高考数学公式

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ᦪᵨᵨ1.ᐗᔠḄᐵ=CA<=>xgA.U2.᥅᪷Q(An8)=஺4U஺8;(Au8)=஺AnG8.3.ᒹᐵAC\B=A^A\JB=BQg8=8=5=AClQ,8=জQqAU8=/?4.ᳮcard(AUB)=cardA+cardB-card(AClB)card(AU8UC)=cardA+cardB+cardC-card(ADB)-card(AC\B)-card(BC\C)~card(CC\A)+card(AC\Br\C).5.ᔠ{%,'…,4*Ḅ+,ᦪᐳᨵ2",12+ᨵ2"-1,156+ᨵ2"-1,156Ḅ2+ᨵ2"-2,.6.89:ᦪḄ;᪆Ḅ=>?(1)BC/(x)=ax2+bx+c(a*0);ফ⚔J/(x)=a(x-7z)2+᝕(a0);PQJ/0)=஺(R—ᓰ)(UBᑐ2)(஺஺°).7.;XYZNn022M-f(x)11Q-------->------./(x)-NM-N8.ij/(x)=0ᙠ(ᓃm)nᨵopᨵB,q᪷,/(ᓃ)/(m)<0YZr,sὅuvὅḄB,w⌕yYuᐙᑖᩩ}.ᱯᙢij2++஺=0(஺W0)ᨵopᨵB,q᪷ᙠḄ)ᑁZr/)/(&)<0,ᡈ
,[ஹ7bkஹ+k?__ixr/1\"i+%2b.f(h)=0oL<--<2ᡈfW)=0o12<--<^.229.PnḄ89:ᦪḄᨬ89:ᦪ/(x)=«x2+bx+c(aH0)ᙠP[p,nḄᨬpᙠX=--ᜐḄJᜐᐹ2a¡᝞]£஻hপ¥a>஺¦,§—¨⏊,ᑣߟ(pg-"ভ};bX=B¯°±p,q³/(X)max=max{/(P)J(4)}/Win=in{/(P)/(?)}•mm2a/?hফ¥a<0¦§º=B¯e±p,q³,ᑣ/஺¼=min{/(p)J(q)},§R=B¯½±஺,ᑣ/(x)max=max{/(/?),/(<7)},/(x)min=min{/(p),/(q)}.

110.ᐗḄ᪷ᑖ஻)f(஻)<0,ᑣ/(x)=0ᙠ(஻)ᑁᨵ᪷./(x)=x+px+q,!"2p2-4<7>0(1)/(x)=Oᙠ(஻?,+8)ᑁᨵ᪷Ḅᐙ⌕ᩩ)*/(6)=0ᡈm[2/(”)>0/(»)>0/(…஺ᡈ/(஻)=0(,஻)ᑁᨵ᪷Ḅᐙ⌕ᩩ)*/(⊈)/(஻)<0ᡈ0ᡈ.«/(«)>0/("?)>()'tn<——0(3)/(x)=0ᙠ(-oo,)ᑁᨵ᪷Ḅᐙ⌕ᩩ)*/(஻?)<0ᡈீrtp---2(-*+8)ḄBC(D᝞F3বH(8,IH±a,+8)7J)345ᦪḄ789/(x,f)20"*5ᦪ)ឤᡂ<Ḅᐙ⌕ᩩ)L/(x,r)>0(xgL).mjn(2)ᙠ>2(-8,+8)ḄB345ᦪḄ789/(x,0>0(H*5ᦪ)ឤᡂ<Ḅᐙ⌕ᩩ)La>0a0ឤᡂ<Ḅᐙ⌕ᩩ)L⁐20ᡈ012.NO⊤PQVPPᡈqPWqNNᎷNNNᎷᎷNᎷᎷNNNᎷᎷᎷNᎷᎷ13.QRSTḄᔲ2D9YSTZ[YSTZ[L7Lᨵ\]ᨵ^L7^L_ᨵᨵ`ᜧb7ᜧbᨵ஻_ᨵ(஻-1)cb7cb_ᨵ஻ᨵ(஻+1)dᡠᨵX,fᙠgX,ᡂ<7ᡂpᡈ-

214.Ì>Í⚪ḄÏÐᐵ15.ᐙ⌕ᩩ}(1)ᐙᑖᩩ}£§png,ᑣ஻uqᐙᑖᩩ}.(2)w⌕ᩩ}£qnp,ᑣpuqw⌕ᩩ}.(3)ᐙ⌕ᩩ}£pnq,o4np,ᑣ஻uqᐙ⌕ᩩ}.Ñ£᝞ÒᵬuÔḄᐙᑖᩩ}ᑣÔuᵬḄw⌕ᩩ}1ÕÖ×ᯠ.16.:ᦪḄᓫÚឋ(1)ÜXiAx?Þß(x,-x)[/(x)-/(x)]>0=àᓃ3^>0o/(x)ᙠáಘnuã:ᦪ;212(__X2)"(xJ_/(x,)]<0=/ভ8/প<0=/(x)ᙠänuå:ᦪ.YB஽(2)Ü:ᦪy=/(x)ᙠè,ᑁéê᝞Ò/'(x)>0,ᑣ/(x)ëã:ᦪ1᝞Ò/'(x)<0,ᑣ/(x)ëå:ᦪ.17.᝞Ò:ᦪ/*)íg(x)îuå:ᦪᑣᙠᐳïðñᑁí:ᦪ/(x)+g(x)òuå:ᦪ1᝞Ò:ᦪy=/(“)í“=g(x)ᙠᐸõöḄïðñnîuå:ᦪ,ᑣ÷ᔠ:ᦪy=/[g(x)]uã:ᦪ.18.᜻Ꮤ:ᦪḄúûᱯü᜻:ᦪḄúûᐵJõýᏔ:ᦪḄúûᐵyþõý;Õÿᩭ
᝞ᦪḄᐵ
ᦪ᜻ᦪ᝞ᦪḄᐵy
ᦪᏔᦪ.19.ᦪy=/(x)Ꮤᦪ
$%|/*+஺)=/(*஺)ᦪy=/(x+a)Ꮤᦪ
ᑣf(x+a)=f(-x+a).20.ᦪy=/(x)(xeR),f(x+a)=/(b-x)ឤᡂ6,ᑣᦪ/(x)Ḅᦪx=78ᦪy=/஺+஺)9:=f(b-x)Ḅᐵ;<:=@>.21./(?=/(x+a),ᑣᦪy=/(x)Ḅᐵ@0)/(x)=—/(x+a),ᑣᦪBC2aḄᕜBᦪ.22.E⚗GᦪP(x)=ax"+a_xn-'+…+4Ḅ᜻Ꮤឋnn}E⚗GᦪP(x)᜻ᦪ=P(x)ḄᏔL⚗(ᓽ᜻ᦪ⚗)ḄNᦪᐰCP.E⚗GᦪP(x)Ꮤᦪ=P(x)Ḅ᜻L⚗(ᓽᏔᦪ⚗)ḄNᦪᐰCP.23.ᦪy=f(x)ḄḄឋ(1)ᦪy=/(x)Ḅᐵ;

3=/(2஺1)=/(%).(2)ᦪy=/(x)Ḅᐵ;="-|(j+x>=!"*)ᑗḄhᦪ.k28.|}~Ḅᦪ(1)Vᦪ/(x)=ex,f(x+y)=f(x)+/(y),/(l)=c.(2)ᢣᦪᦪ/(x)=
f(x+y)=/(x)/(y),/(l)=a*0.বᦪᦪf(x)=log„x,/(xy)=/(x)+/(y),/(a)=l(a>0,aH1).ভᦪf(x)=xa,f(xy)=/(x)/(y),fপ=a.(5)ᦪ/(x)=cosx,ᦪg(x)=sinx,f(x-y)=/(x)/(y)+g(x)g(y),x->0x29.|ᦪḄᕜB(a>0)(1)/(x)=f(x+a),ᑣ/(x)ḄᕜBT=a(2)/(x)=/(x+a)=0,ᡈf(x+a)=—J—(/(x)H0),/(x)ᡈ/(x+a)=-(/(x)w0),/(x)ᡈ;+J/(x)-஻(x)=f«),(/()e[0,1])
ᑣf(x)ḄᕜBT=2a(x+x(3)/(x)=1---]—(/(x)H0),ᑣ/(x)ḄᕜBT=3af(x+a)(4)/(x,+/)=/(«)=1(/()/(x)஺L0<1¡/l<2a),ᑣ/(x)ḄᕜBT=4a21-/¢)/(£2)(5)/(x)+/(x+a)+/(x+জ)/(l+¥+/(£+ᵲ=f(x)f(x+a)f(x-\-2a)f(x+3d)f(x+4a),ᑣ/(x)ḄᕜBT=5a(6)/(x+஻)=f(x)-f(x+a),ᑣ/(x)ḄᕜBT=6a.30.ᑖᦪᢣᦪ¨%1(1)an-,—(a>0,m,neN”,஻>1).nlniyja

4-"1ফa"=ª(a>O,m,஻eN*,஻>1)•a1131.᪷GḄឋ(1)(®"=a.(2)¯஻C᜻ᦪ°
7=a8¯஻CᏔᦪ°
^a\^\a:a~.-a,a<032.ᨵᳮᢣᦪḄ³´ឋ(1)ar-as=ar+s(a>0,r,seQ).(2)()'=a”(a>0,r,se஺).(3)(ab\-a'hr(a>0,b>0,rsQ).¸¹a>QP*ᳮᦪ
ᑣ»⊤½¾Ḅ¿ᦪ._ÀᨵᳮᢣᦪᗩḄ³´ឋ
*ᳮᦪᢣᦪÂÃ〉ᵨ.33.ᢣᦪG9ᦪGḄgᓄGlog஻N=bQa'=N(a>0,aWl,N>0).34.ᦪḄᣚÊËG102NlogN-——--(a>0,a஺1,Ìு0,UH1,N>0).nlog,”aYlÎÏloghn=—log,b(a>0,a>1,U,஻>0,UW1,஻W1,N>0)."m35.ᦪḄÐᑣ³´Ñᑣa>0,aWLM>0,N>0,$(J(1)log.(MN)=log,M+log”N;Mফlog"7=log“M-log,,N;বlog“Mn=nlog„M(neR).36.Óᦪ/(%)=log,,,(ax2+bx+c)(a-0),ÔÓ=Õ4ἄ./(x)Ḅ×ØCR,ᑣ஺>0,A<0;/(x)ḄÚØCR,ᑣa>0,Û20.a=0ḄÜÝ,◤⌕ᓫàáâ.37.ᦪᣚÊrãGäᐸÎta>0">0,x>0,X/Lᑣᦪyuloga/bx)aপ¯a>b°
ᙠ(0ç)Y(L+8)_y=log“r3x)Cèᦪ.aa,(2)¯஺Ì>1
/?>00
a/1
$IIপlog,“+,,(஻+P)

