数值分析第五版_李庆扬__课后习题答案

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ZḄ[\ᓫZS^ᢣ`abJcZᨵᦔᦪef=1.1021,X!=0.031,x!=385.6,x*=56.430,x*=7x1.0.:x=1.1021JOZᨵᦔᦪe;x!=0.031JmZᨵᦔᦪe!E=385.6JMZᨵᦔᦪe!x!=56.430JOZᨵᦔᦪe!ᓃ=7x1.0.JmZᨵᦔᦪe஺4.ᑭᵨrs(2.3)FᑡᔜḄ▲(1)x+x!+x!,(2)x*x*x*,(3)x*/x*.ᐸvx!,x!,x!,x!ᙳ3⚪ᡠzḄᦪ஺I

1£{x|=!xlO4£{x!|=-xlO-32£{E|=!xl{|T£{X!|!X2£{x!|=!xl{|Tপ£{X!+X!+X!|=£{X|+£{X!|+£{X!|],1,13=-xlO-4+-xlO-**3+-xlO-3222=1.05x10-3{2|£{X!X!X!|=,{X!|+k!X!]£{X|+,{X!|=|1.1021x0.031|xlxl0-1+|0.031x385.6|xlxl0-4+|1.1021x385.6|xlxl0-3®0.215(3)f(x*/x*)¡£)+¡£)i,i,0.031x-xl0-3+56.430x-xlO-3m2256.430x56.430=10-55ᳫ⌕▲1,[RᐕḄ▲Jᳫ=&W3ᑣ4ᦪḄᩩ7ᦪ|
?'|R4ᐔR23.£y^^C£S{/?*|=3?{/?*|rp<..•{v*|=l2

2ᦑ[RᐕḄ▲£,(/?*)=gxlX0.336.¤=28,ᢥ⌴§rs¤=ᓃ_1-+©5(n=l,2,...)ᑮKoo஺ª«J¬B27.982(5Zᨵᦔᦪe)S^஺®ᨵᜧ?°±²1UU%m%—³ᔊ33ᓱᓃ=%-V7831o100¶·¸ᐭYSᨵ90=%-100X*ᓽXoo=%_J^ª«77^5=27.982,.%=1!-27.982£{ᐔ|=£{%+£{27.982=!xIM.•/Ḅ▲3*1
3஺007.º»X2-56X+1=0Ḅ¼\᪷,a¾ᐹᨵ4Zᨵᦔᦪe{V783=27.982|஺:X2-56X+1=0,ᦑº»Ḅ᪷À42=28±Á^5ᦑX[=28+ÃÄ=28+27.982=55.982••᳝ᐹᨵ5Zᨵᦔᦪe=28-V783=——«------5------1«0.01786328+V78328+27.98255.982Æᐹᨵ5ZᨵᦔᦪeeN+118.ÇNᐙᑖᜧSÊ᪵f—9JN1+X23

3M+i1J~——Jdx=arctan(N+1)—arctanNva=arctan(N+1),S=arctanN஺ᑣtana=N+1,tan0=N.r-^dxJN1+X2=a-/3=arctan(tan(a-᜛))tana-tan£=arctan------------1+tanatanpN+l-N=arctan-----------1+(N+1)N1=arctan----------Ò+N+l9.ÔºÕḄÖ×ᜧØÙ100cm,ÀÊ᪵ÛÜÝᐸ☢VWLk•ß2?ÔºÕḄ☢4ᦪA{x|=f/.e(A*)=24*£(x*).Çx*=100Sª£(A*)K1,ᑣ£(X*)WX1(T22ᦑÛvÖ×▲VWL0.005cmSÜÝᐸ☢VWL1c/10.s=!gãSᎷågJæçḄS%tḄÛᨵ±0.1éḄSêëÇtìíSḄïìíS%ᓾñ஺•••S=ggf2/>0.£{S*|=gt2£«*|ÇìíSs*Ḅïìí£{5*|-òr{||s*|_gt2£{f*|2"*)t4

4Çf*ìíS£{ã|óᢝVõSᑣS*Ḅñ஺11.öᑡ÷>“ùúû⌴§ᐵý=10y._1-1
n=l,2,...,ªy0=þ஺1.41{ÿᨵᦔᦪᑮᨵᜧᔩyo=0k1.411q••£%*=5x10-'•:!=10”"1M=10’0#1£|*=1஺£%*&•.•%=1஺'-1£)*=1°£%*£%*=10%%*.•£(%*)=10%(%*)=10'°xixl0-22ᑮX஺):xlO,஺12./=⊈-16,/⊈஺1.4,ᑭᵨ2ᑡ456#7ᑮḄ9:ᨬ<=#
3-203,——X-r-,99-70V2»
V2+16
3+2V23:>y=(x-l)6,?@=Ax=1.4,ᑣ£(x*)=gxl()T஺?CJ,yD,ᑣ(72+1)65

51£()'*)=——6x_______(/+1)7=M—yy*£(X*)(X+1)7=2.53y*£(x*)?C(3-2&)3yDᑣ£(y*)=|-3X2X(3-2X*)2|S(X*)=V*£(/)=30yZ(x*)?C#JyDᑣ(3+2V2)3£(>'*)-——3x-------—■£(%*)”(3+2x>''=6x------1y)?*S(X*)(3+2x)7=1.0345ᡭ(!*)C##_7ᑮḄ9:ᨬ<஺(3+2`313./(x)=ln(x-V7cF),e/(30)ḄD஺?fghᵨ6iᦪ⊤kelᦪᨵᜧ?ᦋᵨn#4op5஺ln(x-G^i)=-ln(x+V7cI)elᦪᨵᜧ/(x)=ln(x->/x2-l)/(30)=ln(30-^99)>“=V^,y=/(30)wx*=29.9833*1.,.£(஻)=—X1Oᦑ6

61£(}#ᡠ(=ᯅ)஺3x10-3?ᦋᵨ4op5ln(x-A/X2-1)--ln(x+yJx2-I)w|J/(3O)=-ln(30+£)=1#c£(“‘)30+஻=——----£(»)59.9833=8x10஻cD1.x=L-1,2/(x)=0,-3,4,e/(x)ḄcD⚗5஺஺=1,1]=-1,X?~2,/(%)=0,/(%1)=-3,/(X)=4;2=(#=)஺#)==(X+i)(x_2)(%-%))(%-%)2002Z,(x)=#ᓃ)ஹ=l(x-l)(x-2)(X,-x)(x,-x)602/5©=(x?)(x-a)=(%_i)(x+1)0■(x-x)(x-xJ32Q2ᑣcAᨽD⚗5)2L2(X)=Z"(X)ᦇ=0——3/°(!)+4,2(X)14=_/(x_l)(x_2)+—(x—l)(x+1)2.f(x)=lnxḄᦪD⊤7

