数值分析第四版课后习题答案李庆扬

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1ஹxு0,xḄb,InxḄ஺x*>0xḄᑣᨵ£"(x)=6,&s\x)=a*,()InxḄf(Inx)=|(lnx*)£(x*)=2.=b,£/(Inx)=0ᢤ=—1oInxInx2ஹxḄ2%,x஻Ḅ஺X*XḄᑣᨵ£"(x)=2%,&£*(x)=2%,*|,()x"Ḅ£(Inx)=\(xn)8.£(x*)=:(x*)"T|2%|x*|=2n%•,£"(Inx)=
:ᑏ)=2஻>o3ஹ@ᑡᔜᦪDEFGHIJᐭLᑮḄᦪᓽOPGᨬR
SḄTUᓫSWᢣYZ[E\Sᨵᦔᦪ^/%"=1.1021,x"=0.031,x"=385.6,x"=56.430,x"=7x1.0=x"=1.1021ᨵ5Sᨵᦔᦪ^"x"=0.0031ᨵ2Sᨵᦔᦪ^"x"=385.6ᨵ4Sᨵᦔᦪ^"X"=56.430ᨵ5Sᨵᦔᦪ^"x"=7x1.0ᨵ2Sᨵᦔᦪ^஺4ஹᑭᵨfg(3.3)@ᑡᔜḄ▲ᐸjx",x",x",x"ᙳ3⚪ᡠnḄᦪ஺/1ஹ*»»(I)p+p2+r4e*(x"+X"+X")=£t£(X")=£(X")+£(X")+£(u/)vwxJ"=-xl0-4+-xl0-3+110-3=i05x10-3222(2)x/x"x""

1£(x/)=(|)£(%/)+(x/ᐝ;)£(")+(x/x")£(%")=(0.031x385.6),xl(r4+(ii021x385.6),xl(T3+(O21xO.O31)Lxl(r3/222=0.59768xlO-3+212.48488x1O-3+0.01708255xlO-3=213.09964255xlO-3=0.21309964255(3)x"/x"஺e*(x"/x/)=Z,)য+)k=l56461xlxlQ-3«0.88654xlQ-5(56.430)225ஹᳫ⌕▲1%,TRᐕḄE?/("(A))4ᵫ1%=£"(—(R*)3)=T-------¡,3*)3£*(.(R*)3)=l%xg(R*)3=g(R*)3£*(ᑁ)=4£(7?*)2X£*(R*),()£*(R*)=1%X,R*,ᦑ£"(/?")='(7=1%X—=-^ߟo3rR33006ஹh=28,ᢥ⌴ªfg>=«_1(஻=1,2/-)ᑮᓃ,®¯00V783«27.982(JSᨵᦔᦪ^)W±²³ᨵᜧµ¶⊤¸ᓃḄ,e*(Y)=Y-Y,ᑣe*(y0)=O,º»ᵫnnnᓃ=¼X27.982,ᓃ=ᓃ
—ᯅX¾¡ᓃ—ᓃ=ET—%T-ᯅx(27.982—À),ᓽe*(ᓃ)=/(/„.,)
ᔁx(27.982-A/783)=e*(/„_)
ÃÄ(27.982-V783)=…(2)e*(K)=e*(Ä)-(27.982-/783)=7783-27.982,l00

2W|V783-27.982|<-xW3,ᡠÉf*(r)=-xl0-31)ioo7ஹÊË/—56x+i=0ḄÌU᪷ZÎᐹᨵHSᨵᦔᦪ^(V783«27.982)ᵫx=28ÐJÑÒJÑa27.982(JSᨵᦔᦪ^)¡%1=28+7783=28+27.982=55.982(JSᨵᦔᦪ^)஺)/=28Ñ=28-27.982=0.018,ÓᨵÌSᨵᦔᦪ^OÔᔠ⚪Ö஺Ex,=28-V783=——×==—1—=1.7863x0-2o•28+V78355.9828ஹÙNᐙᑖᜧÝÞ᪵à'
âdx?ᐭ1+x2äP1ߟ;dx=arctan(N+l)-arctanN,ÙNᐙᑖᜧÝÌUᦪ1+x2èa=arctan(N+1),(3=arctanN,éêJN+1=tana,N=tan᜛()/cஹtan-tan/?(N+1)—N_1tan(«-/?)=-----------1+tancrtan°1+N(N+1)-W+N+1r+i1|-----dx=a-0=arctan—"-------fl+x2N2+N+19ஹíÊîḄïðᜧñ100cm,óÞ᪵ôõöᐸ☢OPG1cø2?ᵫ£*((/*)2)=|(/*)2±"(/*)=஻*£*(/*)¡®⌕£*((r)2)=1,ᑣ×((ᔆ)2)1—,ᓽïðóúû/=100а-஺£*(/*)2/*-2x10020020010ஹ5=3/2,ᎷýgEÿḄtḄᨵ±0.1ḄtSḄᓾ஺£*(S)=(ߟ)*£*()=gf*£*(f)=O.lgr*dt£-(5)=/0=1*1=22=4ᡠ67஺Sᩗ()t5t11ஹ:ᑡ

3y=^240`ab“Ḅdefᑣᵫj=10)',1k1V=411bm஺n"pq‘s஺)=”u—s…wᓽ£*(>,)=iO£*(y,T)=io"£*(y஺)}£*(~0)=1010^(y)=10,0xlx10-2=gx1()8,RS[\]^஺012ஹRS/=(k1)6,&al.4,ᑭᵨᑡRSkZ7ᑮḄᨬX———(3-23,----99-7072o(V2+1)6(3+2V2)3`£*(/)=gxl()T,ᡠ6/,(V2+1)6*(£)=/'e*(1.4)=-^-xlxlO-'=6.54x10-4

4e*(U)=(/J*e*(x)------,x-xlO-4(30-V3O2-1)2------5------xlxlO-4=0.2994x10-230-29.98332————xixlO-46*²32³=|²ᨴ³*µ*஺³=x+yjx2-12------------x—x104=0.8336x1()630+29.9833214ஹ¶ᵨ·ᐗ¹`§\ºᓰxᓝ+1IUO10Xr2=-i1Uo10,Ꮇ^Áᨵ/NᦪRS«ÂᔲX+=2p☠Xin101A10_9`Å`/=Ækm஺Çᵨ/NᦪÈS7ᑮ10,°-11010-1⚗=l,x=1,p☠஺215ஹËq/ÌÍ☢Ï$=Lysine,ᐸÓcÕÖ0