515.,n-1a=<üᦪᑡýqJḄûn⚗ḄYC=஻[+஺2+…n40.ãÿᦪᑡḄ⚗a=a+(஻-l)d=dn+aஹ-d(n£N*)nxᐸn⚗஻(q+a“)”(w-l)s,=---!----=na,H-------an212d2./1=—M4~\Cl,--u.2241.&'ᦪᑡḄ⚗a=a^"'1=--q"(nEN*)nqᐸn⚗Ḅ(ᓃ*,,Sn=1l-qnaq-\vG,q=142.&'-ᦪᑡ{a}:a=qa+d,a=b(qW0)Ḅ⚗nn+]nib+(nKl)d,q=14=*(d-1)q஻T-d"J,q-i5qᐸn⚗nh+n(n-\)d,(q=1)sn=\,dA-qnd...l(b--——)ߟ——஻5(qHDl-qq-ll—q43.ᑖ89:(ᢥ<=:)>?@:x=Ḅ"")"ᐗ(=:஺ᐗ,஻?@D5>8ᑭ᳛b).(1+/7)-144.HIJKL&ᐔ(1)MXE(0,—),ᑣsinx1.45.^KJK_ᦪḄ`aᐵcqin0sin2+cos2^=1,tan^=-----,tan0-cotO=1.cos஺46.fgஹigḄjk(᜻mᏔLm5opqr▲)

6n(-1ᡝsina,.ᐔஹnᏔᦪusin(—+a)=0)Ḅᕜ8T=—CD_ᦪy=tan(3x+9),x஺᝕;r+Z(A,3,᜛Hᦪ5AW0,3>0)Ḅᕜ8T=X2co51.fgᳮab—=27?.sinAsinBsinC52.igᳮa2=b2+c2-2bccosA;b?=c?+a2-2cacosB;c2=/+/-2ahcosC.53.☢¢ᳮ(1)S=—ah=—bh=—ch(h>%ஹᑖ£⊤¥aஹbஹc¦§Ḅ¨).h222(2)S=—ahsinC=—feesinA=—easinB.222

7”3y(«¬®¯°2.54.JK±ᑁKᳮᙠAABC³5ᨵA+B+C=஻u>C=µ(A+8)C7TA4-B___¶5C\—=-------------2c=2µ2(A+B).22255.·ᓫḄJK¹Ḅºsinx=a=X=ᦇ¼+(1)5arcsina(ᦇwZ,la\x=2k7r±arccosa(keZ,la\x=ATF+arctana(keZ.ae/?).ᱯ£ᙢ5ᨵsina=sin/?=a=%"+(-1)A/3(kGZ).cosa=cos/30a=2kᐔ±Z).tana=tan/3=a=kjv+Z).56.ᨬ·ᓫḄJKL&ᐸºÀsinx>a(\a\<1)<=>xeQkᐔ+arcsina,2kᐔ+Áarcsina),keZ.sinxXGQkᐔKᐔKarcsina,2kᐔ+arcsina),kwZ.cosx>a(\a\<1)xeQkᐔ-arccosa,2kᐔ4-arccosa),kEZ.cosxXGQkᐔ+arccosa,2kᐔ+2¼arccostz),keZ.ᐔtanx>cR)=>rw(kᐔ+arctana,k7r+—),keZ.2TCtanxXG(kn~—,k7r+arctand).k€Z.57,ÂᦪvᔣÄḄ¢ḄÅÆÇÈᐭஹÊÂᦪ5ËÌ(1)ÍᔠÇÏᐭ(Êa)=(ᐭP)a;(2)ÐᑖÑÇÏ(ᐭ+Ê)a=ᐭa+Êa;(3)ÐᑖÑÇÏX(a+b)=Xa+Xb.58.ᔣÄḄᦪÄ¢ḄÅÆÇÏ(1)a•b=b•a(ÒᣚÇ)(2)(Aa)•b=A(a•b)=Aa•b=a•(Ab);(3)(a+b)•c=a•c+b•c.59.~☢ᔣÄ`aᳮ᝞Õ&ஹe2×^~☢ᑁḄØÙLᐳÛᔣÄ5ËÌÜÝÞ~☢ᑁḄßᔣÄ5ᨵàᨵÜÂᦪá௃ஹᐭãäaᐭ161+ᐭ202.LᐳÛḄᔣÄ&ஹe2åæ⊤¥Þ~☢ᑁᡠᨵᔣÄḄç`è.60.ᔣÄ~éḄᙶ᪗⊤¥Èa=(¯5%)51)=(ì25%)5bWO,ᑣab(b^O)«xy-xy=0.Ie22i53.avbḄᦪÄ¢(ᡈᑁ¢)a•b=|a||b|cos஺.61.a-bḄîïðñᦪÄ¢a•b&ÝaḄòólaivbᙠaḄᔣ§ḄᢗõIblcos0Ḅö¢.62.~☢ᔣÄḄᙶ᪗ÅÆপÈa=(¯5y55b=஺25%)5ᑣa+b=(~+ì25%+%)ফÈa=(ᧅ5%)5b=஺2,%)5ᑣa-b(ù஽5%û)(3)ÈA(%HM),BO2,%)5ᑣA6=஺6-஺4=(>2-ü5>2ý1)(4)Èa=(x,y),/lc/?,ᑣ4a=).

8মÈa=&,%),b=(Z,y),ᑣa•b=(x,x+y%)-2263.ᔣḄᜳcos0=/ߟ+!(4(X],%),b=(஽&%))♦64.'☢)*Ḅ+,-=1/1=J/./=7(x-x)2+(y-y)2(AO”6)&B(x,y)).212l2265.ᔣḄ'9:ᚖ<=a=a&M),b=(X2&y2)&?bHO&ᑣA||b<=>b=Xa<=>xy-xy=0.]22}a_Lb(aW0)=b=0<=>x(4-yjy=0.266.IJḄKLᑖ=[(%,/),P(x.y),P(x,y)PIJ஽QḄᑖ)&XPRᦪ&?m=2Ậ&ᑣ222_᳝+AX2W=1+1஺Y=Z+[\)H|+42]+]W-1+A0^=_+(1-஺`(f=—L).1+467.cdḄefᙶ᪗iABCck⚔)Ḅᙶ᪗ᑖmnAG௃&y௃)ஹB(xy)>Ch&y?),ᑣiABCḄefḄᙶ᪗P2,2x,+x+x%+%+%ஹG(--2—3&---).68.)Ḅ'vx=x+/zx=x-h---:—•—tV.=

9(1)஺,b€/?=>஺2+/22M(º?»º@=1)½¾“=”¿).(2)a,be/?+=>Áf2Â(º?»ºa=b½¾"=”¿).2(3)o'+/?3+c3>3abc(a>0,Z>>0,c>0).(4)ÄÅ·¸(a2+/?2)(c2+d2)>{ac+bd'y,a,b,c,d^R.(5)|a|-|&|<\a+b\<|a|+1&|.72.᩽ÈKᳮÊËx,yÌPÍᦪ&ᑣᨵ(1)ÏÐPKÈp,ᑣºx=y½Òx+yᨵᨬÔÈ2J^Õ(2)Òx+yPKÈs,ᑣºx=y½ÏÐᨵᨬᜧÈs2.4×ØÊËx,yeR,ᑣᨵ(x+y)?=(x-y)?+2Ú(1)ÏÐPKÈ&ᑣºlx-ylᨬᜧ½,lx+ylᨬᜧÕºlx—ylᨬÔ½,lx+ylᨬÔ.(2)Òlx+ylPKÈ&ᑣºlx-ylᨬᜧ½,1ᑮ1ᨬÔ;ºlx-ylᨬÔ½&Ixylᨬᜧ.73.ᐗÞ®·¸ax?+bx+c>0(ᡈ<0)(aH(),i=At—4ac>0),᝞áa:ax?+bx+câ¿&ᑣᐸäᙠ᪷æ᜜Õ᝞á஺:a/+bx+cç¿&ᑣᐸäᙠ᪷æ*.èéætâ¿᪷æ᜜&ç¿᪷æ*.᳝(X-%!)(x-X)<0(XjX<^>(X-Xj)(j-X)>O(X]0½&ᨵ\x\x2-aax2>a2<^>x>a^x<-a.75.ªᳮ·¸[/a)>oপ"(x)>Jg(x)=,g(x)>0.f(x)>g(x)/(x)>0,(2)J/(x)>g(x)o(g(x)20ᡈ{.,g(x)<0"(x)>[g(x)]28/W>0(3)J/(x)0.ja)<[g(x)r76.ᢣᦪ·¸:ᦪ·¸(1)ºa>l½&-*ò=/(x)>g(x);7(x)>0log,J(X)>log"g(x)=0./(x)>g(x)

10(2)º0asW=/(x)olog஺/(x)>log"g(x)=஺f(x)a='0ஹ3462c2ঝ41/=44+452=o3280.ᜳ<=(1)tana=12~-I.1+>(4:y=A|X+?"l]y^kx+b,kkW-1)222t2,A,B—A^B.0(2)tana=1—-I.44+5jB)(4:Ax+&y+G^0,l:Ax+By+C=0,44+“"())•22224"L஺("@"2Ḅᜳ—k,(l)tan6r=-----L.1+k?k[(4:)3=&/+஽"l:y=+D2WT)2A.—AQB,(2)tana-------—.A4+4B?(/]5Ax+8j"+G=0,/:Ax+By+C=0,44+8/2஺0)2222/|JJ,("/1ᑮ"2Ḅ