7X0.40.50.60.70.8Inx-0.916291-0.693147-0.510826-0.356675-0.223144ᵨ¢ឋD¤cDIn0.54Ḅ¥¦D஺ᵫ⊤¨X஺-0.4,X]=0.5,=0.6,©ª=0.7,-0.8;/(x)=-0.916291,/(%,)=-0.6931470/(x)=-0.510826,/(x)=-0.35667523/*4)=—0.223144?«ᵨ¢ឋDln0.54ᓽ/(0.54),ᑣ0.5<0.54<0.6/1(x)-—~¯=-10(x-0.6)ᓰ#஽/()=^Z^_-io(x-O.5)9x=³(X)=f(x,)Z(x)+y(x)Z(x)122=6.93147(x-0.6)-5.10826(x-0.5)”0.54)=-0.6202186«-0.620219?«ᵨcDln0.54,%#µ#஽=50(x-0.5)(%#0.6)0%#᳝஺#஽/,(x)=(1஺)(1_஽)=-100(%-0.4)(x-0.6)(X]-X)(X,-X)O23)=(x-XoXxf)=50(x_04)Q_0.5)(x-x)(x-x))2o24(%)=/(x0)/o(%)+/(XK(x)+/(Z/2(x)=-50x0.91629l(x-0.5)(x-0.6)+69.3147(x-0.4)(x-0.6)-0.510826x50(x-0.4)(x-0.5)J0.54=-0.61531984®-0.6153203.ᐰcosx,T4xW90°Ḅiᦪ⊤¿À/?=1'=1/60஺,?iᦪ⊤ᐹᨵ5ᨵᦔᦪẆÄᵨ¢ឋDecosx¥¦DḄÅÆ஺ecosx¥¦DÇÈᑖ)ÊËᑖ#h☢xÍ¥¦Dᐹᨵ5ᨵᦔᦪᙠ_ḄÏÐ#ḄÑÒÓn#h☢ᑭᵨDeiᦪcosxḄ¥¦D«ᵨḄ¢ឋDDÔ⚗,)0,ÕÖᨵ#Ḅ஺×ÅÆḄØÙᔠȯÊh☢Ḅ×Û஺8

8(TW900,Ü/(x)=cosx7110800ÜÝ=x+ih,i=0,1,...,5400QrrᑣX5400=ὡ=90/¢ឋD⚗5)Xk~Xk+\Xk+\~XkDÔ⚗)^f(^)(x-x)(x-x)R(x)=|cosx—“x)|cki+l&•••ᙠßàiᦪ⊤⊤ᦪáᐹᨵ5ᨵᦔᦪâcosxe[0,l],ᦑᨵÑÒ஺£/*4=310#5<£(7*@))(ã"+åå)Xk~Xk+\4+1-Xk=£(f\x))7(x.-x+x-x)kA+lkh=£(/*(X«))ÅÆ)9

9R=7?j(x)4-7?(x)2=Ó(-cosj)(x—z)(x—x«+|)+£(r(xj)4gx(x-xj6+|-x)+£(r(x*))4(ஹ(Óê)2+£(/*(ë))=1.06X10-8+-X10-52=0.50106xW54.>)ìí⁚ïeð(1)£x*(x)å=0,1,…,஻)ÓJ=o(2)2஺ᔆ©)©0å0=0,1,•M■,«);7=0ðô(1)Ü/(x)=x*?D⁚ï)õ,_/=(),1,…,஻,ᑣiᦪ/(X)Ḅ஻D⚗5)ö0+1)বDÔ⚗)R“(x)=/(x)-4(x)=9~ø%(x)(n+1)!Xvk

10ᵫ⚪£x%(x)=X1J=0.•.=£஺(-ᑐ#$%i=0=(x-x)"=0)*஺5+/(x)eC2[a,b].53)=f(b)=0,0*1max|/(x)|<—a)1max|/"(x)|.a%ᑣ@ឋ;`ᦪ⊤%cᵨef;<0%Ḅgh<,⌕jklmnopq10-%rjᵨ`ᦪ⊤ḄsthvwBxy91c;<⁚>4”ᓰ|ᑣᑖ~ef;

11R>X)=5/"C)(x-c_1)(x-xj(x-J,.)+]|??2(x)|4'(X-x,T)(x-%)(x-%+1)max|/w(x)|+sth,ᓽ%"]=x-h,x=x+hjMteᑘ".5''We%cklmnopq10-6,ᑣ|/?U)|<10-62//?3<10-627.-./i<0.0065.7.c%=2",0A”9%91᪷ᔣnᑖ|nᑖḄ09஺%=2"%=(E-1)4K-ᔳ…=X(T)%.4+%1j=0\JJ-”=(27)==2"5%=(—/)4I=(E^)4(E-l)4y„=ERy“=y-2n=2"-28.᝞f(x)mfB⚗,V(x)=f(x+/0-“X)%*/(x)Ḅk▤nᑖ12

12”(x)(0“4/n)¡4fB⚗,¢."+£=0(/¤᦮ᦪ)஺91`ᦪ/(x)ḄTaylor¦f(h)=fM+fXx)h+^f\x)h2+---+^fm\x)hm+-^fm+'\Ohm+'x+2m\(m+1)!ᐸ஺e(x,x+/z)••/(x)fᦪmḄB⚗H)=0.•.Af(x)=/(x+/)-/(x)I=f(x)h+:/"(x)஻2+■■■+—fM(X)h'n2m\.•.y(x)᪷-1▤B⚗A2/(x)=A(Af(x))¨஻©)ª-2▤B⚗«:q¬⌴®%)A«/(x)ª-¯fB⚗A"(x)°ᦪ±/¤᦮ᦪ²,""V(x)=09.*A(£ড)=+gkM*Mfkgk)=fzgk+fkgk=fk+\8k+i~fkSk+t+fk8ki~fkSk+=g*+i(´+i-A)+£(g«+i-g஺=g“M+fQgk=f^g+gk+Mkk)*10.*X£µ=f“gn-¶0-Zgk+Mk=0A=0*1ᵫ⚪13

13⎃□&=0n-\=E(Mfkgk)-gk+M)k=0஻I஻1=EMfkg)-Egk+Mk=0k=0••,Mfkgk)=fk+igk+fkgk••¹(£&)k=0=(fgl-fg)+(¡2--gJ+…+(fngn-¾g-1)OO=fS-foSonn£fZk=f.gn—fogo—Egk+dfkk=Ok=0)*஺11.*2A2ᑐ=ÀÁH%J=0஻1஻1*2Â=£(%]-Hᓃ)j=0J=0=(M-%)+(Ay->',)+•••+();-Ay“_])2="%)*஺12.cf(x)^a+ax+---+a^xn'1+ax"WnÉoÊ᪷᳝,஽,…%±,Qxnn"xk[0,0

14rfn^U)=U-X)(X-X)---(X-X„)+(X-X)(X-X)---(X-X„)2313H-------b(x-x)(x-x)---(x-x_)12n|•••©(Xj)=(Xj-X,)(X_Z)…(Xj-XjT)(j_Xj+1)…(Xj_)7Ùg(x)=x",«Xkg[X],X2

