2022-2023学年吉林省长春市文理高中高二（上）第一学程考试数学试卷（附答案详解）

《2022-2023学年吉林省长春市文理高中高二（上）第一学程考试数学试卷（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。

2022-2023
ᔡ᪍ḕ᧡ᦻᳮὃᦪᔁ᪗⚪ஹᓫ⌱⚪ᜧ⚪ᐳ16⚪!ᐳ80.0ᑖ஺ᙠ%⚪ᑡ'Ḅ⌱⚗!⌱'*ᔠ⚪,Ḅ⚗1.0ᦪ2⊤34ᦪᓫ5ᑣzḄᐳ80ᦪ9A.-l+2iB.1-2iC.1+2iD.2+i2.l+x6DEF!GPḄ⚗ḄIᦪ9A.15B.20C.60D.36023.MNOL-y2=iḄ⚔TᑮVWOḄXYZ[A.IB.gC.]D.^55554.`aᐰcU,cᔠ4B9ᐸgc!hAnCuB=0,ᑣkUB=A.QuAB.CuBC.AD.B5.lᑁ✌opqᓟstuvᵯxyz□|}ᡬuvᵯ⚗,ᐰᵯ,9ᜧk.v⚜vᵯ'kᜧḄ⌕!¡¢ᵨ¤¥ᑖ¦§,ᨵὅ᪷«¬ᙢ®¯ᦪ«°ᑮ±ᙢḄ¤¥ᑖ¦§:Fx=1-e-µ!ᐸ஽9·¸¹ᦪ!º9v.`av9lm/s¾!F«0.221,ᑣv94m/s¾!FÀ¹ὃᦪ«ÁZnO.779«-i,e-4®0.018A.0.920B.0.964C.0.975D,0.9826.᝞É!ᙠÊËÌÍ·ABC஺!APA.BD,ᚖÏ9P,Ð4P=4,ᑣ•Ò=A.32B.18C.16D.87.ᙠÓᵱ᝕Öᐳ8×ÖØÙ⌱'2×ᵱÚÛ1×᝕ÚᑖܹÝᐰ᪥“à”ஹ“Ö᝱”ஹ“ãä”yoåæ⃩è!`aᐳᨵ90éêÚḄëᫀ!íîᵱ᝕ÚḄïᦪᑖÜ

1A.ᵱ2ï!᝕6ïB.ᵱ3ï!᝕5ïC.ᵱ5ï!᝕3ïD.ᵱ6ï!᝕2ï8.ðñãéòó[ᡃlõöḄó÷økùᐹ.ûᵨðoᙊãýñᡂÿ
.ᙠᨵᓟḄᔊ᪍᳝Ḅ.ᕜ!"#ᶇ%ᐵ'Ḅ()“+ᝯ-ஹ/”ᨵ1234ᙠ5234678%9:ᙊᨬ=◤⌕@Aᙊ9B%2:ᙊᨬ=◤⌕@A2BC(3472<9,71€/7*)%ᐔ:ᙊ◤⌕@AᙊḄᨬ=BᦪGH=K-2+2M1,ᑣ%8:ᙊᡠ◤⌕@AᙊḄᨬ=Bᦪ()A.30B.90C.170D.3419.Q8RSᔣUV=(2,—1,3),h=(-1,4,2).WXYZᚖ\ᑣ]ᦪ^IḄ_`()A.1B.2C.3D.410.\ax-y+2=0Ḅbcd()A.60°B.120°C.45°D,135°11.Q8RS:e4(—2,0,2),B(—1,1,2),ᑣᔣUfḄg`()A.2B.V3C.V2D.112.Vhy=925-ᑐ2⊤kḄla()A.9ᩩnaB.9:ᙊC.ᩩnaD.o:ᙊ13.pq1ḄrVsABCD-48t/WGrVvBCGB1Ḅt,ᓽy•{=()A.2B.—V2C.-1D.114.Q8ᙊCY\ax—y=0|x—y—4=0}~ᑗᙊtᙠ\ax+y=0ᑣᙊCḄVh()

2A.(x+l)2+(y-l)2=2B.(x—l)2+(y+I/=2C.(x-l)2+(y-l)2=2D.(x+I)2+(y+1)2=215.᝞ᙠRS\dᙶ᪗ᨵ\pABC-CA=CCi=2CB=2.ᑣ\aBQY\a4ᜳdḄ_()C.16.ᙊtᙠxḄroo`2ḄᙊCYy~ᑗYᙶ᪗e\aI6x+y=a(a>0)Yᙶ᪗£ᡂdv☢¦`18,¨P,Qᑖ«`ᙊC¬\aḄ:AeᑣP,Q:eSḄᨬ®¯`()A.2(V2-1)B.3V2-1C.V2-1D.V2+1²ஹ1⌱⚪(µᜧ⚪ᐳ8¸⚪ᐳ40.0ᑖ஺ᙠº¸⚪ᨵ1⚗¼ᔠ⚪¾⌕¿)17.Q8Áᦪ/'(x)=AsÄ(tux+Ç)(ᐸA>0,3>0,|Ê|<ḄÌᑖÍ᝞ᡠkᑣ()A.3=2B./(x)ḄÍᐵ'\a=ÎÏÐC./(%)=2cos(2x-5)D./ÔᙠÕ9Ö9×Ḅ_ØÕ92,1Ù18.ᙠrVsABC஺9%ᑡÛ2Ü4rÝḄᨵ()A.AB,&Cß☢\aB.DBLAD11C.DC1Yà☢DBBWiᡠᡂḄd45஺D.²☢dâ9AC-BḄrᑗ_ã19.Q8Áᦪ/'(X)=e«x29%+1),ᑣ%ᑡ⌱⚗rÝḄᨵ()A.Áᦪf(x)᩽¸_1B.Áᦪf(x)ᙠ(-1,+8)ᓫë⌴í

3C.âxe[-2,2]MÁᦪf(x)Ḅᨬᜧ_3e2D.âMVhf(x)=kាᨵ3:ïð]᪷20.Q8Áᦪ/■(*)ôõØR,G/(t)=f(2-%)=f(x),/(I)=1,ᑣ()A./(%)ḄÍᐵ'\ax=2ÏÐB.஻6)=0C./(x)ḄÍᐵ'e(—2,0)tÏÐD.f(2x-1)ᏔÁᦪ21.Q8:ᙊCi6/+ø2-2x+4y+4=0¬C26(x-a)?+y?=4~ùᑣaḄ_ú
`()A.-2B.0C.1D.222.Q8eP`àûfüv4BCDᡠᙠḄà☢᜜9e᝞þÿ=(2,-1,-4)
AD=(4,2,0)
AP=(-1,2,-1)
ᑡḄ()A.APLABB.AP1BDC.AP//BDD.ᔣ=(☢4BCDḄᔣ23.ᙠᙶ᪗
4(2,2,0),8(1,4,2),C(0,2,-l),!ᙶ᪗"஺ᑮ☢ABCḄ%&'ᑮ(ABḄ%&ᑖ*d+d,,┵0-ABCḄ./0ᑣᨵ()2A7V5,2V17,14V5n1/_7RrA.IZ=—D.d=C%=-r=-u,V=-224.!m3456Ḅ7ᦪ
9:MḄ;(x+my=0'9:NḄ;(7nx-y-m-3=0<5P(=,y),ᑡḄ()A.:NḄᙶ᪗(1,3)B.\MN\=V10C.|PM|•|PN|ḄᨬᜧA5D.\PN\|PM|ḄᨬᜧA5BஹD⚪(Fᜧ⚪ᐳ8H⚪
ᐳ40.0ᑖ)25.KSL4MᦪᑡNOPḄQn⚗'
8a2+஺5=0,ᑣT=.n26.U(y=(%-l)ex+Vᙠx=஺ᜐḄᑗ(YZ.27.K3sina—s[᜛=JIU,a+᜛=],ᑣcos2/?=.28.!^ᦪf(x)=_:,K/(x)aᙠᨬHA
ᑣaḄbAdL29.YZe2+y2-2%+6y+5a=0⊤gᙊ
ᑣaḄbAd.