11(1)2z{|}:2z(),)Ḅ{|}*y-y0=Z(x-x0)(◀{|x=x°),ᐸL2Ḅ}ᦪ2zP(x,y)Ḅ{|}*A(x-/)+8(y—%)=0,ᐸA,8L2Ḅ}ᦪ.o00(2)ᐳz{|}`{|/154x+B1+G=0,/254\+82)'+஺2=0ḄzḄ{|}*(4+4)"+6)+஻4+82>+஺2)=0(◀4)"ᐸᐭL2Ḅ}ᦪ.(3){|}{|y="+b᳛k2bH⊤{|}.{|4+333+஺=0Ḅ{|}L4+8)"+/1=0(2^0),L5.(4)ᚖ{{|}{|Ax+6)"+C=0(AW0,8#0)ᚖ{Ḅ{|}L1-4)"+/1=0,L5.83.zᑮ{|Ḅd=τᑘ/+'>h0(zp(x(),)"())H{|/.Ax+By+C=0).y/A2+B284.Ax+By+C>0ᡈ<0ᡠ⊤Ḅ☢¡{|/:Av+6y+C=0,ᑣAx+6)"+C>0ᡈ<0ᡠ⊤Ḅ☢¡LB/0,BAx+By+CJ¢H⊤{|/Ḅ3Ḅ¡BAx+8)"+C£¢H⊤{|/Ḅ¤Ḅ¡.¥¦§HJ¢ᙠ3H£¢ᙠ¤.6=0,AAx+By+CJ¢H⊤{|/Ḅ¨Ḅ¡A4+By+C£¢H⊤{|/Ḅ©Ḅ¡.¥¦§HJ¢ᙠ¨H£¢ᙠ©.85.(A/+B,y+C)(Ax++C)>00ᡠ⊤Ḅ☢¡122ª|C:(Ax+ὡ¬+&)(4%+521+஺2)=0(4/ᵨ®஺),ᑣ(A/+By+C,)(Ax+)H+஺2)>0ᡈ<°ᡠ⊤Ḅ☢¡Lt(Ax+By+C,)(AX+By+C)>0ᡠ⊤Ḅ☢¡3¤`°ᑖ}t222(A,.x+4)"+G)(4x+By+C)<0ᡠ⊤Ḅ☢¡3¤`°ᑖ.2286.ᙊḄ²³(1)ᙊḄ᪗µ(x-a)2+(y-/>)2=r2.(2)ᙊḄ¶x2+y2+Dx+Ey+F^0(D2+E2-4F>0).x=஻+rcos"(3)ᙊḄ5ᦪ".ly=b+rsm0(4)ᙊḄ{·9(x—xj(x-x2)+(y-y)(>—%)=஺(ᙊḄ{·Ḅ¸zL4(%,ᨴ)ஹ/?(x,y)).2287.ᙊ}(1)zA(X1,yJ,8(X2"%)Ḅᙊ}L(x-x)(x-x)+(y-y,)(y-y)+/l[(x-x)(y-y^-Cy-^Xx,-x)]=0122112=0—᳝)0—¼)+(ு%)(y*)+2(4*+8)"+஺)=0,ᐸax+by+c=0L{|A8ḄHXL2Ḅ}ᦪ.ফ{|/:Ax+By+C=0ᙊC:x2+y2+Dx+Ey+F=0ḄzḄᙊ}Lx2+y2+Dx+Ey+F+஻Ax+By+C)=0,ᐭL2Ḅ}ᦪ.(3)ᙊG:/+y2+O/+E1y+K=0ᙊQ52+y2+Dx+Ey+F=0ḄzḄᙊ}Lx222x~+y~+Dஹx+Ey++A(x2+y2+Dx+Ey+F)=0,A.L2Ḅ}ᦪ.x22288.zᙊḄ¿Àᐵ}zÂ(%,ᐜ)ᙊ஺஺)2+(ு6)2=r2Ḅ¿Àᐵ}ᨵijd=J(a-x)2+(/?-y)2,|J00d>rQzPᙠᙊ᜛Çd=rozPᙠᙊ3d

12Ax+8)"+C=0@ᙊ(X-a)2+(y-஺)2=ḄᐵJᨵG:d>ᔆ"QA<0;d=r=ᑗ==();J<=>A>0.|A஺+Bb+(?|ᐸ%d=y]A2+B-90.)ᙊᐵJḄᑨK)ᙊᙊᑖ01,0,ᑖn,r,\00\=d2212dு+G=᜛=4ᩩ=ᑗ3d=r+r<=>᜜ᑗQ3ᩩ=ᑗ3}2,-஽I<"<+G==2ᩩ=ᑗ3d=|-¢=ᑁᑗo1ᩩ=ᑗ30cdeh-4=ᑁ¦=§=ᑗ.91.ᙊḄᑗKL(1)¨©ᙊf+y2+Ox+Ey+/?=0.জ0¨©ᑗ«(x°,%)ᙠᙊ"ᑣᑗ¯ᨵᩩ"ᐸKLAD(x+x)E(y+y)0Qv+y())'+■~+—~-+F=0.²(x°,³)ᙊ᜜("/+K>+2´µF»+P=0⊤¹º)»ᑗ«Ḅᑗ«¼KL.ঝºᙊ᜜«ḄᑗKL½y-%=¾(%-%)"¿ᑭᵨᑗᩩÁÂk,Ã(Äᨵ)ᩩᑗ"ÅÆ&⌕Èᣵ+,ÊyËḄᑗ.ঞÍ᳛kḄᑗKL½y=H+b,¿ᑭᵨᑗᩩÁÂb,Äᨵ)ᩩᑗ.(2)¨©ᙊV+y?=/.জºᙊḄ᜜(ᐭ0"%))«ḄᑗKL஽/+'="3ঝÍ᳛CḄᙊḄᑗKLy^kx±rVl+F.22[—a92.ÒᙊÓ+4=1(஺>b>0)ḄÔᦪKLA"="a"ah[y=hsm02293.ÒᙊÓ+@=1(஺>b>0)ᯖ=ab22\PF\^e(x+—),|PF,|=-x).icc94.ÒᙊḄḄᑁ᜜×2222%6>0)Ḅᑁ×0—Y+Oa~ha222x2Axv>(2)«F(x,y)ᙠÒᙊ"l——=1(஻>/?>0)Ḅ᜜×<=>—y+00a"ba95.ÒᙊḄᑗKL22(1)Òᙊ5+4=1(஺>b>0)«P(x,y)ᜐḄᑗKLAÙ+Ù=1.00aba"b~22(2)ºÒᙊ+Ó=\(a>b>0)᜜«P(x,y°)ᡠÛ)ᩩᑗḄᑗ«¼KLAQab

13(3)Òᙊ=+@=l(a>/?>0)@Ax+8y+C=0ᑗḄᩩÁAA2a2+1=஺2.abX2y296,ÜÝߟ@=1(஺>0,6>0)Ḅᯖ=ab~22\PF'ITe(xH-----)I,|PQ|Te(------x)I.lcc97.ÜÝḄᑁ᜜×2222(1)«P(x,%)ᙠÜÝ■=1(஻>0,Z?>0)Ḅᑁ×u>U■²■>1♦0ahab2222ফ«Ó(%,ᐝ)ᙠÜÝ@áá1(஺>0/>0)Ḅ᜜×Qâ—ã<1.ab"ab"98.ÜÝḄKL@äåKLḄᐵJ2222(1)0ÜÝKLÓ==1=>äåKL5Ó2=0Qy=+-.Xab~ba22(2)0äåKLy=±2x=£±£=0nÜݽá_ç='.aabab2222(3)0ÜÝ@2=1ᨵ=ᐳäå"½2='(³>0,ᯖ«ᙠxË"³<0,ᯖ«ᙠra2b2a2h2yË).99.ÜÝḄᑗKL22(1)ÜÝáá=1(஺>0ு0)«P(x,%)ᜐḄᑗKLAÙé=1.0ahab~22(2)ºÜÝ0-@=l(a>0>0)᜜«P(x0,%)ᡠÛ)ᩩᑗḄᑗ«¼KLAaba2b222(3)ÜÝá@=1(4>0>0)@Ax+8y+C=0ᑗḄᩩÁAA?/—
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15F(x-------——-----,y-------——A----)=0.A2+B2A2+B2108.“²|”db¶Ḅª|Ax2+Bxy+Oy?+ox+@+F=0,ᵨx0xõV,ᵨᐜ)Hõ¬ᵨ.#)$%õ“Hᵨ⊈öØõx,ᵨ&±Zõyᓽê22Axx+B-X°yXy°+Cyy+D-+E-+F^0,ª|Ḅᑗ|HᑗzÖHzÖHÖzᙳLooúêU109.ûü{|{|ḄḄýὃ⌶(1)
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21বAmn;ভnA]=A]]8—A];(5)41c-I(6)1!+2-2!+3-3!+---+»/Z!=(H+1)!-1.153.^ᔠᦪ-.3ntA]_n(n-1)…(஻2N+1)_nI(nGN*,meN,uW஻).A]Ix2x---x/n154.^ᔠᦪḄEឋপer!ফC]+C]i=C]k:+CK=l.155.^ᔠឤ.Q,n_n-m+1"-1.(1)m(2)C]]--Cn-m(3)C”?_2L(jm~l•஻mn~(4)£c]=2";r=Oমc!+c!#W(6)CK+CK+CK+…+C!+…+C88=2".(7)C\+C!+CK+…=C]+GK+CK+….(8)C\+2C!+3C!+…+஻C]=n2'-'.qc;C+cmc]+…+c8o(10)6)2+©2+6)2+…+(cK)2=G”.156.᣸ᑡᦪ^ᔠᦪḄᐵJ157.ᓫᩩ᣸ᑡ¡¢ᔜᩩḄᜧ¤¥¦஻Eᐗ¨©ªNEᐗ¨Ḅ᣸ᑡ.«1¬“ᙠ®”“¯ᙠ®”জ±«ᱯ¬ᐗ²ᙠ±®ᨵA,K1´!ঝ±«ᱯ¬ᐗ¯ᙠ±®ᨵ«⊡·¸¹¬=A'-iAM'«Ḽ½®¾¬=A,'3+ALA;=«Ḽ½ᐗ¨¬´.«2¬¿ÀÁ«ᓽįĬজ+®¿ÀKk[k