'X,=Z^7^M0M)஻xkᑣg[x”…,x“]=X)ÝWXk1Þ"ᐭ=-g[x“஽%…,x,J;=1fUy)a."xk[0,0

15%o(x.-%())í--(x-XjT)(Xj—Xj+I)•••(Xj—x„)y=yy___________/(x%)+gW)____________=î(Xj—X஺)•(Xj-XjT)(Xj—Xj+ï)•••(Xj-X,)£______________5______________)—(ð•…(ð—XjT)(ðXj+i)…(Ôjᜩ)y-----------------------------------)+/ò(Xj—X஺)…(X)—Xj_I)(Xj-Xj+I)…(X/-X“)=/óxo%...,x,ï+góxo%,ஹx“ï)*஺14./஺)=/+/+3X+1,0ó2°,21-,27ï#ó2°,2ï,28ï஺91vf(x)=x7+x4+3x4-1CD=23=0,1,…,8ᑣõ%…%õö/■%ø,…ù=úú=015.*û>üfýþÿᱯ
⚗3஺)=4)(஽)2(%)2/4!,—)XGN%X*+J,
⚗ᩩ"%(x*)=/(a&"(®)=r®)
⚗+K(x)=f(x)-H(x)3ᵫ
ᩩ"-./?(%*)=R(x*+1)=016

16R'0)=/?'(%)=0R(x)-ᑏᡂ/?(%)=g(x)(x-x*>(x-%>ᐸ8g(x)ᐵ:XḄ<=>ᦪ&@AXBᡂUtঢ+JDḄEF=G&H>ᦪI=fপ-Kপ-g(X)«-X*)2(/-%)2᪷N⚗ឋP&ᨵ9(஽)=0,᜛(%)=09(x)=/(x)-H>X)-g(x)(x-x>(x-S+iAk=f(x)-H(x)-R(x)3=0(pXt)^f'(t)-H'^t)-g(x)[2(t-x)(t-xy+2(t-x^t-x)2]kk+ik+k.஺'(U)=0d-ᵫVW=ᳮ-.&Yᙠ[(\,X)]*(x,k),^”&)=0,”)=0ᓽ“aXbᙠK,4ᵨDᨵdEefgG஺᪷NVW=ᳮ&/hᙠ᜛'hḄiEgGjklᨵEgG,ᦑ9஻hᙠa4,oᵪbᑁklᨵrEefgG,stuv&”4
ᙠaU,4+ᑁklᨵEgG஺w+4€a/,/+b^᜛ভয=-4)(J_")())-4!g(x)=0{%ভh=0f(4)ভ17

17ᐸ8Js}:XR(x)=ᑖrWᱯ
&⁚G+\=0,1,…,஻)&+&ᓽx=x+kh,k=O,l,-",nᙠjx*,/஺Dkoᡝ4)বR(x)='J%(X-xk)2(X-X«+|)2••|R(X)|="/ভ᎔(Xf)2(x-%)2WD(x—4)2(4+[-x)2max|/(4)(x)|4!a

18/.²প=(3-2x)x2+(x-l)x2=-x3+2x2(x)="3(X)+&³_/)2(´_\)2ᐸ8&A+<=µᦪPফ=1.•P(X)=-X3+2x2+Ax2(x-iy.A=-4·¸P(x)=-x2(x-3)2417./(x)=l/(l+x2),ᙠ-54x45D¹஻=10,ᢥ»¼⁚Gᑖ½ឋ
>ᦪ4(x)&¾¿ᔜ⁚Gj8GᜐḄ4(x)Â/(x)&ÃľÅÆ஺/=-5,x=5l0ᑣ=1,x.=x+ih,i=0,1,---,10(0/(x)=7■¯1+x-ᙠjD&ᑖ½ឋ
>ᦪ+r”)1+U-X,)1+\+1ᔜ⁚Gj8GᜐḄ4(X)Â/(X)Ḅ+Éx=±4.5&/(x)=0.0471,4஺)=0.0486Éx=±3.5&/(x)=0.0755,(x)=0.0794Éx=±2.5&/(x)=0.1379/(x)=0.1500Éx=±1.5&f(x)=0.3077,4,(x)=0.3500Éx=±0.5&/(x)=0.8000,7,,(x)=0.750019

19ÅÆ1{•••/(x)=1+x2ra)=-2,x("Ë6x2—2(1+x2)324x-24?f'M(1+x2)4Ì(x)=0¤f\xKḄÍG+x=±1]Ï=012஻aÐ2b=(&b=-2.•.Ñ|/axb-/.axbK(18./axb=YᙠKᑗDᑖ½ឋ
>ᦪ/஻axb,ÃľÅÆ஺ᙠj3,ÕD&x=a,x=b,h=x=0,1,---,AZ-I,QniMh=maxh.0ᦪ/axbᙠjK&x,*JDᑖ½ឋ
>ᦪ+4axb=±Öভ+D»a%bM—\ᓝÙ+1-Xi¯Ú\,a᳝+1—Xb+Ü+aX-X,bÅÆ+20

20ᗸ|/a)-/e)|ß&à)|ᝯ•f(x)=x2.•.r(x)=2xj"(x)=2//.'.max|/(x)-/,,(x)|<—1aᦪ/(x)ᙠjDḄᑖWᱯ
>ᦪ+4(x)=(¬r2(1+2±è)/(\)\é+|\+|Ù+(±è)2஺+2±W±L)஻XQZ+I—xixi~xi+\+(2zi±L)2(f)ra)++(X%j(x-x)f\x)MMX,+ëXjì4=-^(x-x)2(h+2x-2x)i+liiY4+-^-(îὅ)2(4.-2x+2x,+i)hi4X.3+/_^(ᑍ⁽+1)~(è᳝)A3,X+—^-(x-x)(x-x)i/+1ÅÆ+\fM-l(x)\b=l|/(4&(^)|(X-X,.)2(X-X,.)2+1vjmaxbভ᎔(Â24&᜜τ1221

21Xv/(x)=x4(./(4)(x)=4!=24hJ|/(x)-/„(x)|

22
lS,
x=1.0000,sv=0.686804஻a/ü-ýb=-5.5200%4=6.fd-o&xÿ=_4.3157%+%d,=6/᧎1/஽_=326402h+h}2d6/%/,=_24300O+ᨴ