430.!a,F2nᙊo*l(a>b>0)Ḅtᯖ
vᯖ%4,9xᯖy2Ḅ(0)x,yḄ<Ḅᑖ*A,Bt
ᑣ(ᙠx,yḄ%'ḄᨬHA.32.94(—3,)Ḅ(
ᙊ/+y2=12<54Bt
94Bᑖ*
Ḅᚖ(e<5C,஺t
K0408=ᑣ|CD|=.ஹ⚪(Fᜧ⚪ᐳ12H⚪
ᐳ140.0ᑖ஺ᑏᦻ
9Zᡈ¡¢£¤)33.(FH⚪10.0ᑖ)⚗ᦪᑡNaP,%=1,a=2,Na"1—¨P©ªL2Ḅ4ªᦪᑡ.n2(1)«NaPḄ¬⚗©_n1111(2)!%=a+a,ᦪᑡNbPḄQn⚗'LS,«┐+°+0+…+┐.nn+1nn34..H⚪12.0ᑖ)᝞³
ᙠ,┵P-4BCD
PA1µ☢ABCD,µ☢ABCD¶·,P4=2AD=4,vPC=2¸,EᙠPC.(1)«ºBOJJFSfPAC_(2)KELPCḄ
«¾☢B-ED-஺Ḅ¿ÀA.35.(FH⚪12.0ᑖ)ᙠÂA8C
ᑁ4B,CᡠÅÆḄ~ᑖ*La,b,c,vÇÈÉ0$4=asinB.প«A;(2)K0=Î
BA-AC=3,ADÂABCḄ(
«ADḄ~.

536.(FH⚪12.0ᑖ)ÐᡃÒÓÔÕᡃÒᦻᓄ×Ø9ḄᕜÆÒÙ'ᙢÛᱯᨵḄÝÞᦻßḄàá⊤â·
ãᜧäÐåæᙠ2022çèéêᦈèæᕒ
¬9ᭁÐஹîÐt⚗Ðᢈðñòóô⌱ö
÷⚗ñòøùᨵ3Þ
ᑖ*Ý4ஹ¾4ஹ44ç
øLÝ4ú3ᑖஹ¾4ú1ᑖஹ4ú஺ᑖ.ᵬüäýþᭁÐñòøLÝ4Ḅᭆ᳛
Ḅᭆ᳛

Ḅᭆ᳛
Ḅᭆ᳛
|;⚗⚗ᵬᑖ"#
஺(1)(ᵬᭁஹ⚗+ᢈ-ាᨵ0
1Ḅᭆ᳛2(2)(fḄᑖ5ᑡ7ᦪ9:.37.(?@⚪12.0ᑖ)CDEᱥGEIy2=2px(00/(x)0).2(1)zk_L%(k7ḄkOᙶ᪗2(2)zb7]ᩩsG"ḄUV(zn+nḄ.40.(?@⚪12.0ᑖ)ᜧᙠ¡¢ᓫ£Ḅ¤¥t¦§¤¥¨ᚖslᙢ☢Ḅ☢¬Ḅ☢¥®¯°¢±ᙊ᝞³CDᙊḄs´AB=12·¡¸᝞³ᡠºḄs»ᙶ᪗¼.(1)ᑏ¾OCḄᙶ᪗¿(¾À¢ᙊḄ᪗ÁWX2(2)z¢ᜧÂÃᓱÅÆ6·Ç4.2·ᔲ-ÉᑭËaÀ¢¤¥ÌÍrᳮᵫ.

641.(?@⚪12.0ᑖ)CDÐABC1¢⚔OḄᙶ᪗ᑖj4(2,3),8(0,1),C(5,0),aBOḄsGIÒÐABC☢Óᑖ.(1)(sG1ḄWX2(2)(44BCḄ᜜ÕᙊḄWX.42.(?@⚪12.0ᑖ)CDᙊCḄWX(x-a/+(y-2aÖ="জ>0),]ᙊC7sGZIx+y-6=0ÙᑗlOP(|.(1)(ᙊCḄWX2(2)zsGmIy=kx—17ᙊCᨵÚᐳO(kḄ.43.(?@⚪12.0ᑖ)ÜDOP(2,2),ᙊCI/+y2-8y=0aOPḄÝsGI7ᙊckla,BOGÞ48ḄßO$M,஺
ᙶ᪗àO.(1)zá4cB=:(ãZBḄäå2(2)(MḄæçWX2(3)|OP|=\OM\,(/ḄWXèÐPOMḄ☢Ó.44.(?@⚪12.0ᑖ)᝞³éê┵P-ABC஺ßì☢ABCD
íîPA☢ABC஺AB=|,AD=>/3,AP=1,DF=AD?(O

7

8õᫀ#÷᪆1.ூõᫀ௃Bூ÷᪆௃÷Iᵫ⚪ûz=£+i=þÿ+1=1+232=1-21.ᦑ⌱B.ᵫᦪḄᐳᦪḄᭆ.⚪⌕ὃᦪḄᑣ!"ᐳ#ᦪḄᭆ$%&Ạ⚪.2.ூ)ᫀ௃Aூ᪆௃ᙠ(l+x)63456T=Cl-xr,r+17r=4:;=15=ᦑ⌱A.>?ᑭᵨBᔠᦪDE⚗345ḄGᵨHIJ.⚪ὃḄKL⌕MBᔠᦪDE⚗345ḄGᵨ⌕ὃNOḄPQDᦪNRSPQ$%&Ạ⚪.3.ூ)ᫀ௃Cூ᪆௃ᵫTUឋWXYZ[ᢴߟy2=1Ḅ⚔M(2,0),bc[y==x,ᑣ⚔Mᑮbc[Ḅefd=⊱=i.ᦑ⌱C.ᵫTUឋWXYZ[Jkஹ2=1Ḅ⚔M(2,0),bc[m=3%,ᑭᵨMᑮ>[Ḅefo5ᓽWqᑮ⚔Mᑮbc[Ḅef.rstuYZ[Ḅ⚔Mஹbc[vw"qᑮ>[Ḅefo5x⚪Ḅᐵz.4.ூ)ᫀ௃Dூ᪆௃:/஺((:~஺•AQB,••A\JB=B.