22NEᜧᳫ஻E"ᳫ᣸ᡂ2ᑡ"ᳫ²ᑖáÎᨵâ´᣸vãA"ä஻>஻?+iæçè!ä"êN+iæᨵT=c;ᵨ´᣸v.4«4¬^àᐗ¨Ḅ᣸ᑡK^ᐗ¨ᨵmE2“…CMC=«u஻¬.=m\u«஻!¬"‘«3¬«ÿᙳᑖᨵ⚪Ḅ…+n”ᱥᑖ஻?ᱥᑖᑖᑮ"஻……#”$஻τ,஻…n'(ᦪ*+,-ᑣᐸᑖ012ᦪᐳᨵmN=C''-᠗„...C"'"-m\=—P'm-•pp1""J”6468ᐰᙳᑖᨵ⚪ḄP6P=%+n2+…+n“ᱥᑖ(ᱥᑖᑖᑮ?஻2,…%$@”2,…஻“'஻ᦪAᑖᨵaஹbஹcஹ…-ᑣᐸᑖ012ᦪᨵFGߟIP'.mla\b\c\..."!K!…@஻/M!c!...6568ᙳᑖP⚪ḄP6P=\+n2+…+%ᱥᑖRSTḄ஻4…"PUVḄ(ᚮ$஽஻.'(ᦪ*+,-ᑣᐸᑖ012ᦪᨵN=Zt—.6668ᐰᙳᑖP⚪ḄP6P=n1+&+…+%ᱥᑖRSTḄ஽@…஻“PUVḄ(ᚮ$஽@…஻“'஻ᦪAᑖᨵaஹbஹcஹ…-ᑣᐸᑖ012ᦪᨵ676▲`ᑖᨵ⚪Ḅp6஻=஽+%+—+஻,”ᱥᑖᵬஹdஹe……-஻?ᱥᑖ᝞gᢣ`ᵬ஽d஻2e஻3…jᑣPk஽஻2,…5-஻?ᦪlᔲᐰᡈ,ᐰᐸᑖ012ᦪឤᨵ159.“┯r⚪”sᐸtuvwᑭy┯z⚪:|஻}|~஻|}ᐰ┯rḄᔠᦪR/6஻=஻!$Z5+Z…+6Ztu஻ᐗ~"rᐸAᨵmᐗ┯rḄ,ᔠᦪR—+6-lpC^6n-p!+-+6-lFC6n-m!=஻!"G+G_+_…+6-iZ+…+6-iy"A=%A]A=IA=n

23160.,`1/+X2+…+x”=mḄḄᦪপ1R+஽+…+x“=஻(¡¢eN*)Ḅ£᦮ᦪᨵ£.ফ1§+஽+…+x“=஻(njnwN*)Ḅ8¨᦮ᦪᨵCn-'.(3)1R©?+…+ª=«(n,meN,)¬ᩩ¯2᝕(k£N*,2WiW஻-1)Ḅ8¨᦮ᦪᨵi1Z5-2)(«-1),(4)1±1+%+…²=³(n,mwN*)¬ᩩ஻-1)Ḅ£᦮ᦪᨵ-C1C'l+C2Cn-l_+(—1)ᔙ2c஻-2l.c-In-2m+n-^-2n-2m+n-2k-3n-2/w+l-(n-2)A161.¶⚗¸`ᳮ(a+b)"=C°a"+C'^-'b+C^an-2h2+•••+Cran-rbr—+CX;n¶⚗º»¸Ḅ¼⚗½¸r=C'an-rbr(r=0,L2---,஻).r+1n162.-¾¿ឋÁḄᭆ᳛163.ÄÅÁA,BᑖÆÇḄᭆ᳛ḄÈP(A+B)=P(A)+P(B).164.nÄÅÁᑖÆÇḄᭆ᳛ḄÈP(A+A+-+A)=P(A)+P(A)+…+P(An).12n12165.ÉÊÁA,BjÆÇḄᭆ᳛P(A•B)=P(A)•P(B).166.nÉÊÁjÆÇḄᭆ᳛P(Aj•A2•••••A)=P(Ap,P(A2).........P(A).nn167.nËÉÊÌÍÎÏAÐÁាÒÆÇkËḄᭆ᳛P,w)=C]P"P)f168.ÓᦣÕÖ(×ḄᑖØᑡḄÚឋÛ(1)>0(/=1,2,---);(2)6+6+…=1.169.ᦪÜÝÞE^=xP+xP+---+x„P+---li22n170.ᦪÜÝÞḄឋÛ(1)E(aJ+b)=aE4)+b.(2)ßJàB(஻,p),ᑣEj=஻p.(3)ßJáâãäᑖØ$Pe=A)=g(A,p)=qip,ᑣ=P171.1åᯠ=(§-ç)2-P,+(஽-ᦑ)2.p+…+(X“Zᦑ)2.p„+•••2172.᪗êåᡈ=7.173.1åḄឋÛ(1)஺(ᗔ+b)=/OJí(2)ßJà8(஻,p),ᑣ£>J=஻p(l-p).বßJáâãäᑖØ$PC=k)=g(Z,p)=qJp,ᑣ=P-174.1å~ÝÞḄᐵð

24”=ñ-6ò2.175.£᝱ᑖØôõöᦪ/6x=-^-e262,xe6-8,+8,¸AḄúᦪN,cr6cr>0lþᦪᑖ⊤
Ḅᙳᦪ᪗ᐔ6.176.᪗᝱ᑖᦪ1-—00,4-00).177.N3,஺?!"#$xḄᭆ᳛x—஻F(x)=জP(Xt)9Stuvwᦪᑡ{q/T}9lqlJf+0182.ᦪḄᜳឋ|ᳮ᝞ᦪf(x),g(x),h(x)ᙠX஺Ḅ▬V:

25(I)g(x).XQXfoUlimf(x)=a.XT᳝)|ᳮᓫ᩽▲{X78Ḅᯠᡂ.183.
ᵨ᩽▲(1)lim—=0,lima"=0(Ial<1)]n->co஻7>8(2)limx=x,lim—=—0x—N)lx0XXQ184.
⌕Ḅ᩽▲0ஹ].sinx(1)lim-----=1]•2°X(2)Iim|1+-1=e(e=2.718281845)IMX)185.ᦪ᩽▲Ḅᑣ¡ᑣ¢lim/(x)=a,limg(x)=b,(j(1)lim[f(x)±g(x)]-a±b8ফlim[/(x)g(x)]=a¤](3)lim'!?=—(hH0).f°g(1)b186.ᦪᑡ᩽▲Ḅᑣ¡ᑣ¢lima"=a¥imb"!(j஻7>8஻7>8(l)lim(a„+b„)^a±b]AT8(2)\im(a-b„)^a-b8nn—>°oবlim—=—(/?^0)ngbbn(4)lim(c•)=limclima=஺•a(c§ᦪ).஻7>8'஻T8஻7n187./(x)ᙠ/ᜐḄ©ᦪ(ᡈªᓄ᳛ᡈ¬ᖪ)®(¯)=MG=limᒹ=lim"஽+——9).•,²At—O\yAr—O\y188.´µ¶:/ஹ..Ass(t+Ar)-s(t)v=s(t)=hm—=hm---------———.A/TO&ATO¨/189.´µ·¶,Avv(t+^t)-v(t)a=v(t)=hm——=hm-------------------.A/f0ZA/-»0Z190.f(x)ᙠ(a¤)Ḅ©ᦪr:(ஹ:dydfAy/(x+Ar)-/(x)f(x)=y=——=—=lim——=lim----------------------.dxdxAx¸70Ax191.ᦪy=/(x)ᙠ/ᜐḄ©ᦪḄ¹º»

26ᦪy=/(x)ᙠxᜐḄ©ᦪ§¼1y=/(x)ᙠP(x0,/(%))ᜐḄᑗ1Ḅ¾᳛/'(X஺)!F¿Ḅᑗ1230§=/'(x())(x-Xo).192.ÀÁᦪḄ©ᦪ(1)C'=0(CÂᦪ).(2)(x,,)'=nx"~

27eQ).(3)(sinx/=cosx.(4)(cosx),=-sinx.(5)(lnx/=-](log6zv)z=-log/.xx(6)(ex)z=ex;(ax)z=axIna.193.©ᦪḄ¡ᑣ(1)(M±V)=U±V.(2)(wv)=wv+wv./cஹ/஻ஹ'wv-UV/Äஹ<3)(-)=-2—WwO)VV194.ÅᔠᦪḄÇ©¡ᑣÈᦪ஻=᜛஺)ᙠxᜐᨵ©ᦪ஻Ë=᜛(x),ᦪy=/(஻)ᙠᐝᜐḄ¿Uᜐᨵ©ᦪÍ=/(w),ᑣÅᔠᦪy=/(Îᐝ))ᙠxᜐᨵ©ᦪ!Sு]=”•஻]!ᡈᑏÑ/](஺(%))=/(஻)஺(X).195,ᵨḄVÒÓÔÕ(Ö|x|ᐙ$µ)(1)Jl+l=1+—X]V1+X=1+—X;2n(2)(14-x)a-l+ax(aeR)]——~1-x]14-xবex«1+x5(4)lO+x)~x8n(5)sinx=x(xÂØ)](6)tanx=x(xÂØ)](7)arctanx~x(xÂØ)196.ᑨÚ/(%)§᩽ᜧ($)#Ḅ2¡Öᦪ/(x)ᙠ/ᜐÛܵ!(1)᝞ᙠ▬VḄÝ/'(x)>0,¸/'(x)<0,ᑣ/(%)§᩽ᜧ#](2)᝞ᙠÂ▬VḄÝ/'(x)<0,¸/'(x)>0,ᑣ/(/)§᩽$#.197.ÅᦪḄFva+bi=c+di<^>a=c,b=d.(.a,b,c,deR)198.Åᦪz=a+biḄÞ(ᡈß#)\z\=\a+hi\=>Ja2*4567+b2.199.ÅᦪḄᑣ¡ᑣ(1)(a+bi)+(c+cli)~(a+c)+(b+d)i;(2)(a+bi)—(c+di)=(a—c)+(Z?-J)z;(3)(a+bi)(c+di)=(ac-bd)+Scஹ+ad)i;/Ä/,•ஹ/,-xac+bdbe-ad....(4)(a+bz)+(c+d!)=d5-----r-+-------i(c+diWO).c~+d2c+d~200.ÅᦪḄà¡Ḅá

28â¹Zi'G,de஺!ᨵãᣚá:z-z=z-z.l22låᔠáË(æ஽2>23=Z]-(z-Z).23ᑖçáËq.Q2+Z3)".è+4.q-201.Å☢êḄëḄìíÔÕd=1&-z1=V(x27+(%—îï(&=᳝+yj,Z=X+yi).2222202.ᔣòḄᚖ0ôõÅᦪ4=஺+ö!t=஺+¤¿ḄᔣòᑖÚ§÷!ø!IùOZ^IOZ^qÔú2ḄûüÂõ=ýÂþÿᦪQlq+Z2|2=lz,I2+\z1224qIZ]-z212T&F+1Z21Qτ%+Z21=14-IQac+bd=0<=>z=Aiz(ᦪ).12203.ᦪᐗḄᦪᐗax2+bx+c^0,—b+yjb2-4acজA=£>2—4ac>0,(Ix,22aঝ=/-4ac=0,ᑣ᳝=X2=—-;2aঞ=஻-4ac<0,#ᙠᦪ%Rᑁ'ᨵᦪ᪷*ᙠ+ᦪ%Cᑁᨵ,-ᨵ./ᐳ1+ᦪ᪷-b±yj-(b2-4ac)ix=(&2-4ac<0).2a23ᦢ5ᑠᱥᡈ9:1.<=%ᔠ?@⌕ᢕC%ᔠḄD⊤ᐗF?GᐗFḄ“I@ឋஹLMឋஹNOឋ”஺