23-6.7593(0.30-x)3-4.8810(%-0.25)3+10.0169(0.30-x)+l0.9662(x-0.25)xe[0.25,0.30]-2.7117(0.39-X)3-1.9098(X-0.30)3+6.1075(0.39-x)+6.9544(%-0.30)xe[0.30,0.39]-2.8647(0.45-x)3-2.2422(x-0.39)3+10.4186(0.45-x)+l0.9662(x-0.39)xe[0.39,0.45]-1.6817(0.53-4-1.3623(x-0.45)3+8.3958(0.53-x)+9.1087(x-0.45)xe[0.45,0.53]ফS"(Xo)=O,S"(X4)=Od஺=2fR=0,4=-4.3157,=-3.2640*=-2.4300,஻=2/A=0%=4=0ᵫ!"▣BCḄ'()*92014'Mஹ'-4.3157ஹ322M=-3.2640255ஹ2.4300,3027+,'()!=-1.8809M=-0.8616,M=-1.0304,%=023E•.•./᪵ᩩ⊤3%*(Xj+1-x),(I/S(x)=Mj+“G6%6%MS2X:L7Mx-xi+(I—+(%-!ohjoh-:MPM%%4=ᐭ!24

24-6.2697(x—0.25)3+10(0.3-x)+1^,Q.25)09697xe[0.25,0.30]-3.4831(0.39—x)3—1.5956(x-O.3)3+6.1138(0.39—x)+6.9518(x-0.30)xe[0.30,0.391•.S(x)=,3-2.3933(0.45-x)3-2.8622(x-0.39)3+10.4186(0.45-x)+ll.l903(%-0.39)xe[0.39,0.45]-2.1467(0.53-4+8.3987(0.53-x)+9.1(x-0.45)xe[0.45,0.53]21.N/(x)eC2[a,,s1)O./᪵ᩩPᦪRSAপ஺/f[s"(x)Udx=f[.f(x)-S"(x)Udx+2fS"(x)[/"(x)-S"(x)UdxফN/(V)=S(xJ(i=0WX,஻)%YW*Z[⁚]^஺=C0

25v□a)A-0஻ᐸY4(x)=IkJ|஻=1}rn4(x)=(1-x)1(x)=X••.4(£x)=/(0/(x)+)(lM(x)(1).71ᐔ=(1-x)sin(—xO)+xsin—|ᑐ=3},(X)=()(l-X)3ᱏ(x)=x(l-x)2=3x(l-x)2বP(x)=x2(l-x)=3X2(1-X)2J,6(X)==1■-B(f,x)=Yf(-)P(x)3kt=o஻=0+3X(1-X)2sin—+3AA2(1-x)sin—+J;3sin—632=-1x(l-x)2+-^^x2(l-x)+x35-3>/33373-6-----------X+-----------222«1.5X-0.402X2-0.098X32.|f(x)=x}+Rv(£x)=xRSAN/(x)=x,ᑣB“(f,x)=£f&Pk(x)k=0஻26

26ஹt/cSx"l—x)"-*k)᜛k…(஻-k+1)/(17k=0Sk\x"l—x)ik=l(D!nn-1=zy(17)"nK=1"஺7x,kk~-\l(i-xyk=\\k-V=Mx+(l-x)r'=X3.RSPᦪl,x,…,x"iឋᐵRS:N4+ax+ax2H---1-ax"=0,VxeAx2nᑖ¢£4¤=஺1,2,¥n%¦§ᙠ0,1n©ªᩗp(x).1Ḅᑁ®,!ஹ11%ஹn+l%01]\aJ0Jn+12/2+1>•••'()Ḅ¯ᦪ"▣*°±oᱯ"▣¥³´µ¶᜻¸,••¹ᨵº,a=0oPᦪ1,X,…,X"iឋᐵ஺4o¼½¾ᑡPᦪ/(x)ᐵÀC0,lḄ|,|Lg||/||A2(l)/(x)=(x-l)3,xe[0,l]1ফ஻x)=x----2ব/(x)=£"(l-x)",mgn*´᦮ᦪ,ভ“È)=(È+1)5,:(l)^f(x)=(x-l)3,xe[0,l],ᑣ27

27r(x)=3(x-l)2>0/(x)=(x-1)3ᙠ(0,1)ᑁᓫÊ⌴ÌIIÎ=ᶚV(x)|=max{|/(0)|,|/(l)|)=max{0,1}=1ML=s|/(x)|=max{|/(0)|,|/(l)|}=max{0,1}=1||/||=(f(i-x)W211i=U(1-47]270V7=ফN/(È)=-,€[0,1],ᑣIK=s|/u)|=1ll/l=l\fM\dx=2px--)Jx-41Ø=(஺«)G=[f(x-f2dxp~~6(3)Nf(x)=xm(l-x)n,mgn*´᦮ᦪ|xe[0,l]},/(x)2028

28f'(x)=mxn,-'(1-x)“+xwn(l-x)"-1(-1)m|xw(O,Û-)}:(x)>0n+m./(x)ᙠ(0,/)ᑁᓫÊ⌴Ü஻+Ý|}/(X)<0Sᓝm/(x)ᙠ(^ߟ,1)ᑁᓫÊ⌴Ü஺n+m/77xe(——l)r(x)<0n+mHL=sl/(x)l==max]|/(0)|,/(—^-)>n+mmmnl(m+Øß”w=a(%)á=k(Ln=P(sin2/)m(l-sin2r)Vsin2rᐔ=Psin2wtcos2ntcost2sintdtn\m\(஻+m+1)!IÎ=[”"(-ä஺n1=[^sin4,,,/cos4,,^(sin2r)rnI=fP2sin4m+,zcos4n+'^]2_](2஻)!(2஻?)!V[2(஻+zx)+l]!ভN/(x)=(x+l)3|[0,1]}f(x)>029

29f'(x)=10(x+l)9e-J+(x+1)1°=(X+1)9^X(9-X)>0/(x)ᙠ0,1ᑁᓫÊ⌴Ü஺IK=sl/u)|==max{|/(0)|,|/(l)|)_210ew=஺/মè=-(x+l),oe-x\_10(x+l)9g-Wxu10=5-----e14=4(È+1ä6-22j5஺RS|f-g|M#_|g|RSAll/ll=l(/-g)+gll+—gll+w6஺¥/(x),g(x)GCta,é,µêপ(£g)=fë(x)g'(xWx(2)(/,g)=£f\x)g\x)dx+f(a)g(a)ìíîOᔲ᪀ᡂᑁ®஺,Aপò/(x).C(C*óᦪ^C#0)ᑣ/'(x)=030

30a(7J)=f/'(x)/'(xWxôg|^õ|ö.0}(/,/)=()÷ø.♦.ùú᪀ᡂ஺û,ünḄᑁ®஺(2)N(7,g)=fr(x)g'(xWx+/(a)g(a),þU(gJ)=fg'(x)/'(xKr+g(a)/(a)=(/,g),VaeK(a/,g)=f[a/(x)ög'(xWx+ÿa)g(a)=a[fr(x)g'(xMx+/(a)g(஺)]=a(f,g)V/zeC^a,ᑗᑣ(7+g,஻)=^[f(x)+g(x)]'h'(x)dx+[f(a)g(a)]h(a)=(f,h)+(h,g)(f,f)=[[f/(x)]2dx+f2(a)>0(")=0,ᑣ£"'(ᑗ2=0,!/2")=0-.f'(x)^0,f(a)=0.1./(x)=0ᓽ&!'&/=0((/J)=0.ᦑ+,᪀ᡂCt”,12Ḅᑁ5஺7778(x)=78(2x-1),:e[0,l],<=>*(ẆAᙠ[0,1]2CᩗḄEO\lx-x2FG⚗IJKZ8(x),TN(:)W*(x)Z*(x)஺PNlNQxR=T,Q2x-lR,x€[0,l]ᑣ31