9ᦑ⌱D.᪷An(QB)=0WqHAc,ᯠḄᓽW.B⚪ὃDḄ"ḄὃPQ$%&Ạ⚪.5.ூ)ᫀ௃Dூ᪆௃•,•?(=l-e-lm/s:,F«0.221,ᓽx=l:F(l)«0.221,1-«0,221)q஽x2,F(x)=1-e*,F(4)=1-e-4«1-0.018=0.982,ᦑ⌱D.x=L(1)”0.221ᐭ(=1—6-(/Wq;2,7x=4:ᐭᓽWqH)ᫀ.⚪ὃ᪷▭⚪⌱¡ᦪ¢£ὃ¤¥¦ᳮPQDPQ$%6᫏⚪.6.ூ)ᫀ௃AAூ᪆௃©4CnBD=஺/K--------^0ᑣª•«=2ª•ª=2|ª||ª|cos404P=2|ª=2x\/16=32,--------------Qᦑ⌱A.ᵫ®☢ᔣ±ᦪ±²ḄᓽW.⚪ὃ®☢ᔣ±ᦪ±²Ḅ$&Ạ⚪.7.ூ)ᫀ௃Bூ᪆௃©ᵱOᨵxµᑣ᝕Oᨵ8-xµ·8>xZ2,ᵫ⚪¸Wq¹wk⚪=90,ᓽ"ὃ»H•6=90,ᓄ½Wqx=3,ᦑ8—x=5,ᓽᵱ᝕¾NḄµᦪᑖÀx3,5,ᦑ⌱:B.©ᵱOᨵxµᑣ᝕Oᨵ8—%µ·8>x22,ᵫ⚪¸Wq¹¹kᵨ=90,ᓄ½WqÁḄÂÃ

10ªqHIÄ.⚪⌕ὃ᣸ᑡBᔠ"ÇÈ&ÉᳮḄGᵨq¹/k“=90,x⚪Ḅᐵz$%6᫏⚪.8.ூ)ᫀ௃Cூ᪆௃ᦪᑡÍᓽÎÏÐÑ=ᓽ_2+2ᔵ1(3íîEᚖ>ᑣñ"b=-2-4+32=0,2=2.ᦑ⌱:B.ᵫᔣ±ᚖ>qᔣ±Ḅᦪ±²0,ᵫòWq.⚪ὃéêᔣ±ḄGᵨ$%&Ạ⚪.10.ூ)ᫀ௃Cூ᪆௃ூᑖ᪆௃⚪ὃ>[Ḅó᳛õóöḄᐵâ$%&Ạ⚪.ᑭᵨ>[Ḅó᳛õóöḄᐵâᓽWqH.ூ)௃©>[5ky+2=0Ḅõóö0,>[x-y+2=0Ḅvw÷y=x+2.tan9=1.

111,,6G.[O,TT).e=45°.ᦑ⌱C.11.ூ)ᫀ௃cூ᪆௃•••4(-2,0,2),8(-1,1,2),AB=(1,1,0).ᑣ|ø|=VLᦑ⌱C.ᵫèKq⊟Ḅᙶ᪗üᵫᔣ±ýḄ.⚪ὃéêᔣ±ýḄx&Ạ⚪.12.ூ)ᫀ௃Dூ᪆௃ᓄ½᦮ᳮvw/+y2=25,ÿyWO.ᡠ
Ḅ⊤Ḅᙊ.ᦑ⌱D.ᓄ᦮ᳮ/+y2=25,◤y<0Ḅ◚ᩩ"#ᑨ%ᓽ'.(⚪ὃ+,Ḅ-ᵨ#Ḅ◚ᩩ"Ḅ-ᵨ#/Ạ⚪.13.ூ2ᫀ௃Dூ5᪆௃578᝞:ᡠ;<=>ᙶ᪗A,ᑣ4(100),D1(0,0,1),ᑣ=(-1,0,1),AG=(-

12ᡠ
D-A07=-1x(-1)+Oxl+lx1=1.ᦑ⌱D.78;<=>ᙶ᪗A#ᵫ;<ᔣRḄᙶ᪗STU5.(⚪ὃ+;<ᔣRḄᦪRWST#/Ạ⚪.14.ூ2ᫀ௃Bூ5᪆௃ூᑖ᪆௃(⚪ὃ+ᙊḄ᪗Z#=,ᙊḄ[\ᐵA#^_/Ạ⚪.ᙊ`ᙠ=x+y=Oc#᣸◀CஹD,hijᙊC,=x-y=0kx-y-4=0lmᑗ#oᙊ`ᑮ=Ḅqrls_tᓽ'.ூ52௃5ᙊ`ᙠ=x+y=Oc#ᑣᙊ`Ḅuvᙶ᪗wmx#yᯠ{᣸◀CஹD4ij4|ᙊ`(}1,1)ᑮ=x-y=0Ḅqr~=#ᙊ`(-1,1)ᑮ=x-y-4=0Ḅqr=3Xᡈ#ᦑA┯.ᦑ⌱:B.15.ூ2ᫀ௃Aூ5᪆௃5ᙠ;<=>ᙶ᪗A|ᨵ=4BC-/11B1G#CA=CQ=2CB=2,ᵫ:#AḄᙶ᪗(2,0,0),BḄᙶ᪗(0,0,1),BiḄᙶ᪗(0,2,1),GḄᙶ᪗(0,2,0),ᡠ
=(0,2,—1)#=(-2,2,1)#ᡠ
cos(Ḅ67>=°&-2)++(-1)x1=ᦑ⌱A.ᵫ:ᑮ=(0,2,-1)#ABi=(-2,2,1).ᐭ¡ᓽ'U5.(⚪ὃ+¢£☢=ᡠᡂ>Ḅ¦T#^_/Ạ⚪.16.ூ2ᫀ௃A