29᝞S%ᔠA={xly=Igx},B={yly=lgx},C={x,yly=Igx},AஹBஹC©ᐗ«ᔜ⊤W®2.TU%ᔠḄVஹWஹ⊡YZ[?\⌕]^%ᔠ_`ab%0Ḅᱯdef஺¯°±²+ᦪLᦻ´µ¶·ᔠ¸⚪஺1·0"ᑗ·ᔠḄ»·M0"ᑗ¼1·ᔠḄ½»·஺᝞S%ᔠA={xlx?-2x-3=0},B={xlax=l}BuA,ᑣᦪaḄg᪀ᡂḄ%ᔠjk:m,o,I}3.¯Y¾ᑡឋÁ=j1%ᔠ{aoa,……?ajḄᡠᨵq%Ḅ/ᦪr2%22A=B=AnB=A,AUB=B*3Â᥅᪷;=CjAUB=CAsnCBs,CjAnBs=CAsUjCBsuuuuuu4.ÅÆᵨ⊡·ɶʸ⚪ᔩ®᣸◀6ஹ2Î6¢᝞Stuᐵ=XḄ\wxy*<0Ḅ%M,3eM,5{M,|ᦪax-aḄÏÐÒ஺a•3-5jV3eM,•32''<0=>ae1,|sUj9,25sa•5—5V5gM,A—........>052-a5.}~ᑨᎷḄ⚪?ᨵ“ᡈ"s,“,”jᐭsa“”jos.pAq?,-pஹqᙳpvq?,-pஹqᨵ/op?,-pᎷ6.Ó⚪ḄBÔ%ÕÖᐸØᐵÚ0®Ø⌮ᔲᐵÚḄÓ⚪0NÝÓ⚪஺¢ÞÓ⚪⌮ᔲÓ⚪½ஹᎷ⌮Ó⚪ᔲÓ⚪½Ꮇ஺7.T᧜#Ḅᭆâã¶ᔩ®᧜#fA-B,0ᔲ¯YᑮA©ᐗ«Ḅ*YឋLB©KTåᐗ«Ḅ"ឋMæç

30<᪀ᡂ᧜(<?<?ᐕB3ᨵᐗFN஺)8.ᦪḄ¡⌕Fr¢£᝞¤¥¦./ᦪrᔲ¨©(@ª«ஹ<¬ᑣஹg«)9.|ᦪḄ@ª«ᨵ®¯°±²³Sᦪy=µ&Ḅ@ª«rlg(x-3)(kS(0,2)U(2,3)U(3,4))10.᝞¤|+ᔠᦪḄ@ª«᝞Sᦪf(x)Ḅ@ª«r[a,b],b>-a>0,ᑣᦪF(x)=f(x)+f(-x)Ḅ@ª«r»(kS[a,-a])11.|/ᦪḄ᪆xᡈ/ᦪḄÆᦪ[?ÇÈᦪḄ@ª«Éᔩ᝞Sf(jx+1)=e*+x,|f(x).Í1=Î11,ᑣt20x=t*-1.•.f(t)=e'2_|+t2-l.•.f(x)=ex2-1+x2-l(x>0)12.ÆᦪÔᙠḄᩩÖr¢£(<ᦪ)|ÆᦪḄ×ØÙÚÉᔩ(জÆxঝLᣚxஹyঞÇÈ@ª«)1+x(x>0)᝞S|ᦪf(x)=,ுḄÆᦪ-x2(x<0)x-1(x>1)(kSfT(X)=\)—V—x(x<0)13.ÆᦪḄឋãᨵ®জLÆᦪḄäᐵ=åæy=x<ç*ঝèÔÉᩭᦪḄᓫëឋஹ᜻ᦪឋ*ঞíy=f(x)Ḅ@ª«A,g«C,aeA,beC,ᑣf(a)=bQL(b)=af'[f(a)]=f'(b)=a,f[f-l(b)]=f(a)=b14.᝞¤ᵨ@ªóÈᦪḄᓫëឋ(ôgஹõöஹᑨ÷ø)

31᝞èᑨ.éᔠêᦪḄᓫëឋ®(y=f(u),u=(p(x),WJy=f[ᦪ?@ABCDᦪḄᓫឋ)FGHI.5f'(x)W0ᕖM᝞NOa>0,ᦪf(x)=x-axᙠ[1,+8)=Rᓫ9ᦪᑣaḄᨬᜧUR()A.OB.1C.2D.3(Vf(x)=3x?-a=3x+4x-g-0ᑣx<-JZᡈx?ᵫNOf(x)ᙠ[1,+8)=9ᦪᑣ=£1,ᓽaW3.aḄᨬᜧÐ3)16.êᦪf(x)ᐹᨵ᜻ᏔឋḄó⌕(¼ᐙᑖ)ᩩö0®(f(x)÷øᐵ+ÞTù)

325f(-X)=-f(x)6ᡂ`Qf(x)᜻ᦪ=ᦪcdᐵ@f)ᓽf(a+x)=f(a-x),f(b+x)=f(b-x)

33ᑣf(x)Rᕜᦪ2|a-b|x:ᕜ᝞18.ᵨḄcdᣚᔩMf(x)yf(-x)Ḅcdᐵ@_Igf(x)y-f(x)Ḅcdᐵ@)HIgf(x)y-f(-X)Ḅcdᐵ@f0):ᓫ£ு¥=f(X+a)¦¢a(a>0):ᓫ£y=f(x-a)=¢b(b>0):ᓫ£)y=f(x+a)+bm¢b(b>0):ᓫ£y=f(x+a)-bkl᝞m“¨ᢚ”ᣚf(x)—>|f(x)|f(x)——>f(lxl)᝞f(x)=log(x+1)2ª«y="og2(x+1)|y=log2|x+Ḅcd

3419.ÅúûüýþᵨêᦪḄµÿឋᔩ?(1)x®ᦪy=kx+b(krO)(2)F±ᦪ¥=&*#0)µ¶¥=6+¸x(1<¹0)R{º0'3b)xx-aḄ஺(3)|®ᦪy=ax2+bx+c(aH0)=ax+=+½¾cd¿ᱥ\2a/4a⚔<ᙶ᪗ÅÆ”Ç)Igjx=x/ÈÉÊᔣa>0,ᔣ=ᦪYmin=4ac-b4ac-b2a<0,ᔣmymax4aᵨজ“”(ᦪஹஹ)Ḅᐵ——ax2+bx+c=0,Ï>()'u᪷XÑஹX?|®ᦪy=ax?+bx+cḄcdyxjḄu:Ò<HR|®B?ax?+bx+c>0(<0)ÓḄÔ

35A>0b,᝞|®ÊÕax?+bx+c=0Ḅu᪷Öᜧ@ku><----->k2af(k)>0x᪷ᜧ@k,x᪷×@kq(4)ᢣᦪᦪy=a*(a>0,aW1)(5)Iᦪᦪy=logZ,x(a>0,aH1)ᵫ;<=ឋ!(6)“IÙᦪ”yᑭᵨ@ḄᓫBឋ#ᨬ)Cᑭᵨᙳ)#ᨬ)Ḅ%EFGHI20.JᙠLMNO'PQR┯TᔩIᢣᦪÚÛa°=l(a0),a-p=—(a/0)ap

36m____man-Va^"(a>0),an==Üு0)VamIᦪÚÛlogM•N=logM+logN(M>0,N>0)aaalog^-=logM-logN,logVM=-logMaaaaaNnIᦪឤ?alos-x=xIᦪᣚÞplogb=10gcb=>logbn=—logbamalogaamc21.᝞VWX<ᦪ1⚪I(Y)Zஹ[᪀]ᣚZ)᝞(1)xeR,f(x)ßàf(x+y)=f(x)+f(y),áâf(x)᜻ᦪ஺(ᐜVx=y=0=f(0)=0äVy=-x,..........)(2)xeR,f(x)ßàf(xy)=f(x)+f(y),áâf(x)RᏔᦪ஺(ᐜVx=y=-t=>f[(-t)(-t)]=f(t•t).\f(-t)+f(-t)=f(t)+f(t)Af(-t)=f(t)……)(3)áâᓫឋ:f(x)=f[(x-x,)+x]=........22222._`#ᦪ)aḄPᵨZᔩI(ᦪZ(bZ)-cᦪZ-ᣚᐗZ-ᙳ)+ᳮZ-ᑨEZ-ᑭᵨᦪᓫBឋZ-fᦪZ஺)᝞#gᑡᦪḄᨬ)(1)y=2x—3+J13-4x2A/X-4(2)y=VT7Tx>3,y=^-(3)x-3(4)y=x+4+j9-x?(åx=3cos஺,0e[0,ᐔ])9(5)y=4x+—,xG(0,1]x23.J=ijkḄ+lᔩImᑏQᙊpqra,strRḄjuvᡧx☢zvᔩI(/=|a|R,Sᡧ=$R=g|a|R2)

3724.çèéᦪḄrsᓫ£ᙊ{èéᦪḄrssina=MP,cosa=OM,tana=ATjr᝞5---<6<0,ijsin஺,8*᝞ᦪy=Jl-⊈ḄrstóUt஺71(*/1-V2cos---X)=1-72sinx>02,B/.sinx<—:᝞c:22kit——WxW2kit+—(kGZ),0WyWJl+25.÷øùú«ûüஹýüஹûᑗᦪḄcdᔩMÿᵫ
ᑏᓫஹஹᔩ

38y|sinx|<1,|cosx|<1koj,keZjrjry=sinxḄ$2kᐔ'()2kᐔ+kGZ,-2kn+~,2kK+y(keZ)
Ḅkᐔ)0,,x=k7t+^keZ,y=cosxḄ$52kᐔ)2kn+n6(keZ)-52kᐔ+ᐔ,2kᐔ+2ᐔ6(keZ)
Ḅ5kTt+g,oj,x=kᐔkwZ,y=tanxḄ$(kᐔ':,kn+keZ26.>?@Aᦪy=Asin®x+p,Ḅ
FឋH⌕JK஺5ᡈy=Acos®x+p,6