5ämåæf¹1ஹ᪷è²2.2³^àḄêℳìᑡí1X஺xj,,xoᓃ²XoX”kᓃ²x³ÂnñV⚗òḄ1X"TX,3•••1XX2…xn᪷ÂX,X2,…,X“TØᓃ²Xox”…,X“T
X=V“TXO
X|'X"TX-XO>-X-X"T஺,k!'k|ᓃ²Xox”…,x,ix³=ôô²ᓃ-õ³•ô²X-Xj³ᵫ<=°>=°7=0p7¤஺?k!=%T²X0,XiøஹX"_³n²X—Xj³j=02ஹx=l,-1,2/²x³=0-3,4,¤/²x³ḄmñæfV⚗஺(x-x1)(x-x2)(X-Xo)(X-/)(X-Xo)(X-X|)4(%)=%---------------r+~(%0-%!)(XOf)(úkXo)(XI-X2)(x2-x0)(x2-%,)(x+l)(x-2)**-Nd)`=Ox(1+D(1-2)(-1-1)(-!-2)3ஹþÿ/
x=lnxḄᦪ⊤ᵨឋIn0.54Ḅ஺X0.40.50.60.70.8Inx-0.916291-0.693147-0.510826-0.357765-0.223144&'()*4=0.5,%1=0.6,ᑣ.=/(/)=/(0.5)=—0.693147,=f(xj=/(0.6)=-0.510826,ᑣ,,ஹX-X.X-XX-0.6x-0.5nL.(x)=y------+y.------=-0.693147x----------0.510826x--------0'x-x,'X1-x0.5-0.60.6-0.5,a0=6.93147(x-0.6)-5.10826(%-0.5)=1.8232lx-1.60475256L,(0.54)=1.82321x0.54-1.604752=0.9845334-1.604752=-0.6202186஺)*8=0.4,.=0.5,x=0.6,ᑣ9=/(/)=/(0.4)=-0.916291,2:=/(xJ=/(0.5)=—0.693147,y=/(x)=/(0.6)=-0.510826,ᑣ22

6(X-Xj)(x-x)(x-x)(x-x)(x-Xo)(x-X|)202LM=y20(x0-x,)(x0-x2)(X|>?0)(ᓰ>ᑐ2)(x2-x0)(x2-xj(x—0.5)(x—0.6)(x—0.4)(x—0.6)=-0.91629lx+(-0.693147)x(0.4-0.5)(0.4-0.6)(0.5—0.4)(0.5—0.6)(x—0.4)(x—0.5)+(-0.510826)x(0.6-0.4)(0.6-0.5)=-45.81455x(x2-1.lx+0.3)+69.3147x(x2-x+0.24)-25.5413(/-0.9x+0.2)=-2.04115x2+4.068475x-2.217097L(0.54)=-2.04115x0.542+4.068475x0.54-2.217097256=-0.59519934+2.1969765-2.217097=-0.615319844ஹCDcosxOWx49(TḄJᦪ⊤KLM%=l'=(l/60)஺K)Jᦪᐹᨵ5PᨵᦔᦪRKẆTᵨឋUcosxVḄWXYZ஺&'([⁚].X()yy>pR(x)=/(%)-4(x)=f(x)-4(x)+L,(x)-L,(x)_%)-“_஽_.+(_%)XX஺,562!x-X]x-xQx0cosj/ஹ/ஹ/_ஹX-X]/_X-xᓃ/\x0=>——(x-x)(x-x)+(y-y)------+(%—%)-------KJe(xoKxj01002x-xx-x0}}0|R(x)|w3cosJ(x-Xo)(x—)|+1%>%|X,+|y,-yja஺LXo>X]11>%/1/71_X-X1_X-Xin5{in5oK—(x—x)(x—x.)H-x10x------------1—x10x----------n22x-Xj2%j-x00<--+-X10-5=-x—1—4-lxlO-5=-x6.94xl0-5+-X1O^5=3.47x10-52422144002225ஹ[=%+ᦇ/z,k=1,2,3,Umax|Z(x)|஺2

7(x-x)(-x)(x-x)max|/(x)|=max032x^y)(12—3)(x-x)(x-x-h)(x-x-3/z)&'(=max00aX1'=33327.4+4+yp71+,x/75/7-5.1_.ஹ.3f(x+---------h)=---------//x---------Ax---------h=------(20+14j7)/z,n°333327ᯠ/
x°+/஻)

8[']·⊡ᐙ⚪3,ᐸº*/m)=/s)=oᓽ³஺8ஹᙠ-4WxW4tCD/*)="Ḅ¼½⁚]Jᦪ⊤K)ᵨU/ḄK⌕¿ÀÁXYÂÃÄ10YKÆ¿ᵨJᦪ⊤ḄLMha*mÈÉ[']ᵫ⚪efgK[X¿ᵨ⁚]X஺=X],X],£=X[+ËÌKᑣR?(x)=(X-x)(x-X|)(x-x)02Í⚗.g3-,=—[x-(x,-h)](x-x)[x-(x+/?)],e(x,x)li026/(x)-[x-(X]-h)](x—x,)[x-(X]+h)]-x3-3xx2+(3x-/?2)x+x(x2-h2),tllᑣ:஺)=3/_6Ï/+(3Ð-ÑK56/(x)Ḅ᩽].Ï=ᵨÒஹ஻KᦑIj.,ஹ]Vs,Vsa72V363max/(x)=——/?•(1+——}h-(1——)h=——h,613339|R,(x)Öᡈmax|/(xÑ⁐Ù஻3=জ஻3,⌕¿ᐸÂÃÄi()qᑣᨵ1-16Ý316927<10-6,ᓽ/M02?r]0-2=3.4863x10>2.472xl0-2o2=027e?7.3899ஹ)y“=2",Ußà஺á”=(£—/)ஹ=E4(-i)y(4.ஹU4->y„=:4(T».y„4-j+è஺é=oé[']=(—l)°Qy“+4+(T)[:ì+3+(>1)(ì2+(>[)[ìM+(T)4(:1°=2,,+4—4x2"+3+6x2Ñ2_4x2,,+|+2"16x2”-32x2”+24x2"-8x2"+2"=2"

9í“=E—î@=8
-1Kï”Kðq=ñ
-1òó"=0\JJèo7

4ஹK4ஹK4ஹ4
4ஹ=T°Oy“+2+
-1
Jy”+i+
-122ᓅ+
>133j"i+
—"14""2°=2"+2-4x2"+'+6X2"-4X2"-'+2"-2=16x2"-2-32x2"-1+24x22-8x2"-2+2"-2=2"-210ஹ᝞ö/*©mm⚗oK÷ø'
ù=/஺+஻-/
ùK¤ú/xḄk▤YᑖÑ/஺
04ᦇீý©ᵨ—þm⚗oKÿN""x=O1
᦮ᦪ஺kᵨᦪ஺11ஹg*="g*+i+fZk஺;0j=014ஹ'/x=a+qx+…+a._X"T+%x"ᨵn)*+,᪷
,4,…,x“agx;_JO,Q