13ூ5᪆௃5¨ᙊ`ᙠ©ªḄ«ªc#t2Ḅᙊ஺,ஹªmᑗ,ᙶ᪗#ᦑ'®ᙊ஺Ḅᙊ`(m,0)(m>0),ᦑᙊḄ(x-m)2+y2=22=4,±ᙊC²ᙶ᪗#ᦑtn?=4,ᓽm=2,ᓽᙊCḄ(x-2)2+y2=4¶ᙠ=#%+y=a(a>0)|#¹º=0,ᑣy=a,¹y=0,ᑣº=a,®=#,ᙶ᪗ªḄ»A(a,0),B(0,a),ᦑ,ᙶ᪗ª¼ᡂḄ>½☢WS=^a2=18,5a=6,ᦑ=2%+y=6,»_|2+0_6|_ᙊ`cᑮ=Ḅqrd=7T=T=92V2>ᙊḄt2#ÂP#QᑖÄᙊCÅ=1cḄÆÇ#ᑣP,QÆ<ḄᨬÉqr2Ê-2.ᦑ⌱A.᪷ÌÍᩩ"ᐜUÏᙊCÅ=Ḅ#¦Tᙊ`Cᑮ=Ḅqrd,᪷ÌᙊḄÐÑឋ#P,QÆ<ḄᨬÉqrᓽd-r.(⚪ὃ+¢=,ᙊḄ[\ᐵAḄ-ᵨ#^_|᫏⚪.17.ூ2ᫀ௃ACூ5᪆௃5᪷Ìᦪ/'(x)=Asin(3x+0)(ᐸ|4>0,3>0,×ḄØᑖ:Ù'A=2,'ÚÛ="+ÝUÞ=2,ᦑ4«ß#ᵫ⚪àᔠâãä:#'2X(Y)+3=0,U஺=æ'f(%)=2sin(2x+9=2sé©+2%-1)=2cos(2%-1),ᦑC«ß,'fg)=2sé(2xì+í=-î஺±2,'/(%)Ḅ:Ùðᐵ_=“sòÑ#ᦑ8┯,Âᓽ,—ó,ᑣ2x+ô€[—?,—ó,'sin(2%+J)E[—1,ù#'/'(%)=2sin(2x+?)E[-2,73],ᦑ஺┯.ᦑ⌱:AC.ᵫᦪḄ:ÙḄ⚔ᙶ᪗UÏ4ᵫᕜýUÏ3,ᵫâãä:UÏwḄw#'ᦪḄ5᪆¡#hᑭᵨ
ᦪḄឋ.

14⚪⌕ὃᵫᦪy=45(3%+")Ḅ$ᑖ&'᪆)ᵫᦪḄḄ⚔+ᙶ᪗&4,ᵫᕜ0&3,ᵫ1+23&9Ḅ5ὃ6
ᦪḄឋὃ6ᦪ7ᔠ9:ᦪ9:Ḅ;ᵨ<=>᫏⚪.18.ூCᫀ௃ABDூ'᪆௃'Fᙠ
HIABCD-4&GD1>᝞,R=4,ᎷT4B,4Cᐳ☢ᑣ4B,Cᐳ☢XYZ[BC\☢]^,••ᎷT┯a.•.AB,&Cb\☢cdᦑA
fgR=B,ᙠ
HI4BC0-AiBiGDi>AD1.AD,ADLDC,XXrADnDC=D,•••AD_Lm☢ABiCD,1rvDB(=m☢4&o…q1DBi6ᦑB
fgrR=C,,.,41(?1_18sDDil&GCiDDi=%•u•&GJ•m☢DBBWi•••/GCOib஺G[m☢DBBWiᡠᡂ}T
HIABC஺~4BiGDi>b1,hin/GDOi==ᓟ=X=30஺ᦑC┯agOCiv22R=஺VAC//AC,41Glm☢XAC1m☢஺88srx•••AC10B,AC1OB,4B10BX☢}-AC-BḄm☢}rᐸ
ᑗ5btan^BiOB==ᦑ8
f.UDᦑ⌱FABD.ᑭᵨ2ᑨ4g41m☢4B1CD,ᑨBgAG_Lm☢ᑮ/6஺஺௃bDQ

15[m☢DBB15ᡠᡂ}ᑨCgAC1m☢DB&D1ᑮ/OBX☢}~AC-BḄm☢}ᑨD.⚪ὃd☢ᚖcḄᑨ[ឋஹX☢}Ḅ&2¡Ạ£¤ὃ¥¦&'§Y>᫏⚪.19.ூCᫀ௃ACூ'᪆௃ூᑖ᪆௃⚪ὃᑭᵨ¨ᦪẆªᦪḄᓫ¬ឋஹ᩽5ஹᨬ5ஹ¯+<=>᫏⚪.&¨f'(x)=xe«x+l),ᑖ᪆/'(x)Ḅµ¶·¸¹;"(X)Ḅᓫ¬ឋ᩽5⌲⚗ᑨᓽ¹Cᫀ.ூ'C௃'F/(x)=ex(x2-x+1),ÀbR,f'@x)=ex(x2—x+1)+ex(2x-1)=ex(x2+x)=xex(x+1).ᡠÄᙠ(—8,-1)(0,+8)Åf'(x)>0,f(x)ᓫ¬⌴Çᙠ(~1,0)Åf(x)<0,f(x)ᓫ¬⌴É,R=4Fᦪf(x)Ê/ஹ5="0)=1,ᦑA
fgR=BFᦪ/Q)ᙠ(-1,0)Åᓫ¬⌴Éᙠ(0,+8)Åᓫ¬⌴Çᦑ2┯agR=CFᵫŹ£ᦪf(x)ᙠ(-2,-1),(0,2)Åᓫ¬⌴Çᙠ(~1,0)Åᓫ¬⌴É.Ë/(~2)=7e-2,/(-l)=3e-1,f(0)=l,f(2)=3e2,ᡠÄᦪ/(x)ᙠÍ-2,2ÎÅḄᨬᜧ5b3e2,ᦑC
fgR=DFÐb/(0)=1,/(-I)=3g-1=ÓᔠᦪḄᓫ¬ឋ¹l

16ᡠÄf(6)=f(2)=f(2-2)=f(0)=Oᦑ8
f,f(x)Ḅᕜ0b4,ᵫ/(x)=f(x+4),f(-x)=—/(x)¹—f(—x)=/(x+4),ᑣf(x)Ḅᐵ=+(—2,0)>äRáᦑC
fÐb/'(2-x)=f(x),ᡠÄ/'(3-2x)=f(2x-1),Ëᦪ/(x)Ḅᕜ0b4,W(3-2X-4)=/(2X-1),ᓽ/(~2%-1)=/(2x-1)ᦑᦪ-1)bᏔᦪᦑ஺
fᦑ⌱FBCD.ᵫæ£ᦪb᜻ᦪàRáâbx=1,ᦑA┯aÓᵫæ£çᦪḄᕜ0b4,ᵫèᓽ¹ᑨ⌱⚗B,᪷éæ£ᩩë,ᔠ/(x)Ḅᕜ0b4,ç-f(—x)=f(%+4),ᓽ¹ᑨ⌱⚗C,Ëᵫ/(2—ì=/(x)f(3-2x)=f(2x-1),ᯠî᪷éᦪḄᕜ0ᓄðf(-2x-1)=/(2x-1),ᵫèᓽ¹ᑨD.⚪ὃ6ᦪḄ᜻ᏔឋÄRáឋὃ6ñòḄ¥¦&'§Y<=>᫏⚪.21.ூCᫀ௃BCDூ'᪆௃'FÐb/+/_2x+4y+4=0,ᡠÄ(ó—1)2+(r+2)2=1,ᓽᙊCIḄᙊäbḄ(1,~2),õöb÷=1,àᙊḄᙊäbC2(a,0),õöbø=2,ÐbùᙊúûᡠÄᓃ~÷|78ஹC,@=A2+=(2,3,4),6•@=-2+6—4=0,ᑣ4P1BD,ᦑB=C┯C>