39(1)NOIAI,ᕜRT=)Sf(x(J=±A,ᑣx=x0஺Sf(Xo)=O,ᑣ(X஺)0),Z[\஺(2)]^
_`3x+(pbc0,5)ᐔ)e)2ᐔ)fxgy,b(x,y)^
஺(3)᪷i
fj᪆l஺(fAஹ(0ஹmn)Xi0x2X3V^4X53X6,+p=0᝞
ᑡjᩩrsfCOஹ(Pnv>ᑗ@Aᦪy=Atan3x+p,,T=—Icol27.ᙠ{|Aᦪ}f'~|⌕~☢——ᐜf'~{|Aᦪn)ᑨ|Ḅ஺᝞_cosfx+—,xeᐔ)—,fxn஺715ᐔ6328.ᙠjᨵ>ஹ?AᦪḄ⚪)(ᑮ)ᵨAᦪḄᨵឋᔩ᝞_Aᦪy=sinx+sinlxlḄn(x20)y=2sinxe[-2,2],x<0)y=0,ye[-2,2])29.J{|Aᦪ
¡ᣚᔩ(£¤¡ᣚஹ¥¦¡ᣚ)£¤§l_(1)P(x,y)¨=(.k)ுp,(X))ª)))ᑣ)_x+h£¤¬

40—y(2)®f(x,y)=0¯ᔣ±a=(h,k)£¤²Ḅ³f(x-h,y-k)=O᝞_Aᦪy=2sin(2x-_)-lḄ
´µ¶᪵Ḅ¡ᣚ¨¸¹ᑮy=sinxḄ
(y=2sin(2x'%1'..J♦ᵦ¼½¾¿'>y=2sin¾x)'Á1£¤1~ᓫÃÄ£ÅI~ÆÇ2sin(x_§-1-------------------->y=2sinx-1—:'ÈÉ.T⁐'>y=2sinxËᙶ᪗¦ÎᑮÏᩭḄ1Ñ------------------------2---->y=sinx)30.JÒ|{|AᦪᐵÔFÕÖ§lᔩ᝞_1=sin2a+cos?a=sec?a-tan?a=tana•cota=cosa•seca=tan—4IT=sin—=cosO=.......1Ḅ×ᣚ஺2“k•ÙÚa”ᓄaḄ{|Aᦪ“᜻¡)Ꮤâ¡)ãäå▲”)2“᜻”ஹ“Ꮤ”ᢣká᜻ஹᏔᦪ஺᝞_cosg+tan|('+sin(217t)=sina4-tanaç᝞_Aᦪy:ᑣyḄncosa+cotaA.>nᡈènB.ènC.éènD.>n.sinaSin(X+cosasin?a(cosa+1)(y=>0,Va^O)cosacos2a(sina+1)cosa+sina31.J|FஹêஹÑஹíî§lïᐸ⌮ᔣòᵨᔩᳮj§l[ḄὶÔ_sin(a±p)=sinacosP±cosasinP——>sin2a=2sinacosa

41`aó)cos2a=cos2a-sin2acos(a±p)=cosacosp+sinasinptan(a±p)^tana±tanP=2cos2a-1=1-2sin2a=>1+tana•tan021+cos2aV-cosa=---------.2tana2tan2a=---------1-tan-a21-cos2asina=2asina+bcosa=7a2+b2sin(a+(p),tan(p=—asina4-cosa=72sin^a+—sina+V3cosa=2sinla+—it3.òᵨ÷ø§l{|Aᦪlᓄù஺(ᓄù⌕f_⚗ᦪᨬüஹAᦪýþᨬü)ᑖ
ᦪ,஺)ᐹpra(1)Ḅᣚ᝞B=(a+F)—a,#$a---I--P22(2)%Ḅᣚᓄ'ᡈᓄᑗ(3)*ᦪḄᣚᓣஹ-ᗩ/0(4)1Ḅᣚ23ᦪ10456ᵨ8ᦪ69஺᝞:;=1,tan(a-p)=-1-,tan(0-2a)Ḅ஺sinacosa_cosa(ᵫ:;C:/.tana=-2sin2a2sina22Ltan(P-a)=—2_1tan(-2a)=tan[(.a)-a]=ᓃᔩ-a)"a=33W,LWJl+tan(p-a)-tana"2.13.232.XஹY'ZᳮḄᔜ]⊤_10`abCᔩc᝞defgஹhᓄijk1?}2+M_ᑖ2Y'Zᳮa2=b2+c2-2bccosA=cosA=------------2bc(oᵨ:;pg3ᜳrgs:;g஺)[a=2RsinAX'Zᳮ3^ߟ=—^-=—^=2Rob=2RsinBsinAsinBsinCc=2RsinC

42S=da•bsinCAA2***A+B+C—71,.*.A+B=TI—C,A+BC:sin(A+B)=sinC,sin-------=cos—22A+B᝞AABC
2sin2-------+cos2C=l2x1yCs(2)^a2=b2+—,cos2A-cos2BḄ஺2((1)ᵫ:;0C1-COS(A+B)+2COS2C-l=1LA+B=ᐔ-C,2cos2C+cosC-1=01cosC=LᡈcosC=-1({)2TFL00=>ac>be(1)a>b,c<0=>acb,c>d=>a+c>b+d(3)a>b>0,c>d>0=>ac>bd

43(4)a>b>0=>-<-,a->-abab(5)a>b>O=>an>bn,Va>Vb(6)lxl0)=—aaqx<-aᡈx>a᝞Lla+blD.-+->2baᫀC35.ᑭᵨᙳ0aa2+b2>2ab(a,bGR+)sa+b>27absab<(ᨬ`ᔲ45ᑮ“a,bwR+”“ᡂ”Ḅᩩ¡¢(ab)ᡈ£(a+b)ᐸ
¥3¦Zc(3Xஹ§Zஹ¨)45᝞a+b2ab(>Vab>------a,beR+)"Va+b'©ª©a=bᡂ஺a2+b2+c2>ab4-be4-ca(a,bGR)©ª©a=b=c«஺a>b>0,m>0,n>0,¬1Jbb+m_a+na—<-------<1<-------<—aa+mb+nb4᝞x>0,2-3x—-Ḅᨬᜧ¦x-------------(®y=2-(3x+±)¯2-2°=2-46©ª©3x=±,LX>0,.•.x=3±y=2-4V3)maxL᝞x+2y=l,ᑣ2²+4,Ḅᨬ³¦(V2X+22y>272x+2y=2A/F,.•.ᨬ³¦2&)

4436.0µ¶Ḅ·¸¹º»¼ᔩcx½¾ஹᑖ᪆ஹÁᔠஹᦪÃÄÅyÆ45ÇᓫÉÊḄoᵨ஺᝞µ¶1+§+1-1—+§<22232n211(I+F22+F32+Hn52-<1H--1--x--2--1--2--x--3---F.......+-(-n----l--);n—,,1111=1+11---------F.......+223n-1n=2--<2)n37.jᑖ00Ìுaa0yḄ3ÎÏÐÑÒ?xÓ⚗ÕᑖᑖÖᑖ×0ᑖjxḄØᦪ¦1,ÙÚjCÛ஺y38.ᵨ“ÙÚ”jÜ*0——“᜻ÙᏔᑗ”ßᨬᜧ᪷Ḅáâãä᝞x+lx-l2x-2y3<039.jᨵåᦪḄ0⌕45æçåᦪḄè᝞æᦪᡈᢣᦪḄêᑖa>1ᡈ0s41.øᵨ0laHbl

45=l(x-a)(x+a-l)l(vlx-al<1)=lx-allx+a—llf(x)ឤᡂu>a>f(x)Ḅᨬᜧ2a>f(x)>ᡂ=a>f(x)Ḅᨬ:2?᝞8@ABᑗDᦪx,F|x-3|+|x+2]>aឤᡂ#IJḄK2M)(Nu=|x-3|+|x+2],O⊤QᦪRSᑮUVW-2X3YZ[XUmin=3—(-2)=5,A5>a,ᓽa<5ᡈὅ8|x-3|+|x+2|>|(x-3)-(x+2)|=5,#a<5)43.`ᦪᑡḄVbcឋeVb8a“+i-a”=d(d0$ᦪ)#a=a+(n-l)dnl`h⚗8x,A,yᡂ`ᦪkU=2A=x+yஹ,(a,+a„)nn(n-l)nn⚗XS_=LB^-=na,+5——n212ឋe8sat)`ᦪᑡ(1)Fm+n=p+q,Ixy+a0=ap+aq{(2)ᦪᑡsa.J#sa},skan+b}0`ᦪᑡ{2nS,S-S,S-S……0`ᦪᑡ{n2nn3n2n(3)Fᦪᡂ`ᦪᑡ#-N0a-d,a,a+d{(4)Fb”)`ᦪᑡ௃0nn⚗X#ᑣ=$L{Am-I

465aj0`ᦪᑡQSLaZ+bna,b0$ᦪ#)ᐵAnḄ$ᦪ⚗00ḄᦪS”Ḅᨬ2-ᦪ$=2?+yḄᨬ2{ᡈὅa0hḄஹᑖ111⚗#ᓽ8a>0ᓽ>0,d<0,L-Snᑮᨬᜧ2Ḅn2஺ᒹ+◍0a-O,d>0,ᵫH'°-S”ᑮᨬ:2Ḅ112஺ᒹ+120᝞8`ᦪᑡaj,S=18,a+a_I+a_=3,S=Lᑣn=nnnn23ᵫa0+a_1+a.2=3n3a.|=3,•¡e=1n¢S3=®{.3=3a?=i,;.a2._a|+ajn_a2+a“j•!!_§+ln_Qn222n=2744.¤ᦪᑡḄVbcឋeVb8=qq0$ᦪ#q஺0,a”=aIqnTan¤h⚗8x^Gஹyᡂ¤ᦪᑡ=>G?=xy,ᡈ6=±47¥q=1nn⚗X8S=-ajl-q11⌕§¨©nIi-qឋe8a)¤ᦪᑡnপFm+n=p+q,ᑣam*an=apaq2S,S-S,S-S……0¤ᦪᑡ2nn3n2n45.ᵫS”a0«§¨*+,n=l#a,=Sni2#a=S-S_Pnnn146.¬៉ᦪᑡ¯⚗°Ḅ$ᵨ±ᔩ,