31/N(x)788(x)P(xRx-iT,S2x-\)Tax-l)-j==dxm7f=(2x—l),ᑣ!W=X,ᦑ2K(X)78N(XWX=[\06Hi\]^•.•ᑗ`abG⚗I>*஺)cᙠde2Cᩗp(x)=7gEF!VI-%20,஻஺j71k<—J1=lW()2ᐔ஻=m=0/IḄEFG⚗I஺.{<(%)}Aᙠ[0,1]2Cᩗp(x)>Jx-x2^p(x)=l”[-l,l].F*(x)=78(2x-1)=1”[0,1]v78(x)=x,xe[-l,l]7f(x)=I](2x-l)=2x-l,xe[0,l],/T(X)=2x2-l,xG[-1,1]2.F*(x)=4(2x_l)=2(2X-1)2-1=8x2-8x-l,xe[0,1],/w(x)=4x3—3x,xe[-1,1].•.T8(x)=78(2x-1)=4(21)3-3(2x-l)=32X3-48X2+18X-1,XG[0,1]8஺yᩗzᦪ᜛(x)=l-/,dej,

32ᓄ(x),஻=0,l,2,3.PNp(x)=l—r,ᑣde[-1,1]2ᑁ5(f,g)=J(x)g(x)p(xMx%(x)=l,ᑣe"x)=(x-4)%(x)—ᨴ%_|(x)ᐸa„={x(p(x),(p(x))/(/(x),q(x))nnP"=®(X),

333222ஹ஻2222ஹz%=(x-—x,x--)/(x--,x--)fI(x-gx)(x?-g)(l+x1)dxJ-1022A=(x_gr?/(xx)L(x?^)(x2-^)(1+x2)dx£x2(l+x2)Jx136525=1716~7015%33)=/g2_.2X570149஺<=ᵫᦟᩞI(2.14)¡Ḅ¢g£ᑗ`abG⚗I¤¥““(x)cA§0,1¨2Cᩗp(x)=Jl-x?ḄEFG⚗I஺=Nsin[(n+l)arccosA-]U"(x)ਮx=cos஺+¯£u,"(x)U”(x)VT//xPsin[(m+1)arccosx]sin[(/?+1)arccosx],=-----------------------------1------------------------dxf<)sin[(/n+l)6>sin[(H+l)6>],,=-------/------dB^Vl-COS2^=£sinf(/n+l)^sinf(n+l)0]cl0&m=஻([sin?[(´+1)᝞6=--------------du12_71-7&jw஻(34

34jsinK஻?+l)8sinK஻+l)ek/e=fsin[(/n+\)0d{—^—cos(«+1)^}M஻+l=¸---cos(n4-Y)Od{sin[(/n+1)^]}Mn+1tᐔTYl+1=\-----COS(H4-l)^C0S(/?2+V)OdOº஻+1=-r^±los[(m+lW/{—sin[(n+1)6]}C¼஻+1஻+1½m+1=-I-~-j-sin[(/?+l)]0d{cos[(m+1)6>])*(n+1)=f(""I)?sin[(n+l)^]sin[(m+V)0]dOJ)n+1=0U-(—-j-)]{sin[(஻+l)e]sin[(஻?+l)0]d0=0^஻ᦑ(----ᔆK1n+\JTsin[(n+l)^]sin[(w+\)0\d6=0¯=஺10஺=ᑗ`abG⚗I78(x)¿ÀÁᑖÃÄ(1-5(ᑘ-Æ)+஻278()=0=Nᑗ`abG⚗IH)=cos(/zarccosx),|x|<1ÇÈᨵ35

35-1T'\x)=-sin(ztarccosx)n(/)Vl-x2tnsin(narccosx)"(x)=---------3sin(narccosx)--------cos(«arccosx)(j2)5I.d.(l-x2)788(x)-x788(x)+n278Wg.nXsin(narccosx)-rrcos(஻arccosx)Vl-x2nx.ஹ2/ஹ-T-—sin(znarccosx)+Hcos(narccosX)=0¯=஺lloᎷË஻x)ᙠa,Ì2ÍÎK/(x)ḄÏÐᨬÒÓÔÕG⚗I?PN••/(X)ᙠÖde×ᔣ2ÍÎgÙᙠᓰ,W2e§஺ÌÛ/(x.)=rnin/(x),/(x)=max/(x),2ÜÝ=ᒃ(ß)+/(%)¨ᑣ᳝á஽Aã,12Ḅ2äåæ“E”ஹ“ç”Ḅèéê஺ᵫᑗ`abᳮìPe/(x)ḄÏÐᨬÒÓÔÕG⚗I஺12o⌱Üîᦪa,Ûmax*-ïᑮ᩽ò^óôäPAᔲö?0

36^N/(x)ḄᨬúÐ⚗ᦪ1,!3ÐG⚗I஺8•û3=ᨬ"()ü஺Ḅèéᨬò஺?"g]£"~4X3ÇÈᨵa=-413oK/(x)=sinxᙠ஺ý2ḄᨬÒÐÔÕG⚗IJþÿ
஺7T*:f(x)=sinx,xe[0,—]ff(x)=cosx""(x)=-sinx<0.b)—f(a)2n-----------——1b-a2cosx=—,7~712x=arccos—x0.88069271/(x)=0.771182_/(a)+/(&)_஽“l2b^aT~=0.10526+,-/(x)Ḅᨬ012345⚗7826(x)=0.10526+-x71ᓽ2TCsinx«0.10526+—ᐔ0037

37Lit——C1b-a*=e—lx=ln(e-1)2h(xj=e'2=e—12b-a2l+(e—D(-In(e-l)=——------(e-D2=Jln(e-1)+,-/(x)Ḅᨬ012345⚗78^U)=|+(e-l)[x-lln(e-l)]=(e-l)x+-^[e-(e-1)ln(e-1)]15oA/(M)=/+3x3-1ᙠOPQ0,1RDḄS2ᨬ01T345⚗7஺v/(x)=x4+3x3-l,xeQ0,lRVf=2(x-,)Xᡭ€[—1,1]2\11ᨴ1x=-f+-22J•/]=(᜛+[+3(5+/Tஹ(/+10/+24/22/—9)Vg«)=16/Q),WiJg(f)=z4+1Or3+24r+22t-9gg]8OPQ-1,1RDḄᨬ0S2345⚗7ὡQ)ijkmax|g]-8("=minmg(f)—8]=±7J]=য4—8p+1)2oq,5⚗7g(D-ὡ]&rs
ᨬt,ᦑ38