10f'(Xj)=4(6-8),:ᵫ;ᖪḄឋ?1A3C:1=1t^-=t——-——M’xtx”…,x“]=LᦇE,QR$஺/=1Hj15ஹn▤ᙳ;ᨵWᑡឋ?%1)'F(x)=(/(x),ᑣ\008,…,x.]=஻
ᵨ,…,x“]^2)'F(x)=/(x)+g(x),ᑣF[x,x,---,x„]=/[x,%,,---,x„]+g[x,%,,---,x„]o0l0017riSF(Xj)(cf(Xj)f[XoX|,…,x“]=--------=--------k4প-a)=°n(Xjf)i=0i=0[]1)”যপ=cf“"X)-=cf[x,x,---,x„]0i>on(x.-x,.)7i=0HjsXoX”…x,tu£“—f/(Xj)+gQj)>=°n(x^-x,)s4(Xjf)i=0i=0HjiA2)//(Xj)/g(Xj)1rI=L-----4----+L------%----=/[Xo,/,•••,x,t+g[XoX|,-,x,t=°zম-8)>on(x.-x,.)7j=o1=0NjHj16ஹ/(x)=x7+x4+3x+l,/[2°,21ஹ27],/[2°,2',-,28]==0oo!o![]/[2஺2,…2]=g=1=1,/[20,2',-,28]O17ஹᱯ⚗R.3(x)=/<4)G)(x-X)2(x-x)2/4!,Je(x*,x),kk+tk+}ᵫᑖᱯḄ;▲஺[]P30P33,;▲
w(/z)+—/?maxido27118ஹXXXXXXXXXX.19ஹ)ᦪ*¨©4Ḅª⚗«P(x),¬®P(0)=P(0)=0,pপ=pg)=l,P(2)=1o

113P(x)=ax4+ax+ax2+ax+a,ᑣP'(x)=4ax3+3ax2+2ax+a),432}0432:ᵫP(0)=P'(0)=0,P(1)=P,(1)=1,P(2)=l$%0=«o0=P(0)=&0=0=p(0)=69<1=P(l)=%+%+&+஺+±=஺2°QR41=Pf(x)=4%+3a3+2a2+/31=\ফ=16a+8%+4a2+2%+a—=%402_=«44*ஹ1433921/2(CஹX2(X-3)2P(x)=-x—x-\—x——(x-6x+9)=---------o4244420ஹ3/(x)eCa,6,µa,ᑖ
n¶ᑖ·᪀⌼)º▤»Ḅ¼ᑖ½ᦪᓄ(x),¿"->8Áᓄ(x)ᙠa,஺ÃÄᦈÆᑮÈ(x)஺supf(x)+inf/(x)Ë0(x)=^^——,i=l,2,3,…,஻஺21ஹ3/a)=1/(1+Íᙠ5WxV5ÃÐ஻=10,ᢥ¶Ò⁚ᑖÔឋ½ᦪ஻(x),ÕÖᔜ⁚ØᜐḄ/஻(x)/(x)ḄÚÕ;஺ᵫ⚪2Ch=l,QR¿xeÛÁ,,,,,,1x-x1x-x1zAx)=f,l.+fJ,=k+lk------7-----------------H----------------------;-------------------k+k+\+k-x-xl+(k+iyx-xkMk+ik11=)+…)22ஹ/(x)=/ᙠazÃḄᑖÔឋ½ᦪ/“(x),ÚÕ;஺3Üಘᑜᑖ
ßà
hḄâãä஺=/å*<…Wx“=b,ᑣ¿xwx«,x*+J,%=0,1,2çஹè1Á,

122Xf_xl(x-x)-xl(x-x+lkkxᓝk+l-X(XA+I~Xk)+Xk+\Xk~Xk+iXk_,\_—AvA*+i+"r"—Art+fAritX4+l-XkQR;
/?2(X)=’,(X-x)(x-X*+I)=(X-x)(x-X«+]),kkh?ᦑ|Ḅ(x)|=|(x-X*)(x-x*|)Kë஺23ஹ/x=x4ᙠ
a,ìÃḄᑖᱯÚÕ;஺3Üìᑜᑖ
ßà
hḄâãäa=xX…Wx“=b,ᑣ¿xe[94+ík=0,1,2,•••,«-1Á,a4(x)=fkk+è4+i+fkPk+H+O+G)(xf)+4xLQR;
R(X)=fJO)(X-X*)2(X-X*+1)2=(X-X«)2(X-X«+])2,2ᦑᡃ2x|=X-஽2X-X“|224ஹòóᦪô⊤᝞W%Xj0.250.300.390.450.53X0.50000.54770.62450.67080.7280·᪵ᩩ½ᦪSX,®ᩩù:1)S'(0.25)=1.0000,S'(0.53)=0.6868^2)S"(0.25)=S஻(0.53)=0஺[]ᵫú=0.30—0.25=0.05,h=0.39-0.30=0.09,h0.45-0.39=0.06,}2

13hhH%=0.53—0.45=0.08,û(8.10)«4=——)--%+%hH+hJh\0.099h20.062Cü4%+/?|0.05+0.0914h+/i0.09+0.065}2z30.0844h+z3-0.06+0.08-72%0.055%0.093Ai஻2h0+h\-0.05+0.09--14/Zj+h,0.09+0.065h0.0632஻3h+%-0.06+0.08--72ᵫ(8.11)«gj=3(/1f+(j=l,…஻-1)C,79τ5/ý-/3)]gi=3(4/[XOX|]+஻J[X|,X2])=3[14x,-x14x-x.02c/90.5477-0.500050.6245-0.54773x(——x---------------------+x—)140.30-0.25140.39-0.30.,94775768ஹ192793x(—x-----1-----x-----)2.7541145001490070002/(X)-/(X,)^3/(X)-/(X)232g=3(2/[x,x]+/z/[x,x])=3[------------------------------1-------------------------------j2212223520.6245-0.547730.6708-0.62453x+x50.39-0.3050.45-0.393X(2X%2)4x256+3x463_-Z.þID590056001000ââஹ—ஹ“4/(x3)—/U),3/(X)-/(X)g3-3(4/ÿ2%3]+஻3/[3ஹ4])-3+431]7x-x7x-x324340.6708-0.624530.7280-0.6708.=3ox(z—x---------------------+—x----------------------)o70.45-0.3970.53-0.4544633472ஹ4x463+9x11814573x(-x------1—x-----)---------------------=-------=2.08147600780014007005209142.7541--x1.0000142.1112231▣:2in2.4132.413255஻?331.787142.0814——x0.68680277

140.9078m0.8278,S(x)=/%(“)+"£/(x)l°2m0.65707=032)()ᯠ+,ᩩ.ᦑg0=322=3ஹ3/54775OSO஺஺.ஹ8Z862:°0'x,-x0.30-0,255000a7280-06708572g“=x“௃=3x-2------>3xB=3x-=2.145,x“Ft0.53-0.45800200095-2.862-D02001414m2.7541E23▣B020m22.413FGH2,55D32.0814D343002m2.145D4774400027S(x)=I[ᐔ%(%)+⊈⊈()]஺j=o25ஹL/(x)eC2[a,b],S(x)PQR᪵ᩩTᦪVW1)[[f"M]2dx-[[S"(x)]2dx=f[f'M-S\x)]2dx+S\x)[fM-S"(x)]d:X2)LJ(xJ=S(xJ(i=0,1,…,஻)\᳝^_⁚aba=/