1770,ᵫD.8=E+E2G=0,H•6=E2I=0,ᑣᔣKL=M,2OP)*☢33333636zABCDḄQᔣKᦑ஺=.ᦑ⌱%ABD.᪷UVWᔣKᚖYḄᙶ᪗⊤]^!ᫀ.⚪ὃ_VWᔣKᚖYḄᙶ᪗⊤]`᫏⚪.23.ூ!ᫀ௃BCDூ᪆௃%ᵫ⚪b^ᵫ&'ᓭ=(—1,2,2)AC=(-2,0,-1).0A=(2,2,0)d*☢ABCḄQᔣKᐗ=(x,y,z),n-AB——x+2y+2z=0,Ui^ᐗ=1,|,22
,OA-n=7,,n-AC——2x—z=0,_gh_7ᡠj+=k=l₞;=OA-AB=2,dopᓭᜳrs஺ᑣ"s'-
'ᵫArtruᦪᐵ^sin஺=V1—cos20=vwᑣᙶ᪗x(஺ᑮᑮYz{BḄ|}d2=IOAIsinG=2~x=*AB-AC=0'^ABLAC,|=|g=3ᡠjtr-4BCḄ☢sS=jxV5x3=t┵0-ABCḄ)U=*x=3ᦑ⌱%BCD.ᵨᔣKQ(☢|}ஹ(z|}ᵫt┵Ḅᓽ.⚪⌕ὃz☢|}Ḅ(z|}Ḅ┵ḄVW{Ḅ',Ạ⚪.24.ூ!ᫀ௃ABCூ᪆௃%(MḄYzx+my=0,᦮ᳮ^(M(0,0)%(NḄYzmx-y-zn-3=0,᦮ᳮ^m(x-1)2(m+3)=0,^ᑮ(ᙶ᪗N(l,3)>

1874%ᵫ⚪b^%(4(0,0),B(l,-3),ᦑA=>7B%ᵫ&'ᩩ¥^%|MN|=+(_3)2=A,ᦑB=>7C%ᵫªᩩYz«¬ᚖYᑣᐸ®(P(x,y)²ᙠj48sY´Ḅᙊᕜ¶ᡠj·¸2+¹ᵨ2=\AB\2=10.22᪷U»Ḅឋ½ᵫ|P¸|PB|¾·¸=5,PÀÁP|PA|=|PB|ÂÃᡂÅ.ᦑC=ᦑ஺┯C.ᦑ⌱%ABC.✌ᐜᑭᵨ(ḄYz(Ḅᙶ᪗2ɪ(WḄ|}Ê»Ḅ~ᵨᑨÌ4ஹBஹCஹ஺ḄÍÎ.⚪ὃḄ'⌕(%(ḄYzª(WḄ|}»Ḅ~ᵨ⌕ὃÏÐḄÑ{ÊᦪÏÒÓ{`᫏⚪.25.ூ!ᫀ௃-31ூ᪆௃%•••5“sÕᦪᑡ×aÚḄ@n⚗Ê8a+a=0,dÕsq,n258aq+aq4—0,:.q——2,rta(l-q10)1ᑣ.=Ý=l+qS=—31,S5à(j5)rl-qᦑ!ᫀs:231.᪷UÕᦪᑡḄ8⚗jâ@71⚗Êᓽ.⚪⌕ὃÕᦪᑡḄ8⚗Ê@n⚗ÊḄ~ᵨ᪷Uᩩ¥Õ)ä⚪Ḅᐵå,Ạ⚪.26.ூ!ᫀ௃y=x-1ூ᪆௃%ᵫy=(x—l)e*+x,^y'=e"+(x—l)e*+1=xe*+1,y'\x=o~1>ìx=0Ây=—l,íîzy=(%-l)ex+xᙠx=0ᜐḄᑗzòó)y=x-1.ᦑ!ᫀs%y=x-l.xuᦪḄôuᦪ^ᑮuᦪᙠx=0ᜐḄôᦪõx=0ÂḄuᦪõᑭᵨYzòóḄö÷^!ᫀ.

19⚪ὃᑭᵨôᦪẆùîz¶ú(ᜐḄᑗzòóûDüuᦪḄôuᦪ)ᐵå)Ạ⚪.27.ூ!ᫀ௃Iூ᪆௃%ýs3sina—sin,="/TU,a+0=sinS=cosa,ᓽ3sina-cosa=V10,ᡠ(sEacosa)=V10»A.c%3V10MinS=—&cosOn='-&sin(a—0)=1,a—J=]+2/CTT,kEZa=6+]+2/CTT,kEZffsina=sin(0+]+2/CTT)=cosO=᝕€Z&ᡠcos20=2cos2/3—1=2sin2a—1=^.ᦑ2ᫀ45ᵫ78ᑭᵨ;<=>?@(AsBa-Ccosa)=710,Jsin஺=ἠcosO=F&a=6+3+2/C7T,fcGZ,ᑭᵨ;<=>?sina=cos஺=J&KLᑭᵨMNO=>ᓽ?Pcos2/?410ḄT.U⚪ὃXY;<=>&MNO=>ᙠ[O\ᦪᓄ_?T`Ḅaᵨ&ὃXYbcdefgᓄhi&jklẠ⚪.28.ூ2ᫀ௃[0,1]ூP᪆௃P5sa=0t&/(X)=,x>01"f^min=0xsaVOt&z—8t&/(%)->—8,ᦑ/(%)ᨵᨬT&ᔠ⚪⌕?xsa>0t&zV஺t&f(x)=-஺+1ᓫ}⌴&/(%)>/(a)=-a2H-1,LஹW&°VaV2zX2at&f(x)-in=ka-2)2,a[2'M•-a2+1>0ᡈ-a?+1>(a—2)2,

20P00t&\ᦪy=-ax+1ᨵᨬT&ᦑ/(%)ḄᨬT¡d¢y=(£2)2ḄᨬT¤?Pᓽ.U⚪ὃXYᑖ\ᦪḄᨬT&¥ὃXYᑖhi&jk`᫏⚪.29.ூ2ᫀ௃(8,2)ூP᪆௃P5x2+y2—2x+6y+5a=0,ᓽ(x—+(y+3/=10—5a,©ª«*2+y2—2x+6y+5a=0⊤®ᙊ&10-5a>0,Pa<2,ᦑaḄ¢T±4(-8,2).ᦑ2ᫀ45(-8,2).᪷78ᩩ&²ᔠMᐗM´ª«⊤®ᙊḄᩩ&ᓽ?P.U⚪µ⌕ὃXMᐗM´ª«⊤®ᙊḄᩩ&jklẠ⚪.30.ூ2ᫀ௃¶+<=162ூP᪆௃P5᪷⚪·&¸ᙊ¹4=l(a>b>0)Ḅᯖ½¾4,ᓽ2c=4,ᑣc=2xÀÁᯖÂF2ḄÄÅƸᙊk4BÈÂ&sAFiABḄᕜʾ4Ë&ᓽ|&4|+|&B|+\AB\=\FiA\+|F$|+\FA\+\FB\=4a=476.ᑣa=O,22ᑣᓃ=Va2—c2-2,ᦑ¸ᙊḄª«41+4=1;62ᦑ2ᫀ451+1=1.62᪷⚪·&᧕c=2,ᵫ¸ᙊḄÒÓaḄT&?ÔbḄT&²ᔠ¸ᙊḄ᪗Öª«&ᓽ2ᫀ.U⚪ὃX¸ᙊḄ×ØឋÙ&ÚÛ¸ᙊḄ᪗Öª«&jklẠ⚪.31.ூ2ᫀ௃V2