38JQ)=gQ)—-Q)73=10ᡝ+25/+22/——8wx/(x)ḄS2ᨬ01T345⚗78‘zপᑣ/(x)ḄS2ᨬ01T34165⚗78I73ὡ]=1\0(2x-I)+25(2x-I)2+22(2x-1)—--]168,51129-5cx——x2+—x----4412816o/(x)=NᙠDAᐵ+জ=spanp,—,/Ḅᨬ0345⚗7஺V/(X)=|x|,X6[-l,l]g(/g)=fJ(x)g(x)Jx%=l,(p[=X1=X4ᑣIJ=2,|=:11=£()=1,(/)=g,(/,%)=:,2290,91)=13),᜛2)=3,02)='ᑣ8(22](\§%ஹ1---"஺2221———a=13572222H1579)-a=0.11718750

39S(x)=a஺+2+ax^2=0.1171875+1.640625᮱—125/0820317oAᦪ/(x)ᙠᢣOPD+=spa஻{l,x}Ḅᨬ0345⚗7:প/(X)=L[1,3];(2)/(X)=",[0,1];x(3)/(x)=cosx,[0,1];(4)/(x)=In“1,2];(l)v/(x)=i,[l,3];Xg(/g)=f/(x)g(xMx%=1,0]=%,ᑣᨵI=2,¥;g,(¦᜛τ)=4,(᜛0)=E3,()=2,ᑣ8¨x-4=1.14101%=-0.2958ᦑ/(-V)ᐵ+জ=span[i,x]Ḅᨬ0345⚗78S(x)=a+ax0t=1.1410-0.2958x(2):஻x)=e\[0Hg(g)=^fMg(x)dxe0=1,=X,,ᑣᨵ40

40I;=1,¥;=;,/ஹ1(஺0/)=ὡ(feo)=eT,(/,0i)=l,ᑣ8/1\12q=©]ll3J¨x-%=0.18781%=1.6244ᦑ/(%)ᐵ+ª=span{1.x]Ḅᨬ0345⚗78S(x)=a+qx0=0.1878+1.6244%বf(x)=COS^-X,XG[0,1]g/g®=f/x®gxRx00=1M=°ᑣᨵ±:=1,¥:=('¦□®=5,2(/஺0)=°(/஺1)=----71ᑣ8(£19ஹ2஻02q123)¨x-Ja=1.21590[a,=-0.2431741

41ᦑ/(x)ᐵ+জ=spᓽ´1,%Ḅᨬ0345⚗78=µ+஻[%=1.2159-0.24317%(4)f(x)=Inx,xG[1,2]g(/g)=f/(x)g(xWx%=1,0]=X,ᑣᨵ±;=1¥;=(/ஹ3(%%)=]3(/,)=21n2-l,(/,^)=21n2--,%ᑣ8(c1-zx<21n2-l)37[a.)21n2--oI4/1205J¨x-a஺——0.63711%=0.6822ᦑ/(%)ᐵ+জ=Wᓽ´1,%ᨬ0345⚗78S(x)=¶+஻]X=-0.6371+0.6822%18஺/(x)-sinjx,ᙠ[-1,1]Dᢥ¹º»5⚗7¼½AS2ᨬ0345⚗7஺TTv/(x)=sin—x,xe[-l,l]ᢥ¹º»5⚗7´6(¾,R(x),P(x),P,(x)¼½242

42-1(/(x),Q(x))=Jsin^-iz/x=—cos^x=01flTT86ஹ)/À1ᵫ5Mx=/(/(x),£(x))=£(|x2-^)sinyxJx=0/—ஹD,Ã*3348(1110)(/(x),8(x))=(-x--x)sin—xJx=---------Ä2227tᑣ/=(/(x)4(x))/2=012q=3(/(x)/(x))/22714=5(/(x),Åপ)/2=0168(/io)@=7(/(x),jx))/24¨xf(x)ḄS2ᨬ0345⚗78SJ(x)=aJq)(x)+aJq(x)+4Jg(x)+஻JA(x)12168(^-10)5_3X+(X3X)TCTC22420("-10)3120(21-2/)------:----x+-----------a1.5531913x-0.5622285/19oÈÉᱥËḄÌÍÎÏ-ÐÑÒᦪÓ:qPt(s)00.91.93.03.95.0ÕÖs(m)010305080110AÎÏ஺×ÈÉᱥËḄÎÏÕÖ&ÎÏqPᜧË8ÍឋᦪᐵÚ¨x⌱ÜÍឋs=a+btVজ=span\i,t}ᑣIIJ=6,MilJ=53.63,(᜛OM)=14.7,(%,s)=280,3/)=1078,ᑣ8(614.7RÝR_(280ஹQ14.753.63ÞᔆQ1078,43

43¨x-a=-7.855048%=22.25376ᦑᱥËÎÏ8S=22.25376—7.85504820oàáâãᦪÓ᝞Ò:1925313844Xi19.032.349.073.397.8yjᵨᨬtæçAè᝞s=a+bx2Ḅéãê7ëìíᙳ
஺:gs=a+bx2ᑣজ=spanᑣh5ïẓ=7277699,᜜□®=5327,%®=271.4,/ᵨ®=369321.5,ᑣ855327®Ý]_271.4ஹ153277277699ò஺11369321.5,¨x-a=0.9726046,6=0.0500351ᦑy=0.9726046+0.050035lx241ᙳ
8b=[ZyX/®-X®2]2=0.1226ó021oᙠôõᚪ÷iªᵫâã-ᑖᱥùú&qPᐵÚ᝞Ò:qPf0510152025303540455055ùú01.272.162.863.443.874.154.374.514.584.624.64Xxio-4ᵨᨬtæçAy=44

44ÈûᡠýᦪÓḄᱯÿ
ᵨ-by=ae1(a,h>0)9ᦪᑣ..bIny=In஺——tজ==

45y,x=--ᑣS=a*+L=11ML=0062321,(0°M)=-0.603975,(%,/)=-87.674095,(J)=5.032489,ᑣ(11—0.603975/]_/—87.674095ஹ[-0.6039750.062321IQ*)—(5.032489,!"“*=-7.5587812«y=7.4961692#$a=a~=5.2151048eb=6"=7.49616927.4961692.•y=5.2151048c22o%&'()*/+=(4,3,2,1,0,1,2,3),ᵨFFT,-*/+Ḅ/ᦣ1஺!2*3=(4,3,2,1,0,1,2,3),ᑣ஽=0,1,…,7,N=8/0==1,15-74,co=co=e,co1==e2=-i,3"j=co1=e4,45

46k01234567Xk43210123A4442co404-2ᶭ4840482V20-272c,164+2604-27204-27204+20Ms23,ᵨ789◀;<,(x)="O'*ᓄ>ᑖ@஺x2+6x+6!3x2+6x/?22