47᝞(1)#(ᖪ)Z᝞8a#³´+µa?+.......+^ran=2n+5<1>8n=l#—a,=2x1+5,.*.a,=142n>2:—aτH——a?+.......H-------a.=2n-1+5<2>2222n-1-<2>8Ba=22nn•,•a=2n+,n14(n=l)a„=<,2n+l(n>2)ᦪᑡat³´Sn+S0+1=¶ᵪ#a|=4,a”s(§¨ᑮaz=SM—S”¸ᐭ82=4n¢º=4,#S)¤ᦪᑡ#S=4nnnnN2#a=S-S_,=……=3-4n-'nnn(2)Z?᝞8ᦪᑡah#a1=3,5==#a”nann+1a2.a……a_12……n-1.a_13nbna,aa_23na,n2n13¢a1=3,.*.a=—nn(3)⌴vᵫa1,-a^i=f(n),a,=a,a»ᵨ¼½±0nN2#a-a,=f(2)'2%B¿Tব#UÂý,8♦♦♦♦♦a-a_,=f(n)nna-a,=f(2)+f(3)+……+f(n)n.•.an=ao+~2)+2)+……+f(n)

48ᦪᑡsa஺},aே=1,an=3"T+a.Æ(n22),a”(a=|(3n-l))n(4)⌴va=ca_,+d(c>d0$ᦪ,c#0,c"l,dwO)nn-.ᓄ0¤ᦪᑡ#Nan+x=c(az+x)=>a=ca_,+(c-l)xnnË(c-l)x=d,x=—c-1••Ja+±Æ)✌⚗0%+—J,c0°¤Ḅ¤ᦪᑡn1C-1Jc-1.d_("a"+c-l-la#1c••i+c-lÐidc-1ÑÒÓÆᦪᑡsaj³´0=9,3a+a=4,n+1n+D(5)᎔ᦪ±?᝞8a,=1,an+1="‘a"a”+2ᵫØÙ8B!B=3+211-——=-+Ban+i2A2an...j____L1=^n+l2rஹ—=L°`0à0`ᦪᑡ#a12•'ÞB1=1l+/(n-l)•-14(n+i)aLn._2"a"-n+1

4947.¬៉ᦪᑡnn⚗XḄ$ᵨ±ᔩ,?᝞8$1%á⚗±8âᦪᑡᔜ⚗äᡂU⚗ᡈå⚗[X#æ[çᡂ@è0ÃéᦪḄ⚗஺JL1᝞8sa})°`0dḄ`ᦪᑡ#nk=l^k^k+15f11if11I/1\8ᵫ--------=--------r=----------(d0)a*aa(a+d)d1aa{kk+lkkkk+lUJ____Lஹdlaேai)n+ÑÒÓÆ1+J-1-+1X:H----------1+21+2+31+2+3++nî.....=....:=Z----—>n+1$2%┯ñÃò±8Fsat0`ᦪᑡ#sb}0¤ᦪᑡ,ᦪᑡsab_}`¤ᦪᑡnn⚗nnX#-ᵫSn-qS”S”#ᐸhq0s>}Ḅ°¤஺᝞8S=l+2x+3x2+4x3+...+nx"T<1>nx,S=x+2x2+3x3+4x4+...+(n-l)xn-1+nx11<2>n<1>-<2>8(1-x)S=1+x+x2+....+xn-1-nxnn(IT)nnxXH1#S——/-----n(1-x)21-xrin(n+l)x=1:S=1+2+3+...+n=-------nn2(3)᎔ôý±8âᦪᑡḄᔜ⚗õô᎔ᑏ#÷cøᩭõôḄᦪᑡý஺S=a.4-a+...+a,+a|,,nn12?n1nnýSn=a+a_,+...+a+ajnn22s=(a,+a)+(a+a.,)+……+(a,+a)...lin2nn

50ÑÒÓÆx2ᑣf(l)+f(2)+f(g)+f(3)++f(4)+=ØÙf(x)=---1+x22XX1(ᵫf(x)+f-----H=1------=11+x2]---------lx21+X2+.•.ø=~1)+f(2)+fg)[+f(3)+fg)+f(4)+f(J=-+l+l+l=3-)2248.⍝ஹ⚪ᔩ᦮(ᓫᑭ)ᑭᐭ"Pᐗ%ᑭ᳛'r,n+%ᑭ'S=p(l+r)+p(l+2r)+....+p(l+nr)=pn+"3"r....45⚪nᢥ7ᑭ%᝞⚪——ᢥ:Ḅ<(ᢥ:=ᑖ4?@<AḄBCD)(ᔣFGB)pᐗ%Hᵨᑖ4?

51nτA=n(n-l)(n-2).......(n-m+1)=-----(mn+C!an-'b+Can-2b2+-+C^an-rb'+-+C^bn13⚗ËÌKḄÍ⚗ÎKÏ+i=CaiM(r=0,1……n)C'3⚗KÐᦪ(ÑÅÒÓ⚗ḄÐᦪ)ឋ

52(1)ÆÔឋC=C7(r=O,1,2,……,n)(2)ÐᦪC+C+…+C=2஺C+C+C+…=C+C+C+…=2"T(3)ᨬÛn'Ꮤᦪ°%n+1'᜻ᦪ%¡=⚗Ḅ3⚗KÐᦪᨬᜧ½'P(£+1)⚗%3⚗KÐᦪ'Cn'᜻ᦪ°%(n+1)'Ꮤᦪ%¡Ä⚗Ḅ3⚗K11n-1n+1ÐᦪᨬᜧᓽP3⚗àP*+i⚗%ᐸ3⚗KÐᦪ'cF=cF22᝞ᙠ3⚗K(x-l)”ḄËÌK%ÐᦪᨬçḄ⚗Ðᦪ'(ᵨᦪè⊤ê)(Vn=ll10...ᐳᨵ12⚗%¡Ä⚗ÐᦪḄíÆÛᨬᜧ%½'Pî=6ᡈP7⚗2ᵫC|X“T(-l)r,.•.r=5ᓽP6⚗Ðᦪ'öÛ'ᨬç-3=-C=-426÷᝞(1-2x)2004=a++ax2+...+ax2004(xeR),ᑣ022004(a+a,)+(a+a)+(a+a)+...+(a+a)=(ᵨᦪèûü)0020302004(ýx=0,þa=10ýx=l,þa+a+...+a=1022(K)4=2003a+(a0+a[+....+a,j=2003x1+1=2004)000452.Ḅᐵ៉ᔩ(1)!ᯠQ,P(Q)=1,%&'஺)P(<1))=0(2)ᒹ,ᐵ-AuB,“A23!45B23”7Bᒹ,A஺(3)Ḅ8(9)-"A;B<=ᨵ?@23”ABA;B

53Ḅ8C9D஺4
ḄECFD-“A;BGH23”ABA;BḄE஺$5%IJCI%KLD-“A;B%'GH23”ABAஹBIJ஺A•B=஺$6%NCI⌮D-“A%23”ABA23ḄNC⌮D)AA!JA=Q,ADA=(|)$7%PN-A23;ᔲB23Ḅᭆ᳛TᨵUV)W᪵ḄY@ABKIPN஺A;BPN)A;Z)A;B,[;ᔲ\KIPN஺53.]?ᭆ᳛Ḅ^_-ᑖaᡠ^Ḅc-$1%d&'Ḅᭆ᳛Cefᵨ᣸ᑡjᔠḄl_)ᓽAᒹ,Ḅd&'no=m?pqrḄd&'noḄsᦪ?%(2)vAஹBIJ)ᑣP(A+B)=P(A)+P(B)(3)vAஹBKIPN)ᑣP(AB)=P(A)•P(B)(4)P(A)=l-P(A)$5%᝞oᙠ?pqrzA23Ḅᭆ᳛cp,{|ᙠnpPN}~qrzAា23

54kpḄᭆ᳛-Pn(k)=C-pk(l-p)᝞-10zᨵ4p)6)^ᑡḄᭆ᳛஺$1%z2cp$2%z5ាᨵ2pI2C-஺21J$3%zᨵᙢ3<=ᨵ2p᪆-ᨵᙢ3pCp1D).n=103<=ᨵ2p“ាᨵ2p”8“cp”..m=C426'+43426+4344..P=-----Z------¢—33103125$4%z¥p5ាᨵ2p஺᪆-,??Cᨵ¦§D*.n=A,,m=CAA-op_C^A|_10LET?ᑖa$1%ஹ$2%cjᔠ°⚪)$3%c&}~᣸ᑡ°⚪)$4%c²}~᣸ᑡ°⚪஺54.᪵l_³⌕ᨵ-µᓫ᪵C·_ஹᦪ⊤_Deeᵨ¹sº@ᦪ»=H)¼Ḅᱯ¾csºz⌲@À᪵)eᵨ¹sº@ᦪ»ÁH)¼Ḅ³⌕ᱯ¾cᙳ⊝ᡂvÅÆᑖ)ÆᑖÇ?@ᑖÈ᪵)³⌕ᱯ¾cᑖÈᢥÊË᪵)³⌕ᵨ¹sºzᨵÌÍÎÏ)¼ÐḄᐳGᱯ¾c@@ºÒᑮḄᭆ᳛Kd)ºÔÕ᪵ḄÖ×ឋ8Ùdឋ஺55.sºᑖÚḄÛÜᵨ᪵ÝḄ⚣᳛ßsºḄᭆ᳛)ᵨ᪵ÝḄàáCÙᙳâD8lÎãÛÜsºḄàá8lÎ஺⌕៉᪵Ý⚣᳛älåḄß_-C1Dæᦪç᩽ÎXM-XJ$2%éêjë8jᦪ$3%éêᑖì$4%ᑡ⚣᳛ᑖÚ⊤$5%í⚣᳛älå஺ᐸz)⚣᳛=ïðlñḄ☢E=jëX⌕jë᪵ÝÙᙳâ-x=—Cx,+x,+...+xDnn'7

55᪵ÝlÎ-S2=^[(x-X)2+(x-X)2+……+(x-X)2)2n᝞-10÷᝕3;5÷ᵱ3z⌱6÷û3üýÊþ)᝞oᢥឋÿᑖ
᪵ᑣᡂḄᭆ᳛C4C2C656.ᔣḄᨵᐵᭆᔩ(1)ᔣ——ᨵᜧ!ᨵ"ᔣḄ஺(2)ᔣḄ'——ᨵᔣ()Ḅ*+l7l—>(3)ᓫ0ᔣla()l=l,ao=—lai—>(4)8ᔣ0,101=0*+<=(5)<=Ḅᔣ<=>—>—)OA-OB=BA(8)H☢ᔣklDᳮ(ᔣḄᑖnDᳮ)—>—>—>e,,ezqH☢ᑁḄstQᐳ(ᔣavH☢W^ᔣᑣ\ᙠ]^—>—>—>—>—>_ᦪwஹ%,bya=%ei+3e2,{ஹe?}~⊤^H☢ᑁᡠᨵᔣḄ^k஺

