¡ᳮ-±=±''sin/lsinCᡠ6sin4=2=1,cos/1=Å3ᦑsin24=2sin4cos4=—,cos2A=1—2sin27l=99ᡠ6sin(24+-)=5sin24+—cos2/l=-x—+—x-=f'+7".V322292918ூ!᪆௃(1)ᵫÉsoᔠ`¡ᳮʲËCᐵÍÎᓄRcosC,ÍaCÄ(2)ᵫÉsoᔠ±²³☢ÑᯠKoᔠ¾¡ᳮᓽ!Ä(3)oᔠ`¡ᳮᐜsin4ᯠKcos4oᔠÒ²Ó²Ḅ`.O⚪Ô⌕ὃQ`¡ᳮ¾¡ᳮÖ²Ò²±²³Ḅ☢ᙠ!±²³-Ḅᵨ-᫏⚪.18.ூ"ᫀ௃!$(1)b'ᐔ=Ù:ᦑtn=lv%=3,tnN2vS_=-Üija”=S-Snr=3n(n>2),nxntn=lvḄ=3ßàdᡠ60=3nÄn(2)ᵫ(1)á=-----------=-^ߟ=4G-ᓰ)logalogan(n+l)Sin+Y3n3n+1ᡠ6஻=^+&+634-+b=4x(1--+---4--••+---)=4(1——)=2n4nn+1'ᦑᦪᑡèbéḄl஻⚗஻=n

13ூ!᪆௃(1)᪷ëìsíîḄᐵïð=W±ÍÎY᪗Ḅòó᦮ᳮᓄRᓽnaÄn(2)ᵫ(1)-ᡠᓽ'ᑭᵨö⚗Tᓽo÷.O⚪ὃQᦪᑡ⌴ùö⚗=ú-᫏⚪.19.ூ"ᫀ௃!$(û)üý$PC_LË☢ABCD,ACuË☢ABCD,0.AC1PC.vAB=4,AD=CD=2,ABLAD,AB/ெCD,0.AC=BC=20.•■AC2+BC2=AB2,•••AC1BC3BCCPC=C,AACË☢PBC.■■ACuË☢EAC,••Ë☢EAC1Ë☢PBC.(ÿ)᝞Cᨔ,ᑖxஹyஹzᔣᙶ᪗ᑣP(0,0,2),6(2,-2,0),4(2,2,0),E(l,-l,l),ᡠ=(2,—2,—2),=(1,—3,1),"#PD$AEᡠᡂ஺ᑣcos஺=|ᘤ|=|.|=*,+,஺e[0,j],ᡠsin஺=Vl-cos26=-ᦑ#PD$AEᡠᡂḄ012.(3)4ᔠ(3)ᡠḄᙶ᪗ᑣC(0,0,0),4(220),8(2,-2,0),"P(0,0,2a)(a>0),ᑣEQ-],89=(2,2,0),CP=(0,0,2a),CF=(1,-1,a),:;=(1,1,0),ᑣ<•ᑐ=;•=0,☢PACḄ@ᔣA."ᐗ=(x,y,z)☢EACḄ@ᔣAᑣᐗ•5=ᐗ,=0,ᓽ[x+y,0:x=a,y=—a,z——2,ᑣᐗ=(a,—a,—2),D⚪F|cosGH=I=J/=Lplija=2.MNk=(2,—2,—2),m=(2,2,-4).O14⚓ᐳ19⚓