21ூP᪆௃P5ÄÅ2%+a2y-a-0(a>0),Üy=0,Px=3&Ü=0,Py=Ý&PQÄÅᙠX,yÞḄß½àfá+â22ã=ᡈ&zäåz5=â&ᓽa=VIt&æçᡂé&ᦑÄÅᙠX,yÞḄß½àfḄᨬT¾&.ᦑ2ᫀ45V2-᪷78ᩩ&ᑖê?ÔÄÅᙠ,yÞḄß½&¤²ᔠlUæ>Ḅ=>&ᓽ?P.U⚪µ⌕ὃXÄÅḄß½>ª«&jklẠ⚪.32.ூ2ᫀ௃4ூP᪆௃P5ᵫ⚪·8ÄÅëḄ᳛íᙠ&î4À4(-3,ï)&ðÄÅy—ï=k(x+3),ᓽkx-y+3k+8=0&î4ñ4OB=ᡠᙊò(0,0)ᑮÄÅ1Ḅ½ô4d=2V3x^=3,|3k+V?|„&ᡠõö=3,᦮ᳮ&Q=1,Pk=ᑭ+13(x2+y2=12ὶéëúL'üýy&X2+3x=0,Px=0ᡈ-3,(y=yx+2V3ᓽÄÅ1þᙊḄÈÆÂ44(-3,ï),8(0,28)xᑣÀÂ4(-3,ï)äþÄÅ1ᚖḄy-R=-V3(x+3)y=0,=-2,ᓽ஺(2,0),B(0,2)IᚖḄy-2V3=LRx6y=0,x=2,ᓽ஺(2,0)ᡠ|CD|=4.ᦑᫀ:4.ᑭᵨ"4OB=ᑮᙊ%ᑮḄ&'()*/Ḅ,᳛.IᙊḄ/ᙶ᪗2ᑖ4ᑏ6(-3,75),8(0,26)ᚖḄ()*x7Ḅ/ᓽ8*9.;⚪ὃ>?ᙊḄ@AᐵCDEF᫏⚪.

2233.ூᫀ௃9:(1)ᵫ⚪M,aj-al=3,OPW+i-aᑖV✌⚗3YZ2Ḅ\Zᦪᑡᡠ_+i-`=2n+1,bnN2d4=&-g_])+(a"-W-2)+-+(al-W)+Ẇ=(2n-1)+(2n-3)+-••+5+3+1=n2,nO☘=1pqᡠấ=stᔠv0ᡠa=n.n(2)ᵫ(1).5=CLn+a+ib”=2n+1,ᡠz=3,nn{=(3+2*)71=(2)n,n+,,1_1_1,11ஹᦑ᱘=n(n+2)=2^n~n+2)f1,1,1,,11~lx,1zl.1zl1X++ᕖ+…+=2(1-§)+2(5-0+…—)11113n+4=-(14-i---------)=--------2---212n+1n+24(n+l)(n+2)ூ9᪆௃(1)ᵫ⚪M8W+1-=2n+1,nW=(`-1)+(«n-l-an-2),+----(_)+aj,2tᔠ\ZᦪᑡḄ*.Yᓽ8*Ḅ(2)ᵫ⚗*9ᓽ8.;⚪ὃ>ᵫᦪᑡḄ⌴*ᦪᑡḄ⚗Y⚗*.DF᫏⚪.34.ூᫀ௃(1)OPA1☢ABC஺AC.BCu☢ZBCD,ᡠ24LAC,PA1BD,ᡠ4C=yJPC2-PA2=2y12,CD=y/AC2-AD2=2=AD,ᡠ¤¥/BCDV¦¥ᡠBD_L4C,OP4nac=a,ᡠBD1©☢P4C.(2)9ᵫ(1)ª4Bஹ40ஹ4P««ᚖ¬C᝞®

23A(0,0,0),D(0,2,0),P(0,0,4),C(2,2,0),£(1,1,2),B(2,0,0),°=(-2,2,0)DE=(1,-1,2),±=(2,0,0),©☢BEDḄᔣ´µ=ᑣ)•µ=0,DFm=0,ᓽ%i+yi=0,x-y-^-2z=0,111ᡠ8»µ=(1,1,0),©☢EDCḄᔣ´¼=(%2½2/2)ᑣ¾•¿=0À•ᐗ=0ᓽ2s=O%2+222=0,8»Ã=(0,2,1),,Tஹmn2V10cos=-==—,=?r/OË☢ÌB-ED-C┦Ë☢ÌᡠË☢ÌB-ED-CḄÎÏÐÑ.ூ9᪆௃(1)ᵫᩩÓ8P4,AC,PALBD,ᯠÕ4cḄÖ×8¤¥4BCDV¦¥ᯠÕ8BD1AC,ᓽ8(2)ABஹAD.AP««ᚖ¬ØÙÚÌᙶ᪗Cᑭᵨᔣ´*9ᓽ8.;⚪Û⌕ὃ>☢ᚖḄË☢ÌḄᐵÙÚᔣ´ᐸÞᵨÙÚßà6Ḅáâ\ªãDEF\⚪.35.ூᫀ௃9(1)A+B+C=ᐔbcos^Y~~<^sinB,A•bsin-=asinB,♦ᵫ¦Ïåᳮ8sinBsin^=sinAsinB,VBG(0,7T),•sinB>0,

24.A.A•smA=sin5,nêsinA=2sin^cos~,sin9H0,A1•cos-=5vAE(0,7T),ATCHn.27r(2)••z5•ë=3AB,AC=-3.27rvA=—^cb-cosA=—3,9be=6,ᵫÎÏåᳮ8஺2=᮱+02+í9/+C2=13,:4஺Vî6BCḄF■•.AD=^(AB+AC),AD2=1(AB2+AC2+2AB-AC)=^(c2+b2-6)=^,.•.|)|=ðᡠ6஺ḄÖñ.ூ9᪆௃;⚪Û⌕ὃ>ᑭᵨ¦ÏåᳮஹÎÏåᳮ9òÌ¥ᑭᵨᔣ´Ḅᦪ´ó*ᔣ´ḄôDEF᫏⚪.(1)᪷ö÷ªᩩÓtᔠòÌ¥Ḅឋù¦Ïåᳮ8sú4=sin?,2tᔠ4Ḅ»Ðüᓽ8*9(2)tᔠ©☢ᔣ´Ḅᦪ´óYÎÏåᳮ*ý=6,b2+c2=13,2tᔠþ=(ÿ+AC6ᓽ.36.ூᫀ௃(1)“ᵬᭁḄᑖiᑖ”(i=0,1,3),ᑣp(4)=!P(&)=3,p(y>)=i-|-1=i,0ᙳ“ᵬ(Ḅᑖiᑖ”(i=0,1,3),