15fs-S\x)]dx={S"M[f'M-S7x)1}B5f"'(x)-5'M]S\x)dx=S஻(b)"0)-SW-5"ভ"'ভ—S'(a)]—A"'(x)—S'(x)]dx=S"(R"0)-S'S)]-S"(a)"'(a)-S'(a)]-A[f(x)5S(x)]B=S"(b)"0)-S0)]-S஻ভ"'ভ5S'(a)]⊡ᐙ⚪B1ஹxx()=0,x,=1,ᑏzy(x)=e-Ḅ5R^_|⚗L/x),~^_⚗஺ᵫ=y(Xo)=e"=1%=y(X1)=e"FqX-Xx—X-1_Ix—0L(x)=y--------]+y--------=1x------+ex-------]0{'/_X,-x0-11-0,0=5(51)+e"x=1+(e"-l)x⚗&(x)=(x—x0)(x—/)=?x(x-1),H(0,1),\e~^Ixmax|x(x-1)|=-xlx—=-ᦑῖIIτo

16maxf(x)-[f\a)+௃max/"(J)-max(x-a)(x-b)£b—d2""£a<>x<,bo=:max/"C)-J(b-a)2=4(b-a):max/"(x)2a<^

1757N4(x)=4-3(x-1)+(x-l)(x-2)-(x-l)(x-2)(x—4)ooO+on('-D(52)(x-4)(%-6)18஺,^_⚗=4-3(x-1)+(x-l)(x-2)-(x-l)(x-2)(x-4)o60+(x_D(x_2)(x—4)(È-6)1oO&(X)=C(x-l)(x-2)(x-4)(x-6)(x-7),Je(1,7)06ஹ᝞Ê⊤¼TᦪBi=0,l,2,3,4,01234/ËÁÃ36111827Ìz(ᑡ⊤TᦪḄᑖ⊤~ᑭᵨ¿ÀᔣÐ^_ѼzÒḄ^_|⚗஺᪀⌼ᑖ⊤BÕ/,A2/,A3/,A"03320016520211723189427N*°+th)=f஺+M஺^A2/O+-ᵫᑖ⊤F^_|⚗B_2=3+3f+^^x2=3+3f+fQ-l)=f2+2f+3

18×QØTᦪÙÚÛÌ1ஹ(a)ᑭᵨÂÜÝᣚßzÂÜa/Ḅà឵âᚆ|⚗;(b)å“x)=sinxᙠ0,^¦1R\3Rà឵âᚆ|⚗~çzè~ÛéêḄëìí᪍ïᦪðᑖ\ñòzóô஺(a)xx=a+(Z?-a)f,e1஺õ,à឵âᚆ|⚗ö(/x)=£/(÷R)A(X)ᐸùᐘ(X)=஻ஹxk(b-a-x)'-kok=Onk,(b)xx=ûeheo,là឵âᚆ|⚗ö(iýþÿᐸ
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2511199x201x202a=-------------x375.243201202a103103x104=GQ•ᓽᙠ᜜\'11h1,-98x202x203203J[104²b=---------------«-375.148202ெ104x103(375.243-375.148)o22ஹ/(x)=Wᙠ41,1H\7ᙠ0=ᓺᓽÚ1»2,/Ü\ḄᨬgÑÒ=>஺[G]ᵫ\x\dx=^xdx=1,=£-x3dx+Ë3dx=—22152a----35[ai128Ý4kldx=x5dx+Ë5dx=Ã222i,210=GQÞb=---o3572128cJ222L1105c------,579..3.128·ßᨬgÑÒ=>?⚗@'*)=◤+á/-◤-23ஹ”,,(â)=ᒹᔩ2åæZçèéᑗnop?⚗@bcᨵ⌴ìᐵîVl-x2w(x)=2jfw„(%)-«„_!(x)on+1[bc]ó=஺$6,ᑣU,ஹ,ஹcsin[(n+l)arccosx]sin(narccosx)2x”“(x)-«„.1(x)=2x-------==------------—Vl-X2Vl-x2_øsin[(஻+l)8]sin(஻6)2cos0sin[(n+1)^]-sin(n0)sin6sin0sin6sin(஻+2)6+sin(஻e)-sin(஻e)sin(«+2)0,ஹ=~=w,i(x)sin0sin024ஹ"x)=singxᙠ\ᢥûüý?⚗@|ᑗnop?⚗@þÿ
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28d?=MaZ,/YqZZ=Zy4xii=l=0x0+10x0.9+30x1.9+50x3+80x3.9+110x5,=9+57+150+312+550=107864=MYx,Z/Yx,ZZ=Z/x>/=1=0x02+10X0.92+30X1.92+50x32+80X3.92+110X52஺=8.1+108.3+450+1216.8+2750=4533.26sYY3ZᵨYx,.ZZ=Zl=6,i=l6Y9]Yx,.Z,

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33,-.ᑖ«/”¬)=Ò/ᐭT®|°:(§1+2+3/)/3=[xdx=0ফτ+3x,=19)ᓽ22[(-I)2+2x»+3x»]/3=02dx=-ெ2᳝+3X=122-372X]=7-TÕ1+2V232=7¶·/Of¸8=[§1+2*8-36&+*4Ö3]+6×+24+Ø343343#§36-11Ö஺…343L3(3[(—1)3+2+3]/3,c8+36Ú+108+54ÚJ-6Û+24-16@r[-1+2x----------------------------+3-------------------------],343343-36+114Üᦻ343ʼE½&ᨬᐹᨵ2¾ᦪ஺4)ff(x)dx«M/(0)+/(//)/2+ah2f'(Q)-஺,-.ᑖ«//(x)=§ᐭTᑮ