14"#PA$R☢EACᡠᡂ஺ᑣsinO=|cosYZ=[=\,ᓽ#PA$R☢EACᡠᡂḄ01].ூ_᪆௃bcdef4CJ■R☢P8CᓽmnHR☢o4C_LR☢PBCsb3dᑏᙶ᪗uvᡠw=b2,—2,-2d,=b1,3,1d,|ᑭᵨcos஺=|⅙ᯅ|ᓽmuv#஺$AEᡠᡂḄ01|ᑭᵨᦪᐵu01ᓽmsb3dᑏᙶ᪗ᐜ᪷☢P-4C-EḄ01]uv”Ḅ1ᯠ|#PA$R☢E4CᡠᡂḄ01.⚪ὃ☢☢ᚖḄnHὃ☢#ᡠᡂஹ#☢ஹ☢Ḅu@ὃᔣAᙠḄᵨὃ¡ᦪ¢£Ḅ᪶¥¦§¨M᫏⚪.᪷ᦣᑨ¬y=c#〉ᔠ°├Ay$ᨴ³xḄcµ¶·¸;b2dºy=c/w»¼:½ᵨºᦪ¾¿Igy=Ige4-xlgd,"Igy=v,ᑣ”=Ige+xlgd,,Ç=4,v=l.54Es=iÉ=140,Ë1WLᔙ50.12-7x4xl.54ᡠ=0.25,Xixf-nx2140-7X42=1Í᪵¥(4,1.54)Ïᐭu=Ige+xlgd,¾Ige=0.54,ᡠu=0.54+0.25%,ᓽIgy=0.54+0.25%,ᡠuᐵMxḄcµ¶y=10054+0-25x=IO054X10025x=3.47x10025x,

15Íx=8ÏᐭÕÖ¾y=3.47x102=347ᡠ⚜Ø2021Ù8ᨴ³Ḅ├A347ÚÛ(34700Û)s(3)ᵫ⚪F¾Q=yP=3.47x10_005x2-4-85x(xeNß10),ᐸºåx=æs=8.5,çxu.un,xeNß1Wxீ12,ᡠêx=8ᡈ9¼/(%):ᨬᜧ1ᓽ2021Ù8ᨴ³ᡈ9ᨴ³ᑭïᨬᜧ.ூ_᪆௃(1)ðᙠᙶ᪗ñᵫMòóᑖôᙠᩩö#▬øᡠm⌱ú¶·¸(2)ºy=ccfxw»¼:½ᵨºᦪ¾¿Igy=Ige+xlgd,"Igy=v,ᑣD=Ige+xlgd,ᯠ᪷ýþḄᦪ¡ÿ
ᓽx=8ᐭ⚜20218ᨴḄ├(3)
!ᑭ#Q%ᨴxḄ&ᦪ᪷)*+&ᦪḄឋ-
.ᐸᨬᜧ2.4⚪ὃ78Ḅ⌱:;<
ᵨ>!⚜?@᫏⚪.(4a=821.ூCᫀ௃F()ᵫH=3Ia.a=2,b=V3,ᡠ;NᙊCḄQ1+1=1.43(S)TUV/ḄQX=my-1,M(my-l,yi)/V(my-Ly2)P(-4,yp),N(-4,yQ),12x=my-1ὶd,3x2+4y2-12=O'ᡠ;3(my-l)2+4y2-12=0,ᡠ;(3?n2+4)y2—6my—9=0,ᡠ;yi+y=Q6,yy=-,212kJ<3m2+4kJ"3m2+4ᵫP,M,AmnᐳV.yppᳮ.%=stᡠ;Hu=vᑘ=I18τS^AMN\yi-yi\(7nyi-3)(7ny-3)2xτwi2yy-3m(y+y)+91-2஺⊈+4)ߟ1212.Hl=±V2,ᡠ;UV/ḄQy=±y(x+l).ூ᪆௃4⚪ὃ7NᙊḄUV%NᙊḄ~⚪⚪◤⌕xḄ,?@᫏⚪.(@)ᵫ"2ḄᕜQ8,\MN\=3,ᑡ.a,b,ᓽ.!Cᫀ.16⚓ᐳ19⚓