25ᑣP(B3)/P(BI)=|,P(B)=1-1-|=|O஺“ᵬᭁஹ(2⚗4ᢈ6ាᨵ9:;<”ᵫ⚪?D=+A^BQ+AQB^+»ᵫḄ@AឋCDEឋP(D)=P(AB+&Bo++AB)=P(AB)+2(4%)+30033QPQMi)+PG%%)=P(4)P(Bo)+P(4)P(Bo)+P(A°)P(B1)+PQ4O)P(B3)=|XI+|X1+13+113-X--X--656510ᦑᵬᭁஹ(2⚗4ᢈ6ាᨵ9:;<Ḅᭆ᳛L.(2)ᵫ⚪?MNOPf6ḄQR0,1,2,3,4,6,11l-X-=-ᵫḄ@“ឋSDEឋP(f=0)=P(AB)65003011131PT=1)=P&Bo+AB1)=P(4Bo)+P(AA)=|xilx|=i,+13111PG=2)=P(&&)=ix|=i,P(f=3)=P(_AB+&=PC/Bo)+P(AB)=U+30O3112-X--P(f=4)=P(4Bi+4ἔ)=P(_AB^+P(?lF)=i1x31+l1x1i=i11l,6531315WDJDUillP(^6)=P(AB)=-X-=~,33ᦑMNOPfḄᑖXᑡ0123461112111p3065153010ᦑᦪ[\E(f)=0x*+lx*+2x"+3x5+4x^+6x2=U-ூ᪆௃(1)᪷_`aᩩcᔠḄ@AឋCDEឋᓽ.(2)ᵫ⚪?MNOPf6ḄQR0,1,2,3,4,6,ᑖefghḄᭆ᳛icᔠ[\jkᓽ.l⚪m⌕ὃpqᦣsMNOPᑖXᑡḄtu[\jkḄhᵨwxy᫏⚪.37.ூᫀ௃(1)ᵫ⚪aI+?=|ḱ=2ᡈ=()•ஹQ22'஺2ᦑᱥEḄ=2x.

26(2),),N(,2)y—y„yR1ᑣPMḄy90=^2x-y,᦮ᳮ2x-31+yy+y0o=0.1-T|8+3¦1_9PMSᙊC¡ᑗᡠt¤my+4-2,᦮ᳮ4-_*98yoyi+4ª-48=0,ᳮ4-ygWy2~8yoy2+4M-48=0,ᦑy«2¬4-yoy2-8yoy+4-48=0Ḅ2᪷,8y4y%-48nᑣ%+=¯°,±±=L2•4y及-当yl。1-2及好MNḄ³y9_2-242T80O᦮ᳮ29⌚y+嵋=--·X=6¹ᐭMNḄ12—ᔜy+<¥=0,y=-y°,4-%4-y0ᦑMN¿Àூ᪆௃(1)ÁÂÀùᐭᱥCÃQᑮᯖÃḄÆqÇAÈᓽ¦(2)fÃM,N,⊤ÊfPM,ᑭᵨPMSᙊ¡ᑗᑮ(4-%)Ì-8yoy1+4-48=0,ᳮᑮ(4'-)Î-8yy+4%-48=0.cᔠÏÐÑᳮfy1+y>y^y⊤ÊfMN,0222¹ᐭ=6ᓽ.l⚪m⌕ὃpᱥḄSᙊ┵ÓḄÔÕᐵ×ÏÐÑᳮuᐸhᵨឤÀÑÃÚ⚪0å<(%)>0,ᓽ2a2ᒹéឤᡂA.lnx+1/ஹíஹëgx=—>0ᑣg'(x)=—î00,x>låg

27ý◤ex—Inx0),ᑣh'Q)=᧕(x)ᙠ(0$ᓫ⌴ᙠ(,+8)ᓫ⌴ᑣg)9=()=0ᡠ")XdN0.ex'(W(x)—ex—ex(0<%<1),ᑣ“(%)=e—ex,0<%<1/"(%)>0,%>0/“(%)<0,᧕9(%)ᙠ(0,1)ᓫ⌴ᙠ(1,+8)ᓫ⌴ᑣ=0(1)=஺ᡠ"ex-ex<0.23/i(x)6ᡂ@.ூB᪆௃(1)EFGHᦪ((x),ᵫK(x)20ᙠ(0,+8)ឤᡂ@ᑖOPᦪᓄ32஺2RS'EFTHᦪḄᨬᜧXᓽZ(2)8=>[\3ex-e]bcdedfHᦪḄᨬXghiZ8=>ᡂ@.j⚪ὃmᵨGᦪẆpHᦪḄᓫឋir8=>ஹtᓄuvwxRḄyzu{|}⌕E⚪.39.ூᫀ௃B(1)ᓃ(n-l)x-2y4-4=0,lMx+ny-3=0,2,**J-q>n—1j1᦮ᳮZn=-l,x=lᡠ":BZ—y—3=0y=WᓽP(|,_).(2)46%ᡠ"n=-2ᵫdᩩḄO/,

28|m+3|_ᦑ1,2,N=75,BZrn=2ᡈ8(X¡)qi+(-2)ᡠ"m+n=2-2=0.ூB᪆௃(1)£ᑭᵨᚖḄᐙ⌕ᩩ§EFnḄX¨©ª@«¬EF®Ḅᙶ᪗(2)ᑭᵨḄḄᐙ⌕ᩩ§EFnḄX¨©ᑭᵨdḄO±>EFmḄXᨬaEFm+nḄX.j⚪ὃmḄ²⌕³ᚖḄᐙ⌕ᩩ§dḄO±>´⌕ὃmxRḄµ¶|}³ᦪxu{|}·᫏⚪.40.ூᫀ௃B(1)᝞ºᡠ»:¼⚪½ᙊḄ¿48=12Àᡠ"r=6,ᡠ"ᙊCḄᙊÃ3(0,0),Ä¿r=6ḄÄᙊᦑᙊCḄ«¬+y2=36(y>0).(2)Åx=3/ᑭᵨÆÇÈᳮᡠ"y=V62-32=3>/3>4.2À2ÊËÌÍ/ᓱÏÐ"ÑᑭÒÓ.ூB᪆௃(1)£ᑭᵨÔᩩ§EFᙊḄ«¬(2)ᑭᵨÆÇÈᳮḄÕᵨEFÖ×.j⚪ὃmḄ²⌕ᙊḄ«¬ÆÇÈᳮ´⌕ὃmxRḄµ¶|}³ᦪxu{|}·᫏⚪.41.ூᫀ௃B(1)ØABCÛf⚔Ḅᙶ᪗ᑖÝ4(2,3),B(0,l),C(5,0),ᡠ"4cḄ·ᙶ᪗£>á,|),ᦑKB஺=