47"C0=0,G=LG=oc11c,=---=—,33!6c=o,4_1__Lr5-5!-120'஺6=஺—஺m—C)b?—஺3ᓃ]=C4—C2b3-஺3஺2—c4bl=C*5--C4b2-஺5_=஺6ᓽI6120b!"&=0nJ220b,=04-1de=ZCjbk_j+C(k=0,1,2,3)kJ=oᑣ%=G=°a=Cffy+G=0{a=Cb+C&=02Q27a3=C*3+Cb+C2bl+G=-—x26()ᦑ47

4823nஹa+ax+ax+஺pz}}7&@qrs%~~1+3+bx~+Z?x323Y71,6020_60x-7x3ߟ60+3V25o-/(x)=6ᙠy=0ᜐḄ(2,1)▤DEFG&z)஺!:ᵫ/(x)=eᙠx=0ᜐḄIJKLex=\+x+—+—+■■■2!3!G1,IG2;2,26-C4=C3ᓽ1,1—b.——216!"b=--13d~=£Cj*+QZ=0,2r7=0ᑣ2a\=GA+G=§…_+G=248

49ᦑ2D(ஹa^0+a^1x+a^-x1+&XI2121+-X+-X_366+4x+x?6-2xফfs"(x)/(x)-S"(x)]dx=fs”(x)d[r(x)—S'(x)]b,=S"(x)[r(x)—S(x)]a—f[r(x)—S[x)]d[S"(x)]=S஻(b)[r3)-S3)]-S"ভ[/ভ-S(-£[r(x)-S

502h=A—[j+4p+AiÛ/(x)=x,ᑣO=-A_h+Aht}Û/(x)=f,ᑣ2-h3=h2A,+h2A.3t1!"A.=—h13Û/(x)=d,ᑣJ/(x)Jx=x%x=oA_J(-/o+4/(o)+A")=oᦑI"(xMx=A,/(-/i)+4/(0)+AJWᡂÏ஺Û/(x)=x4,ᑣ£f(x)dx=fx4dx=1/i5J-nJ-h52A_/(—஻)+4/(0)+AJ(/0=”5ᦑ$£f(xyixHAT/T)+4/(0)+AJ(஻)J-hᦑff(x\lx«+A)/(0)+AJWᐹᨵ3îᦪ¯°஺(2)×ff(x)dx«A,/(-/2)+4/(0)+A,/(A)J-2hÛ/(x)=l,ᑣ4஻—A7++Aj50

51Û/(x)=x,ᑣ0=-Ah+A,h—1tIÛ/(x)=x2,ᑣ—h3=h2A,+/?2A3t1!",8,

520=—1+2xj+3%2Û/&)=/ᑣ2=1+2Xb+3Xb!"[x,=-0.28994M=0.68994ᡈi[x=0.5266_1%,=0.12662Û/(x)=/,ᑣ^f(x)dx=]/dx=0[/(-1)+2/(X,)+3/(X)]/3^02ᦑ1j(xMx="(-1)+2/(%)+3/஺2)]/3ÄᡂÏ஺#$ë-¨@ᐹᨵ2îᦪ¯°஺(4)×f/஺ì=M/(0)+f(/z)]/2+ah2[f(0)-fXh)]Û/(x)=l,ᑣff(x)dx-h,h[f(o)+f(h)]/2+“/?"(())/(%)]=hÛ/(x)=X,ᑣ[f{x]dx=[xdx=g//M/(0)+f(h)]/2+ï"(o)_/(//)]=1A2Û/(x)=/,ᑣf/(xRx=£X2JX=1/23h[f(0)+/(/i)]/2+«/?2[/\0)-/7/z)]=1A3-2ah2ᦑᨵ52

53-h^-h3-2ah232Ûf(x)=X3ᑣ£f(x)dx=£x3dx=bh4h[f(0)+f(h)]/2+^-h2[fX0)-f'(h)]=^h4-^h4=^-h412244Û/(x)=/,ᑣff{x)dx-[x4dx=

54h77=/ভ+2%)+2/(᧤஺1(l-e~xyফ஻=10,6/=0/=IM=—f(x)=------—910xᓄ
$=4"(஺)+2^/(x,)+f(b)]=1.391482k=iᓄh995o=-[/(«)+4E/(x,)+2^/(x)+/(Z)]=1.454711i?Ok=02^=1(3)஻=4,a=1=9,/i=2,/(x)=4,ᓄ
78=4"(a)+2±)+/(&)]=17.227742k=iᓄ^335--[/(«)+4^/(X;)+2^/(x,)+/(஻)]=17.322224+0k=02k=l(4)஻=6,(7=0,/?=—,h=—,/(x)=^/4-sin2cp636ᓄ
h5"=?"(஺)+22@%)+f(b)]=1.035622k=\ᓄ$6=A/(஺)+/(xj)+2C)+/3)]=1.035776k=O22=13oDEFGHᱯJᦟᩞ(2஺4)ᐹᨵ5OPᦪRS஺GTUHᱯJ஺(V=W[7/*0)+32/()+12/(Y,)+32/*3)+7/(%)]%90Z/஺)=1,ᑣ54

550(V=\*[7/P0)+32/(])+12/(஽)+32/*3)+7/*4)]=8-஺Z/(X)=Xᑣ1f(x)dx=[xdx=^(b2-a2)^[7/(x)+32/(x,)+12/(x)+32/(x)+7/(x)]=l(^-a2)0234902Z/஺)=/,ᑣjf(x)dx=[x2dx=_q3)a[7/(%)+32/(b)+12/(஽)+32/a3)+7/a4)]=8(/c/)Z/(x)=/,ᑣ[f(x)dx=d%e=8(ᓃ4_44)^[7/(x)+32/(x)+12/(x)+32/(x)+7/(x)]=l(Z4-a4)01234>Z/*)=/,hIj1f(x)dx-[x4dx=1(/-a;)\[7/(%)+32/(b)+12/(஽)+32")+7/(5)]=*—jZ/(x)=x5ᑣ^[7/(x)+32/(x)+12/(x)+32/(x)+7/(x)]=l(^-a6)0123490oZ/(?)=36,ᑣr/(x)Jx^^[7/(x)+32/(x)+12/(x)+32/(x)+7/(x)]01234“)9055

56no;pHᱯJᐹᨵ5qPᦪRS஺4oᵨstᑖvwxyz஺{US=?"ভ+"⊍)+/(~o2o;a=Q,b=l,f(x)=e'\ᨵ1_1,S=-(l+4e2+e-i)=0.63233yzca(?ᡭভ1oO2<—x^-xe°=0.00035,஻e(0,1)18024,5oᑡstU/(xMx=S—3—஺)28@2ff"=(b-a)f(b)—S(b-a)2;2f/(=9-஺)/+4*S-a)38Al224GTU(1)f(x)=f(a)+r(?8)(x—a),஻e(a,b)ᙠa,ᑗtᑖ;f/(x)Jx=S-a)/(a)+r(஻)f(x-aRxᓽf/(x3S-a)/ভ+*(b-a)22(2)v/(x)=f(b)-f'(.rj)(b-x),rje(a,b)ᙠa,ᑗtᑖ;f/(xMx=S-a)/(a)-/'(77)f(ᓃ-xMxJtl56