341/V8A1[-]=164+ç256+/+?+2(2+⁐+4+2+&+"+⁐"]«0.111402576526517281733055i77s=-[/(«)+4X/(x,)+2£/(xJ+/3)]8°k=022A+1k"+4ê§ߟr+2^—^+1484î4+(ï)-(1]54+JI1ð16(2ñ+1)+2)«0.11157484£1024+(24+1)2t^h4f—--ln(4+x2)l'=-ln-»0.11157஺A4+X22242)faHydx,H=IO»ᶍ)x3)(yfxdx,஻=4»3[-](ᶍ)8^dx=-x^l^=-(27-l)=—o°3334)r/6-J-sin2(pd(p,஻=6»ᶍ)஺3ஹÛôõöᱯø(2.4)ᐹᨵ5¾ᦪ஺[õ¢]ùᯠ⁚üýþ,i,Ñÿ
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35b-a[7a^32.+/+12=+:)2+32("+3b)2+7g+90424=h~^[7a2+2(9a2+6ab+b2)+3(a2+2ab+b2)+2(a2+6ab+9b2)+7b2]="4"(3002+305+30b2)="4/=(2dxx9030Lb_Clr_3CC/3஻+Z7ஹ3…»/஺+3\3--7«3+32——)3+12--3+32——)3+76390424=^^■[7/+^(27^+27a2b+9ab2+b3)+^a3+3a2b+3ah2+b3)+g(q3+9a2b+27ab2+27b3)+7b3]b—ci453452145.2453b—a.2»,2Bஹ=---(—ci4---cib+—ubH---b1)=----(a+b)(a—ctb4~b+ab)90222244Lb-al44cc/3a+A\4஺+஻ஹ4”/஺+3E4r,4\----[7(2+32(-----)+12(----)+32(-----)+7஺4]90424="஽7஺4+(81஺4+108//+54஺2/2+12I+/)?790831+](஺4+4஺38+6஺2ᓃ2+4஺83+//)+—(஺4+1243^+54஺2b2+108஺K3+8L4)+7//]^^—^^ai+\8a3h+lSa2b2+\Sah3+\Sh4^^—^-(a4+a3b+a2h2+ab3+b4)905^^[7a5+32(^^)5+12(^^)5+32(^^)5+7&5]90424=ᔢ஽7&5+—(243a5+405a4h+270ayb2+90a2/73+15«&4+Z?5)90323+-(஺5+5஺4b+10஺3஺2+]042ᓃ3+5“ᓃ4+/)8+—(a5+15a4h+90a3h2+270a2h3+405ah4+243h5)+7h5]32=^^(15஺5+15a4h+15a3b2+15a2b3+15ab4+15h5)90=-——(a+b)(a4+2a2b2+b4)=---=(x5dx66L

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/rஹ+1/r௃S=-^-[/(n)+4/1I+f(h)]=-^-[/(0)+4/1I+/(I)][n]i.1i=-(e-°+4e2+e-1)=-(l+2.42612+0.36788)0.63233664b-a(b-aQ4)()=_t2J_ef,VWx|4L-L=3.472x10-4஺Rs180218016151180165ஹyz{ᑡ}~YZ[\(f(x)dx=f(a)(b-a)+^-^\b-a)2L2f(x)dx=f(b)(b-a)-?(b-a)2d(f(x)dx=/()S-a)+(b-a)3L2*224
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ᑣa=µ2R+"+/z/2,c=”-/2஺ᡃ⚩⌼ᙢh=439!,"ᙢ#2384!%&'(⍝Ḅᕜ,஺,2R+H+h2x6371+2384+439u234ᵫa=---------=------------------=7782.522H-h2384-439=972.59:22

383510ஹ=>?@஻sin—=F/^d---------&IJ஻sinK஻=3,6,12ḄL%ᵨn3!/5!஻4n᜜PQR'FḄSL஺2=>4T#Toব=3sinK=2.598T6=6sin-=3,0T(12)=12sin^=12^(1-y-)=3.1058,ᵫo4’"Ih\1T%%%t)=\஺,“I5_—[Il᝞9:,41417](6)=—"(3)-c(6)=—x2.598x3=2.464,4141T(12)=-7d(6)--7d(12)=-x3--x3.1058=2.9647,IT,(12)=—T.(6)-—7',(12)=—x2.464--x2.9647=2.43062஺1515151511ஹᵨfᑡhRiQjᑖ/l%mnopq஺1rsthRd2uvwxy@d3zjᑖ{|ᑖ#}?ᑖ%ᵨ~ᓄxy@஺[3]%=lnyl=ln3=1.0986஺12ஹᵨu@w@'/x=Jᙠx=1.0,l.l1.2ᜐḄᦪL%mi%/xḄLᵫf⊤:X1.01.11.21.31.4/X0.25000.22680.20660.18900.17361fl2234ᵫu@஺=~3஺+”{—+7/,1h2/⚗=w5'஺+஻%஺4\c

391h2/^)=[/(X)-4/(X,)+3/(X)]+(J)9,2022h3/“(x°)=5^[3X0,25+4x02268-0.2066]=-0.247,0.12-240I2#M(x0)|=---x-------<—x24=0.08d3஺+&)53[)=—[-0.25+0.2066]=-0.217,#2x0.10.12-240I2|M(x,)|---x-------<^-x24=0.04,6(1+ᔉ6f'(x)=^[0.25-4x0.2268+3x0.2066]=0.18720.12-240I2#|"(2)|=---x-------<^-x24=0.08o3(1+ᔉ3ᵫw@9/,(x)=---[-25x0.25+48x0.2268-36x0.2066+16x0.189-3x0.1736]012x0.1==[-6.25+10.8864-7.4376+3.024-0.5208]=-0.2483(¡)=—1—[-3x0.25-10x0.2268+18x0.2066-6x0.189+0.1736]12x0.1=A[-°-75-2,268+3.7188-1.134+0.1736]=-0.2163f'(x)=---[0.25-8x0.2268+8x0.189-0.1736]212x0.1=£[0.25-1.8144+1.512-0.1736]=-0.18831ஹiQ[-1,1]¤ḄjᑖI=£/(x)dxḄ'j@£f(x)dx~g/(x0)+§/(X|)o234'j@Ḅ¨ᦪ©ª\«¬2/1+1=3,z'j@x,x,'jᦪ00,®¯0#4°±²ᦪ%I³´µj¶ᦪ/(x)#¨ᐭ'j@%:ᑮh¹º:

40g=10)Q+69=21®=1+¿À=0=_¼%½¾'j@#<222,9Á3:+sX]=33gxd+0|X-0-T"(x3/(—Â+/Ã)஺2ஹÄÅÆ=ÇÈ@ff(x)dx^—[f(a)+f(b)]ÊËÌÈ@¤2f/(X)dxaS-.)/(Î)ᐹᨵ³¨ᦪ©ª%¾ÑÒl@[f(x)dx«^[/(«)+4/(?)+/ম]ᐹᨵu³¨ᦪ©ª஺[=>]পI³zy(x)=i,x,x2¨ᐭÇÈ@Ë,:ᑮb—ab—a)"ভ+/ব]==(1+1)=b-a=11¨224b—af£/ஹb—a..b~-ci~~.x+/(/?)]=——(a+b)=---=xdxd222Øb—a,b—a12\b'—ab?+crb—a,b—a'pdrr/22+f(b)]=~^(a+)=---------------஺---=[dx,½¾ÇÈ@ᐹᨵ³¨ᦪ©ª஺(2)I³z/(x)=l,x,/¨ᐭËÌÈ@Ë%:ᑮ3-=(b-a)xl=b-a=jIdxd(b-=(6-a)x=b7=£xt/xd…°ᡭ…X(ᵨ="Ã"/Þi=fx2ß½¾ËÌÈ@ᐹᨵ³¨ᦪ©ª஺(3)I³z/*)=1,%/,»4¨ᐭÑÒl@Ë%:ãU