56(9)ᔣḄᙶ᪗⊤->—>i,jq^<ᚖḄᓫ0ᔣᑣᨵᨵ^_ᦪX,y,bya=xi4-yj,(x,y)ᔣaḄᙶ᪗ia=(x,y),ᓽᔣḄᙶ᪗⊤o—>—>a=(X|,yj,b=(x,y)22ia±b=(X|,%)±(%,2)=x±y)22->Xa=X(Xj,yj=(Xxj,XyJA(X1,yj,B(X,y)22ᑣAB=(X2-X|,2-%)IABI=-J(x-xj2+(y-yj2AஹBs¡L¢£¤¥2257.H☢ᔣḄᦪ¦—>—,—>—>—>—>(1)a•b=lal•Iblcos஺}~ᔣaVbḄᦪ¦(ᡈᑁ¦)஺஺ᔣªVtḄᜳ0e[0,ᐔ]ᦪ¦Ḅ±²X³ia•b=´laiVbᙠaḄ"ᔣµḄ¶·Iblcos஺Ḅ¸¦஺(2)ᦪ¦Ḅ¹ºfᑣজa•b=b•aঝ(a+b)c=a•c+b•c

57ঞa•b=(xjy,)•(x,y)=xx+yy22t2(2—>——>—>¾Xiᦪ¦Q¿ÀÁᔠÃ(a♦b)•c஺a•(b•c)->—>(3)Ä⌕ឋÇia=(X],yj,b=(x,y)22TT—>^জa_Lb=a,b=O«Xj•x+yey=0212—>—>—>—>—>—>—>—>—>—>ঝa஻b=a•5=E1É1ᡈ2•b=-lai•Ibl-,—>—>=a=2ib(bwO,ÊË^ÌD)Qxmfy[=072Tঞa=lal2=xª+yª,la•bl(3)ÑÒaஹbᙳᓫ0ᔣÜÝḄᜳ60஺Þßla+3bl=ÖᫀiV1358.()ḄDàᑖ¡R(X1,yj,P(x,y),ᑖ¡P(x,y),RஹP?q(/µs¡P¡ᙠ222/µQ@´RஹP,\ᙠ^_ᦪᐭbRP='PP2ᑣᐭ}~Pᑖᨵᔣ()2-PRᡠᡂḄà(Ê>0,Pᙠ()PRᑁÊ<0PᙠPR᜜)X]+kx2X1+x2x=x=1+Ê2,pPF2å¡Ú,ã+ä2V+2y=y=1+X2

58᝞iAABC,Açx,,y,è,Bçx,yè,Cçx,yè2233ᑣAABCÄéGḄᙶ᪗që+/+,yi+^+y-JX.íᑖîÔḄÄéஹᚖéஹ᜜éஹᑁéïᐸឋÇᔩ59.ñò±²åHMஹᚖᐵóôõḄö÷ᔩHMᚖḄôõø⌕ᑭᵨ(☢ᐵóḄûᓄi(஻(ý——þ(஻☢ý——þ☢஻☢ᑨு,☢☢-ឋ⚗-஻——1☢——☢஻☢☢Ḅᑨa஻b,bu☢a,aana஻☢aa☢Ḅឋa஻☢a,/=☢0,aDB=bna஻b"ᚖᳮ%⌮ᳮ':PA,a,AO,P0ᙠaᑁ/0au☢a,ᑣa±OA=>a±PO4a±PO=>a±AO☢ᚖ5:a_Lb,a_Lc,b,cua,bPlc=0=>a±aab.☢☢ᚖ5:

59☢a_L☢0,aDp=I,aua,a±/=>a±pa_La,b_LjHana஻b☢a_l_a,BJ_ana஻B60.qḄ+l#Z(i)☢ᡠᡂḄqe,o°=☢>a—/—BḄ☢>஺0°<0<180°

60(ᚖ+ᳮZAGaᡈABL6B,BO_LO,AO,ᑣAOL/,.\NAOBrᡠ#஺)qḄ#Zজ¢QᡈQᨵᐵḄq஺ঝ¤ᐸ¦ᔠ+l-¨ᢣQᡠ#Ḅq஺ঞªOᜧ¬(Wqqx-ᡈᵨ®+ᳮ)஺(1)᝞;-OAraḄ¯OBrᐸᙠaᑁ±²-OCraᑁ³O´µ4஺?@cosy=cos0,cosp6,☢ᡂ>ZAOC=y,ZBOC=p(2)᝞;-¶·¸ABCD—AiBiGDi¹.qBD௃=8,BD
C»☢BiBCQᡠᡂḄr30°஺জ#BDi¼☢ABCDᡠᡂḄqঝ#☢BDiADᡠᡂḄq4ঞ#☢qG—BDi-B|Ḅᜧ¬஺AB

61(জarcsin—4ঝ60"4ঞarcsin—)43(3)᝞;ABCDr½x-ZDAB=60°,PDJ_☢ABCD,¾PD=AD,#☢PABC☢PCDᡠᡂḄ┦☢qḄᜧ¬஺AE(.AB஻DC,Pr☢PABC☢PCDḄvᐳ´-PF஻AB,ᑣPFr☢PCDC☢PABḄÁ……)61.Ã&ᨵÄÅÆÇI᝞V#ÆÇI´C´-´C-´C☢-C-C☢-☢C☢&ÆÇ஺ÈÃ&ÆÇÉᓄrË´ḄÆÇ-᪀⌼qx-Wqx#ÍḄu(᝞ᚖ+ᳮZ-ᡈὅᵨzÉᓄ᝞¶xABCD—AWiGDi¹-ura,Ï(1)´Cᑮ☢ABiGḄÆÇr(2)´Bᑮ☢ACB
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62RtASOB,RtASOE,RtABOEffRtASBEEFᔜᒹIJKᐗMNSO᩽┵R=gch'(C——S☢ᕜUh',VW)V┵=gS☢YXW63.ᳫᨵJKឋN(1)ᳫ\]^☢ᙊ\Ḅ`ᚖ5a^☢r=>/R2-d2(2)ᳫ☢bcdḄefghijcdḄᜧᙊḄlmU஺,n⌕pᳫ\>!(3)᝞s஺,tu>Eg☢ᡂ>4a,hu>Eg☢☢ᡂ>஺(4)Svᳫ=4TTR2,3Vᳫ=-nR3(5)ᳫᑁwUxyḄz>gᳫḄ5{஺O|☢yḄ᜜wᳫ~{Rᑁᑗᳫ~{r,Rr=31.᝞O|☢yḄUᙳ,O|⚔dᙠᳫ☢bᑣnᳫḄ⊤☢Y,()A.3ᐔB.4ᐔC.36ᐔD.6ᐔᫀA64.ᑡᔩN(1)/5ḄV>ae[0,7i),k=tana=~~~—fa,Xi'x?]X-X1v2J2PI(XI,yj,P2(X2,2)g/bcd5/Ḅxᔣᔣ=(1k)(2)5xdVy-y=k(x-x)(kᙠ)00V^y=kx+b^e-+^=1abAx+By+C=0(AஹB;,)|Ax0+By+C|0(3)dP(x°,y°)ᑮ5/Ax+By+C=OḄefd=A/A2+B2

63k?.M4Lᑮ4Ḅᑮ>tan8=1kMk—k4/,Ḅᜳ>tan®=±"265.᝞¢ᑨ£c5ஹᚖ5NA.B=A'B[?A,CACJ'222k,=k=>l//\¤ᡂ¥'2[2A,A+B,B=0<=>Z,_LZ222k,,k=-1=>/,_L/2266.¦᪵ᑨ£5/ᙊCḄ¨©ᐵ«Nᙊ\ᑮ5ḄefᙊḄ~{¬஺5ᙊ®;¯°ᑭᵨᙊḄ“ᚖ{ᳮ67.¦᪵ᑨ£5ᙊ┵´Ḅ¨©Nὶ¥x¶nᐵax(ᡈy)Ḅᐗ=·xn¸>0=®4¸=()=ᑗ4¸<()=f68.ᑖ»ᙊ┵´Ḅ¼‘¾ᙊo|PFj+|PB|=2a,2a>2c=|F,F|2¿¼À´Á|PFj-|PF2||=2a,2a<2c=|F,F|2ÂᱥQ|PF|=|PK|¿=¼e=H=-|PK|a0laÀ´4e=l=Âᱥ22\+3=la>b>0

64a2=b2+c2(c2=a2+b2)222269.À´=5=1ᨵᯖdḄÀ´«,=5='Ì஺0'ab'ab"70.ᙠᙊ┵CὶÝ#WÞ-ßᐗàiᑮḄ-⌕âãᐸ⚗ᦪFᔲråIæçèéḄ▲ᑴ஺è#Á´-®u-¹´-¯᳛-./íᙠឋ1⚪îᙠæçèégïð஺éÎUpBl="1+k?'X[+X'2-4X,X22+-j^j[(y>+y)?-4Y1Y2271.ñᵨ+l#ᙊ┵ḄᯖstᔩI᝞

6522=-ᓃ=1a2b2IPFJ..(a2)y=e,|PF|=e[--j=ex-a2Xoo|PF||=ex+a0y2=2px(p>0)ótFôᱥḄᡠᨵᯖ´®¹ᨬöὅ÷ᯖ´®rtḄᙊCÓøᑗ஺72.ᨵᐵ¹´®1⚪úὃ⇋ᵨ“ý´Z᝞¾ᙊmx?+ny?=15y=l-x®aMஹNcdâdMNãd`ḄV᳛,åᑣæç,þem0ÿᫀ
n273.᝞“”⚪(1)C.F(x,y)=0ᐵM(a,b)ᡂA(x,y)CA'(X',y')AᐵMḄ஺,x+x',y+y',,~ஹz(ᵫa=-----:b=-~—=x=2a-x,y=2b-y)22ë⌕?@Aீ2a-x,2b-y)íᙠ´Cbᓽf(x)=yAA'l/(2)dAஹAᐵa5/zñQ4AAãdᙠ/b,ki=-1=AAãdᙶ᪗õö/xY—rcosA74.ᙊx?+y2=r2Ḅùᦪx,.û(஺,ùᦪ)y=rsinO

66Y2..2x=ᑖ¾ᙊ0+4=1Ḅùᦪx,U:(஺,ùᦪ)abIy=bsin075.þÿ
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