57ᓽff(x)dx=(b-a)f(b)-^-(b-a)2“2/cஹrzஹr,a+bஹr“a+bஹ/a+b/"(஻);a+b.(3)•••/(%)=/(——)+/(——)(x---)x+^-^(x--x2e(a1)vvvvv¥ᙠa,¦tᑖ;(*//ஹ;,,..a+b.,.a+b(*.a+b.,f"Ma+b^.§/(x)dx=3—a)/r(—y-)x+/(—7-)x§(x-c—Wx+^—§(x---)-JxᓽFrx/ஹn/,ஹr,a+bஹ/”(஻)஻ஹ3f()dx-(h-a)f—(Z?-a);60®ᵨᓄ
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58.f(4\x)=e\.•.!/?„(/)1=c——/Z4I/,4)(7)I<-^/Z41"128802880®|Reݱ;x"5,ᑣ4
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59fle~xdxkT(k)20T,00.771743310.72806990.713512120.71698280.71328700.713272030.71420020.71327260.71327170.7132717no1=0.713727(2)/=]x^mxdxkÓÝýÝ03.451313xlO-618.628283x10þ-4.446923xIO-21no50(3)/=[Uxjl+x2dxkÓÝýÝzz4ব014.2302495111.171369910.1517434210.44379610.20127210.204574954310.26636710.20722410.20762010.2076692071410.22227010.20757110.20759410.20759310.20759322396510.211260710.20759010.20759210.20759210.20759210.20759292222no/210.20759229ᵨn=2,3Ḅ
■■ᑖOexsinxdx./=I'exsinxdx.59

60f=x-2,ᑣ1,1]ᵨ஻=2Ḅ
ᑖIX0.5555556x"(—0.7745967)+/(0.7745967)]+0.8888889x/(0)«10.9484ᵨ஻=3Ḅ
ᑖI«0.3478548x[/(-0.8611363)+/(0.8611363)]+0.6521452x"(—0.3399810)+/(0.3399810)]*10.9501410ᙢᳫ123⍝567ᙊ97ᙊᕜ;Ḅ5S=af/1-(£?@2ḄAB5a57ᙊḄCDE9c5ᙢᳫGHI3⍝GH(7ᙊGH)ḄJK9LhNOᙢPJK9HNRᙢPJK9R=6371(km)NᙢᳫCD9ᑣa=(2R+஻+/0/2,c=(”-஻)/2.ᡃXY⚩ᙢᳫ12OᙢPJKh=439(km),RᙢPJKH=2384(km)[\1023⍝Ḅᕜ;஺•••/?=6371,`=439,"=2384abᨵ஺a=(2R+"+/i)/2=7782.5c=(4—/?)/2=972.5S=4a^l-(-)2sin2keTkT{01.56464011.5646461.56464821.5646461.5646461.5646461.564646S-48708(7᪷)ᓽh⌼123⍝Ḅᕜ;N48708kmllolmn35.71TC71nsin—=7t----7+---7n3!஻25"60

61[rsnsin(-)(n=3,6,12)Ḅt9ᵨ᜜vw\ᑍḄOxt஺ny/(஻)=஻sinz9nT7=13155Csinxx----xH—x—,•,3!5!..|}ᦪḄN/஻=஻sinzn=/?[---!--3+—-5—••]n3!஻5!n71ஹH----D—”5!«4ᑐ=3,nsin-=2.598076n஻=69nsin—=3n஻=129஻sinz=3.105829nᵫ᜜vwnᶭ))32.59807663.0000003.13397593.1058293.1411053.141580ᦑ^3.1415812ᵨᑡwᑖ/?9஺0পw(2)PP
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6201.33333311.1666671.09925921.1166671.1000001.09925931.1032111.0987261.0986411.09861341.0997681.0986201.0986131.0986131.098613ᦑᨵ/a1.098613ফ§ᵨ
1=[@Jly|”[1,3],x=y-z,UXG[T,1],1=(—^—dx,f(x)~—9x+2ᑭᵨP
9ᑣI=0.5555556x[/(-0.7745967)+/(0.7745967)]+0.8888889x/(0)«1.098039ᑭᵨP
9ᑣ/®0.2369239x[/(-0.9061798)+/(0.9061798)]+0.4786287x"(—0.5384693)+/(0.5384693)]+0.5688889x/(O)«1.098609(3)§ᵨ¤ᓄ¦P
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63¶·ᣚyᓱ,ᑣdx,1/3)=x+7/x/(-0.5773503)+/(0.5773503)«0.28767122¶·ᣚ½?’ᑣ/পx+9'ha/(-0.5773503)+/(0.5773503)»0.2231405,ᑣ/®/(-0.5773503)+/(0.5773503)«0.18232044¿|9ᨵ/«1.09853813.ᵨPÀᑖ\Á஺ᡝ^ᙠx=1.0,l.l,À1.2ᜐḄÅᦪt9(1+x)-ÆÇÈ஺Ḅtᵫ⊤ÊË:X1.01.11.2F(x)0.25000.22680.2066:1/3)=(1+X)2ᵫÍÎ⚗ḄP\ÅÐ63

641h2ruo)=T7[-3/u)+4/(x)-/u)]+—ol22h31h2[-/(x)+/(x)]--r(^)022h61h2f'(x)=Ô[/(x)-4/(x,)+3/(X)]+—rG)20212h3Öº/(x)=0.2500,/(Xj)=0.2268,/(x)=0.2066,02.")J-3/(x0)+4/(/)-/¡)]=0.2472n/'Qi)«½[—/(x0)+/(x)]=-0.21722h/'(%)=]"(/)-4/a)+3/(%)]=-0.1872hÖ/(X)=——!~~7(l+x)2-249Ü=(1+x)XVXG[1.0,1.2].Ý/”ᱏß0.75ᦑÇÈᑖàNá/|=Ü”2.5x10-3|R%|½h”L25xlr36|RX2|=H©42.5X10-3ᑭᵨᦪtᑖ\Å9å*x=rx/Mi=/4+çexWxᵫêë\}x
dx=ì᜛4+0x“ÝïJxk2abᨵ64

65hf(x)=f(x)+-r^(x,)+᜛(%])]Mkᦑ9(x())+᜛(%)=1[/(x)-/(x)l10h2^(Xj)+(p(x)=-[/(x)-/(x,)]27hÖ/(X*+1)=/(k)+1%x/Jxk-lðr(p(x)dx=h[