41஺6""ভ+4/["d"1/S)]='6"*6=6-a=fIdxd^[/(«)+4/få]+/ম]=Tᓃ+4çè+ᑗoy1Jo2.22'b—abf~—a'p=----x3(a+/?)=——-——=Jxdxb_arr/ஹ(4+஺ஹ//7ஹ1b—Cl2(,9—[/(a)+4A/rl—l+/(^)]=-[«-+4Axl—I+b']b-ac,2I>2x/—a2J-x2(a+ab+h)==xdx6------------------3b-aa+b\.....b-a.(a+b\^.f{331-^-[/(«)+4/1+/(&)]=+4x+b]»=---x—(a3+a2b+ab2+/)=-=I*x3Jx62%4J,b-a..(a+by,,b-a஻(a+b\,-^-[/r(«)+4/l-y-+/(/z?)X]1=-^-[ta44+4x1I+/4]1f=-~—x(—a4+a3b+—a2b2+ab'+—b4)w————=fx4dx64244½¾ÑÒl@ᐹᨵu³¨ᦪ©ª஺3ஹ'S'j@+2/(}]Ḅ¨ᦪ©ª஺[3]I³z஻x)=l,x,x2,x3,x4¨ᐭ'j@Ë%:ᑮ—/(g)+2/(1)]=1(2-l+2)=l=pJx;|[2/(1)-/(1)+2/(|)]=1(2xl-lx|+2xi=1=[xdxdJ*14*1J4,14/2/(d)-/(1)+2/(1]=#2X,)2_1X(f2+2x(|)2]=d=]%dxd-/(1)+2/(1)]=|r2x5_1x(1)3+2x(1)3]=g=fx3dxdI஺ñ-ò+2/óóñ4ᔩஹ2ᵬö÷÷øTùᡠ'j@ᐹᨵu³¨ᦪ©ª஺4ஹ'u°\ûḄ⁚\33ýᦪC,ÿ
£/(x)jx=cr/(x)+/)+/஺2)]ᐹᨵḄᦪ஺0!"#$஻X)=l,X,x2,x3,x4ᐭ
,-.ᑮ:

422C(1+1+1)=3C=2=c=L.2c——C(x]+x2+x3)=0=^xdx3__V2XY\~-ᓽ.ᓛ+஽+?3=°,..-DE272f.9C(X[+^2+X3)=9=Jx~dxXj-+XF+XF—1GH=0C(x,3+%J+^2+NF=0DOI+XJ)=0=K"x3PQ
R£/(x)dx=|[/(-*)+/(())+/(¥)],ᐹᨵ3#ᦪ஺W/(x)=/ᐭ
,-.ᑮ:-[/(--)+/(0)+/(—)]=)4+04+(-)4]=-[-+-]=-^-=f4dxx32232234435ᓃᡠ[P
ḄᦪIᨵ3#஺5ஹᵨE^⁚`(஻=2)ḄGauss
ef
ᑖ/=(yLdx(=2%)஺[]E^⁚`ḄGauss
R[f{x}dx+1/(0)+jk)ᡠ[X,f4,548.54I=I---Z-dx=----------H-x4H------------%+x9(rs99(rs1+----1+——55஺\7\/25322519,1891836ஹuvwxᦪA,B,C{a-|.ᦪ}
ᑖ[j(x)dx=Af(-a)+”(0)+Q(a)RGauss஺[]⌕|ᦪ}
ᑖJFf(x)dx=4/(-a)+"(0)+஺(0RGauss-ᑣᐸᐹᨵ2஻+1=5#ᦪ஺"#$/(x)=l,x,/,x3,x4,x5ᐭvᡂ-

43A+B+C=4=^\dxA(-a)+8x0+Ca=(C—A)a=0=”-A+B+C=4A(—+5x02+Ca2=(A+C)a2=^x2dxC=AᦑᨵWCa2=-'^A(-ᶭ+BXO3+Ca3=(C-A)a3=0=^xydx3A(-a)4+5x04+Ca4=(A+C)a4=y=£x4JxA(-a)5+BxO5+Ca5=(C-A)a5=0=[xbdx12,26102A=B=99957ஹuvwxᦪA,B,C{-|.ᦪ}
1f(x)dx«4/(0)+Bf(xஹ)+(7(1)ᐹᨵḄᦪ஺PQḄᦪ9ᔲGauss!"#$/(x)=l,x,x2,Dᐭ
-.IJJ1A+B+C=l=^\dxA+8+C=1王=-22Ax0+Bx(+Cx1=Bxt+C=—=-xdxBx,+C--B--1232/,-ᓽ-C1,1-.-AxO2+Bxf+Cx{2=Bx^+C=-=^x2dx+C=§-61Ax஺'+BxJ+Cxl3=8+஺=F=K3dx1+C=-A--46
Rff(x)dx«1/(0)+1/4)+77(-1)-W/(x)=/ᐭ.ᑮJ6326-xO4+-xfiYlxl4=A^lK-
Iᐹᨵ3#ᦪ,+=63ব6245AGauss஺

44¡¢£x¤ᑖ¥¦ᦪ}§1ஹ¨j}©⚪y'=ax+஺-y(0)=0ᑖ«¬®¯¥§{ᦋ±Ḅ®¯¥§Ḅ²³Ḅ⊤µ-¶·¸vy=gad+§º»¼஺[]ᵫ®¯¾y=y+h(ax+¿),ᓽy-y„=h(ax+b),n+[nnn+1ny“+iDÁ=Z"(Â+b)=>?7[Æ0+Ç+È*=0k=0,ᓽ=Z+kah2)+bh]-ah(n+l)x+<"ah2+(n+l)bh0A=02y“=%+ah*+"v+nbh,ÊËR%=0,x=0,ᡠ[0y஻="·Dah?+nbh஺ÌᵫÍ=Î-¾ÏÐRy(X“)DÑ=gaxF+bx-[”“FDÒ+ᑴ1n஺212,2,,n(n-l).,nah---anh+bnh-----------ahl2-non=-------222Ki=+h(ax+b)+nhᵫᦋ±Ḅ®¯¾,y"+i=y“+/[(ax“+6)+(ax“+|+b)],ah..,,^y„+—(x+x)+bhnn+lᓽyi-=ya”+x“+i)+▬-n+y”+i-Á=£[k(4+/+1)+6Õ=¿{Ö[/+(2%+1)×+6/1}k=0Lk=lLah(n+1)(1+2n+l)(n+1)ah2=-xx+-------ᱏ-----+(n+\)bh,1ᓽ3rl0ah(n+1)(஻+l)2,/,,=-G~-x+-Dah2+(n+1\)Xbh0y\=yo+~~~xo+^-ah2+nbh,ÊËRÁ=0,x=0,ᡠ[n+02y“+i=*ah஺+nbh஺Ìᵫx=nh,¾ÏÐRn