29ᦑLBDy=+1.(2)ãA4BCḄ᜜£ᙊḄ«¬3x2+y2+Dx+Ey+F=0,ᵫᙊåÓ4(2,3),8(0,1),C(5,0),4+9+2஺+3E+æ=0ᡠ"1+E+F=O6(25+5D+F=0(D=-5BZE=—1.(F=0ᡠ"%2+y2-5%-y=0.ூB᪆௃(1)✌ᐜᑭᵨ·ᙶ᪗±>EF·Ḅᙶ᪗¨©EFḄ«¬(2)ᑭᵨᙊḄé>ª@Ûᐗ뫬¨©EF஺ஹEஹFḄXᨬaEFᙊḄ«¬.j⚪ὃmḄ²⌕·Ḅᙶ᪗±>Ḅ«¬ḄEìᙊḄ«¬ḄEì´⌕ὃmxRḄµ¶|}³ᦪxu{|}·᫏⚪.42.ூᫀ௃B(1)ᙊCḄ«¬(í-a)2+(y-2a)2=r2(r>0),ᦑᙊÃC(a,2a),Ä¿3r,23ᙊC6Ã%+î6=0ïᑗñá3).ᡠ"CP1I,23òḄó᳛3-1,ᦑCPḄó᳛k=l,72=2a一-5=1M-21z29••a=1,r=-ᙊCḄ«¬(x-I)2+(y-2)2=I(2)•••6ᙊᨵ±ᐳ,ᡠ"ᙊÃC(l,2)ᑮmḄOd

30ூ᪆௃(1)᪷ᑗᐵCP1Z,ᑣ᳛-1,ᓽὶ!"#$,(2)᪷ᙊ'ᑮḄ*+,-.Ḅᐵᑡ0123ᓽ$.5⚪ὃ89,ᙊ"#:;<=ᐵ>?@᫏⚪.43.ூDᫀ௃F(1)ᙊCḄ᪗H"#I+஺4)2=16,ᙊ'C(0,4),-.4,ᡠ:\AC\=\BC\=4,ᵫQRSᳮU|4B|=JlACI2+\BC\2-2\AC\■|J3C|cosy=4](2)^_M(x,y),b_M1,_Pcᔠeᓽbx*2gy*2eᵫᚖ.SᳮCM1AB,ᓽCM1PM,^M(x,y),ᑣi=(x,y-4)MP=(2-x,2-y).ᵫ⚪^j•l=0ᦑx(2-n+(y-4)(2-y)=0,BP(x-l)2+(y-3)2=2.b_M,_Pcᔠe_PḄᙶ᪗qrs"#(x-1)2+(y-3t=2,ᦑ_MḄuv"#஺-I)2+(y-3)2=2F(3)^_ᑣ10Ml=|OP|=2ᡈ(m2+n2=8ᵫ⚪|U}~1)2+(—3)2=2,U11/ᓽ²◤)’ᡠ:kpM=_g61Ḅ"#y-2=-—2),ᓽy=—g%+k=1,ᑣOPḄ"#—y=0,g|OP|=2VL0P_MᑮOPḄ*+d[=ᡂ,ᡠ:P0MḄ☢0P|.d=Fx2&x^=D.ூ᪆௃(1)ᑭᵨQRSᳮ$U|4B|(2)^_ᵨ(x,y),_M,_Pᔲcᔠᑖᙠ_M,_P1cᔠeᵫᚖ.SᳮᔠᔣᚖḄᙶ᪗⊤$0_MḄuv"#ᙠ_M,_Pcᔠe¡¢ᓽ£ᔠU0_MḄuv"#(3)^_᪷⚪|U0ᐵ?mஹnḄ"#¦0§¨©ᦪḄ«U0_MḄᙶ᪗ᓽ$U1Ḅ"#¬$0|0P|:;_Mᑮ0PḄ*+ᑭᵨ®¯Ḅ☢°3$UP0MḄ☢.5⚪ὃ8,ᙊḄ<=ᐵḄ£ᔠ±ᵨ>?@᫏⚪.44.ூDᫀ௃(1)¢µFᵫ⚪|EPD@_,᝞¹ᡠºBD,,4c»?_஺º0E,

31¼½☢ABCD¾¯,ᡠ:஺BD@_,ᡠ:OE஻PB,¼OEuÁ☢4CE,PBCÁ☢ACE,ᵫ☢ÁḄᑨÃSᳮUPB஻Á☢4CE.F(2)¼P41Á☢4BCC,AB,4஺uÁ☢ABCD,ᡠ:PA14B,PAA.AD,ᦑP4AB,4஺ᚖ:4ᙶ᪗Ä_Å!᝞¹ᡠḄÆÇ®ᙶ᪗4-xyz,ᑣ4(0,0,0),஺(|,],0),D(0,A/3,0),F(0,y,ÈP(0,0,1)-^Á☢4CEḄÉᔣᐗ=(x,y,z),Ë•Ì=|Í+V3y=0ᑣÎUË=(-Ï,1,-b),n-AE=^-y+=0^PC,Á☢4CEᡠᡂ®8,jT).(-Ó,1,b)|3ᑣsin஺=|cos(n,PC)|=10ᓽPC,Á☢4CEᡠᡂ®ḄÔR«U(3)Õ_EÖEH14஺?_H,ᑣ᦮=᦮=Ø=Ù

32¼AP=lMD=bᡠ:EH=4,DH=V3AAH=V3-V3AᦑE(0,Ý];I"),Á☢/WPḄÉᔣâ=(1,0,0),^Á☢4ECḄÉᔣã=(x,y,z),111ᑣå=/+¹௃=஺ÎU~=(æ1,çè,n,AE=(V3—V3A)y+Az=0x1¼eeᵨê,ᡠ:cos஺egë|ìí1মï.ì1o0ð1ᓽcos஺=|cosìrnmð|=-j46Jᓽᘤ+1+ìóð213ft得-<-A<--24ᡠ:;IḄõ«÷ூ᪆௃(1)ᵫ⚪|UEP஺@_ᯠù¢µÁᨬùᵫ☢ÁḄᑨÃSᳮU☢Á(2)Å!ÆÇ®ᙶ᪗ᑭᵨÆÇᔣ$UḄ"ᔣᔣûÁ☢ḄÉᔣU☢®ḄÔR«;(3)ᵫ⚪|Uᑮ_:0,6-61"),$0Á☢ḄÉᔣᯠùᔠ⚪|Uᑮᐵ?IḄ123$123UIḄõ«÷.5⚪ü⌕ὃ8☢ÁḄᑨS☢®Ḅþÿ
Ḅᨬ⚪ᔣᐸᵨḄ⚪.