16(S)TUV/ḄQ%=my--l,yi)^N(my-1)(x4,%),%(-4,%),2ὶdUV/%NᙊḄᵫᳮ.Q+2,%ஹ2ᵫPM,AmnᐳV.Pnᙶ᪗pᳮ.஺nᙶ᪗ᑣ1=2"ᓽ.ᵨḄ2.S^AMN\yi-yi\22.ூCᫀ௃F()/Q)=2ax+(2—a),ᵫx=1Q/(x)Ḅ᩽2nᡠ;f'(l)=1-2a+(2-Q)=0,.a=l,¡¢£⚪¤,ᡠ;/(1)=-1+(2-1)=0,/c=/z(l)=1-2+2-1=0,ᡠ;§n(1,0)ḄᑗVḄQy=0.(0)5(%)=f(x)+ax=Inx—ax2+2x,ᑣg'(x)=F-2ax+2=-2ax~2X-F>®a=0¯g'(x)=(+2>0,ᡠ;g(x)ᙠ(0,+oo)²ᓫ´⌴¶·¸¹(%)=2ax2—2x—1,4=4+8a,¹(0)=—1<0,»¼½QX=¾®a<0¯¹(%)=2ax2—2x—1¿Àᔣ»¼½QX=^<0,ᡠ;;Ä)ᙠ(0,+8)²ᓫ´⌴Å/i(0)=-1<0,ᡠ;¹()VOᡠ;g'Q)>0,ᡠ;g(%)ᙠ(0,+8)²ᓫ´⌴¶·®a>0¯4=4+8a>0,/i(x)=2ax2-2%-1=0ᨵÇÈÉÊËᦪ᪷,2—4+8a1—11+2a,kl+Vl+2aஹXi1=<0,x-------->0n,2x2a2a242aᡠ;g'(x)<0.!x>²Ìᡠ;g'(x)>0.!00¯g(x)ᙠ(0,ᓃἠ%²ᓫ´⌴¶ᙠ(²Ì,+8)²ᓫ´⌴Å.(S)ÕÖFf(%2)-fCxi)=ln%-ax2+(2-a)x-[Inxi-axf+(2—a)x]22x=InÙ-a(x+/)(Ú2-ᑘ)+(2—a)(x-%)22X1ᡠ;/'(Xo)=ÛÜ2=m—a(%2+/)+(2—a)x2~xl%2x%1Ý/'Qo)—•--2a%o+(2—a),

17ᡠ;^--2CIXQ+(2—Q)=--------Q(X]+%2)+(2-Q),XQX2~X11Inßᓽà-2ax=—-Q(%1+%2)Xo0X2~X1á’(2ã)_/z(x)=-a(x+%)x£x2aç)0T22è=----------------a(%i+é)-------—++Ú1)%]ᓝ%2%2—%12èX+%2X2~X1112(x-%i)r2=-------------1--------------------%2—%+%2ᵫìVìᑣX2—>0T£=—>1^X1Tít)=᱅ߟInt,ᑣ“(£)=-ò<3ᡠ;0(t)ᙠ(1,+8)²ᓫ´⌴Åᡠ;À(£)<ó(1)=0,ᡠ;(ã)xf(x)<0ឤᡂd0ᓽ/'(H)l),ᵫa0,ᡠ;((%)=1-2ax+(2-a)ᙠ(1,+8)²ᓫ´⌴¶3X],XG(1,4-00),X6(%1%2)2oû/'(ü)?h(x)ᙠ(0,+8)ḄDᦪEḄFG'"gQ)ᓫIJ.(K)᪷MDᦪḄ-᪆O'fS)-f(a)=PQR%]+)+(2—a),Uf'(X)=--%2%2QZZQ%]x01In[2ax+(2-a),\]'ᑮᐵ`---2ax=——-+᜜)ᵫ/(%)ᙠ(1,+8)cᓫ0XQ0X2-X1d18⚓ᐳ19⚓

18⌴hi◤/klmn/஺0ᓽOqrst☢Ḅᐵ`vᐭ᪀⌼DᦪᓽO.