45y(x)-y=Fax4-\-bx-ah2-\-nbh]=dan2h2+bnhD;ah2-nbh=0஺ltnn2ஹᵨᦋ±Ḅ®¯¥§j}©⚪v=x+y'0

46y=1.105x3.01236352327260443898828125+0.05x1+0.055x0.910=3.32866169321644890508205078125+0.05+0.0495஺=3.428161693216448905082050781253ஹᵨᦋ±Ḅ®¯¥§K'='+”DᓃÚÛÜà=0.1efy(0.5),¶·¸vb(o)=o'y=-e~x+/—#+1º»¼஺[]ᵫᦋ±Ḅ®¯¾â“+1=ᐜ+à(X+x,,-y)n<ᡭ+1=y+-{^,+X-y++x,-[y„+h(xd,+x„-y,,)}Êᵫ=0-nnnt+l.h~.h(\-h),ஹh,ஹZ12=(1D஻+—)y„+---(X"+xj+-(x,|+x)1+n+l>0=0,h=0A,.y“+]=0.905y“+0.045(xF+x“)+0.05(xF+i+x“+]),X=0.905x0+0.045x(02+O)+O.O5x(O.l2+0.1)=0.0055Fy=0.905x0.0055+0.045x(0.12+0.1)+0.05x(0.22+0.2)2=0.0049775+0.00495+0.012=0.0219275%=0.905x0.0219275+0.045x(0.22+0.2)+0.05x(O.32+0.3)=0.0198443875+0.0108+0.0195=0.0501443875y=0.905x0.0501443875+0.045x(0.32+0.3)+0.05x(0.42+0.4)4=0.0453806706875+0.01755+0.028=0.0909304706875%=0.905x0.0909304706875+0.045x(0.42+0.4)+0.05x(0.52+0.5)=0.0822922569721875+0.0252+0.0375=0.144992256972187554ஹᵨè饧j}©⚪ᔆ‘=ìíᐸ²³R¶ìíî1>'(0)=1{2+hJhf0Q:ᦈðñòj}©⚪Ḅ¸vy=஺!ᵫèé¾-[×)-(1+஽Ò=(>ᵴ“-ᓽ2-h2-hX%+1=ô7ᡭ-?=%,ÊᵫÁ=1¾-2+h2+h,

472nhx-(—+D2/,+12h1Dᓝlimy=lim=lim1-=limnJTO/-O12+hJTO(2+h)/-o2hJ5ஹᑭᵨ®¯¥§ef
ᑖNJdfᙠ`x=0.5,l,L5,2Ḅ²³}஺(f_x2!Wù=\e'2dt,ᑣ)'=',W஻=0.5,ᑭᵨ®¯¥§.ᑮ:J)y(0)=0y\=y,.+hf(xn^y)=y+»Êᵫû=஺-.ᑮJn+nnÞ=Vo+0.5xe°=0+0.5x1=0.5F%=ý+0.5xe05J=0.5+0.5xe025=1.1420127FR=%+0.5xJ=1.1420127+0.5e=2.5011536FL=R+0.5x/W=2.5011536+0.5e225=7.2450215஺6ஹÚ/?=0.2,ᵨ▤ÿᐺḄ-ᛞᑡ⚪|Y=x+y,0

48hy=y+(K2K2KKJn+ln]+2+i+oh«/ஹJhஹ/ஹஹ…h62ஹGhh2.xz=%+H{(x஻+y஻)+2[+(1+)(x஻+y஻)]+2[(+)+(1++)(x஻+y“)]OZZZ4Z4h2h3h2h3+(M+2+4)+(1+M+2+/(N+%)}hh2h2=ᐟ+/[(X"+y“)+/?+(2+/?)(R+>“)+(஻+)+(2+%+)(x“+y“)OZZh2h3h2h3+(h+2+T)+(1+/?+2+4)(x“+y”)]hh3h3=y+.[(3/1+h2+)+(6+3஻+M2+,)(x“+yj]n644ciy„=y+—[0.642+6.642(x„+y„)]WᵫY=0.2*+,Mᵨ

4930=y+0.0214+0.2214(x„+y„)=0.2214x„+1.2214y„+0.0214n^_ᵫx0=o,y0=1*`y,=0.2214x0+1.2214x1+0.0214=1.2428;%=0.2214x0.2+1.2214x1.2428+0.0214=0.04428+1.51795592=1.58363592;y=0.2214x0.4+1.2214x1.58363592+0.02143=0.08856+1.934252912688+0.0214=2.044212912688,%=0.2214x0.6+1.2214x2.044212912688+0.0214=0.13284+2.4968016515571232+0.0214=2.6510416515571232'%=0.2214x0.8+1.2214x2.6510416515571232+0.0214=0.17712+3.23798227321187027648+0.0214=3.4365°efgy=2e*—x—l஺=3y/(l+x),0

50[lm]|gKτ=/“,K=fthDf^D2f+-,2n+n+nK3=Z“+QT
hDf“+12”D2fᡠ~h6=%+5(+/)=y„+y{/„+thDf“+^-D2f„+(l-t)hDf„+1}D?f”+•••}=K+^[2f„+hDf„+(2஻ߟ+1)/8/"+…]=K+hf“+^D+“—+஻/…_j,J?"Jஹy.+i=y„+hy”+—y+—y„+---n_,26,ᦪ*+,ᡠ-ᛞth2஻3=y+,tfn+KDf“+—{D'f+fஹDf),+-••n2ouvw▤eḄ஺8ஹlmᑡ-ᛞv▤Ḅ:hhyi=%,+1(3+3K3)y“+i=y"+X(2-+3◍+4)n+K”K\=(1).,/h஻“ஹ;(2)

51%஻+/1Ḅ=,|_ᐹᨵ▤e஺ᐭ3Pqs=721413(2)4=—,4=—,4=—,p=—,q=—,r=0,s=loᓽgᡠ,93924r+5=14+4+4=1+,|_ᐹᨵ▤e஺"+4஺Xipqs=—9ஹᑖᵨw▤u¡¢w▤◚u¡ᑡ⚪y'=l-y,y(0)=0,M=0.2,=0,y=0.181¤¥y(l.O),¦§fy=l—**¨஺$%ᵫ%=0.2*+,©ᵨw▤u¡ª,hy\=y«+2(3/"M1)=~+0-13(1-)(1y“_1)*஺^_,n+=%+0.1(2-3y“+y,i)=0.7%,+0-2%=0.7y,+0.ly+0.2=0.7x0.181+0.1x0+0.2=0.3267,0g=0.7«+0.1y,+0.2=0.7x0.3267+0.1x0.181+0.2=0.22869+0.0181+0.2=0.44679y=0.7%+0.1y+0.2=0.7x0.44679+0.1x0.3267+0.242=0.312753+0.03267+0.2=0.545423%=0.7y+0.1%+0.2=0.7x0.545423+0.1x0.44679+0.24=0.3817961+0.044679+0.2=0.6264751

52©ᵨw▤◚u¡ª,hy-y+-(3¬,-3)=%+0.1[(l-y„)+(l-y)]=y“+0.1(2-y„-y„),ᓽn+inn+1+19?l.iy=0.9y„+0.2^_ᦑn+i,92923629w-+——=1Q12710JQ/Q/.,n11111111229249691V,wVn+—=X0.3299+—=…==0.451736;01®111111119292=6.065624=055]42ᡭ+——=—X0.451736+—1111111192926.96278G/cccc%=4+——=3x0.55142+—==-------=0.63298o1r11111111—1efg1-e==0.6321o1h10ஹlmy'=f(x,y)Ḅᑡ°ᑖtuy,“|=-(y„+y„_)+-(4/-y'+3y;,_)11+ln1vw▤Ḅ,²³´µ°Ḅ✌⚗஺Y3[lm]|gy=y“+hy'+fl+ln26h2h3h2y,i=y“—hyd+,M_^),+…,»º=M+᝞:+,¼+…,2o2yL=y-᪍+gy+…,ᡠ~1h5(y஻+y-\)+-(4y*i-y'+3¬”)n+n1h2h3=5(y“+y஻-hy'+-y"-—y^+---)nhh2h2_+/4(y+hyn+Ày;'+…)-M+3(y-/iy;+À஺"+…)],^_ᦪ*n1h2h3hlh2=-(2y„-hy'+—y"--^~Â+…)+,(6y+hy"+--y™+•••)nZZO4Zh31Q/135`°ᑖtuᐹᨵw▤e,³´µ°✌⚗g:y;-ᔁ“'=-;y;஺11ஹɲᐹᨵᑡÊuḄ▤=+1=Ëᐜ+஺2%2+Íd6+dy-i+/yL஺

53M2b3ᑐ4[]|gy„=y„+hy'+y+Ï+ÐÑ4'+…,+In2o24஻,¬(2/7)2(26)3(2/7)4”-2ᡭ2Ò+——K—y„+…Zo24y„-2hy4+2h2y"-Óy4+Ô)+…~2=%-2Õ:+Öᱏ-Ø+…=M2᝞:+2/ÂÙÔ;…,2o3&Ú+%%T+஺2y“2+஻(g"+dyi+%M-2)A2Y34h=&y“+஺Üᓅ-y'+—y'',--y"+—y^+---]nG4஻3o/,4+Ḅெ,“_2ky4+2M—y™+ߟ/,4>+,•■]1.2Mᡠ~+h{by'+~ᓃ-hy"+,x+2+-]onn2o4஻3b[y'-2hy42h2y4-^-y^+-]}+2n+h2,=(a஺+—+ci)y+(—-2a+%+4+b}hy[+(%+4a—2bl—4b)—2n2222+(—஻]—8a2+3Z?j4-12b)—+(a+16%+4&-32b)—y^)+•••21f2o24Q஺+%+O,2=1^_ãtuᐹᨵ▤e,ᑣåæᨵç20+%+?+62=1஺a+4%-2-4b2=1}—I—8a2+3b]+12b2=112ஹèᑡéᓄg▤éë1)y"-3y'+2y=0,y(0)=l,yz(0)=1;yf=.nV(0)=1[]íy'=p,ᑣp'-3p+2y=0,p(0)=l,^_ᨵç,,<',P=3p-2y[p(0)=l

54(01ஹWᑣ⚪gñ=y,y(o)=$efgy(x)=e,%ïíT(3-2)প2)yff-0.1(l-y2)y,+y=0,y(0)=1,<(0)=0஺y=n$%íy'=p,ᑣp'-0.1(1-V)p+y=0,p(0)=0^_ᨵ'P=0.1(l-y)p-yy(0)=lP(0)=03)/")=-T,<஺)=-¦"="+y2,x(o)=0.4,xf(0)=0,y(0)=0,<(())=2஺X=py=q$%íx,(t)=p,y,(x)=q,ᑣp'=--q=-y,^_ᨵ

553110165'r0ஹå=0.49438-3111y—0`,ý=095786஺162ஹ—1.6M%=1.361481-31016;14ஹnéy"=/(x,y)*þÿᑖᵨ=,2y-y_+h2f(x,y),ᵨnnlnny"=lV-2_V⚪ឤ!"y(x)=$>(0)=ᑘ=0''-2/i145ஹ)*ᵫᑖ,-./012'-2/21y21-2h)
y-Jn(1+x2)yn-xy'-3y=6x-315ஹMXA=0.2,ᵨᑖ0=>⚪?y(0)—y'(0)=l,yপ=2)*Bᯠ”=5,y=2,yd=>8-22+0EF="92*:(஻=t23,4),5h2hKᐭMᑮO(1+Qy,M_+“_X&"+;"I_3%=6x“-3,ᓽh"2h(2+2xd-W,)yᵨ(4+4xX+6/)y,+(2+hx„+2QY1=6h\2x-1),nZᵫ[-\]=1-M(+1)0-5=/7,_`ᵫa=0.2M012b:hX/ஹ1.2-1000y஺‘0.2ஹy=1.0148702.12-4.42.0400-0.144y.==1.0178502.4-4.882.240b=-0.048,-gMh>2=1.07010o002.84-5.682.60.048=1.219300003.44-6.87ஹ6.096,)4=1.51329

56klm01᪷▅pᩞᧇOsḄnvw⚗01a“x"+a“_H'T+…+%%+ᓽ=0}bnvKᦪ01஺3vஹ4vḄ01hᯠ]-gᙠᦪ\ᑮhᩖ஺5vg\Ḅ01ᨵᡂḄ஺Kᦪ01-gᨬᓫḄឋ01hbᯠᙢḄ᪷h¡-g¢⍝hnv01sᐹᨵn¥᪷஺sᵫ¦▭⚪¨©MᑮḄ01ª««¬ᨵ®¯ᦪஹᢣᦪ¯ᦪஹᦪ¯ᦪ±²¯ᦪh᝞sinx,eh,lnx,᪵Ḅ01·¸±²01஺±²01¹ᨵsḄh`º»¼½¾01¿ÀhÁÂÃᔲᨵ᪷ஹᨵÅ¥᪷h]ÆÇgᑨÉ஺±²01Ê“22vKᦪ01ËÌ}bឋ01hÍÎ/(x)=0,ᐸÐ/(X)¥ᓫÑÒḄ¯ᦪh-gw⚗¯ᦪஹ±²¯ᦪÓᡈὅÖḄ2ᔠÓ஺ᡠÙ01᪷hÚÛ¥X*,ÝM/(x*)=0ᡂ/h᪵Ḅx*·¸01/(x)=0Ḅ᪷()h]·¸¯ᦪ/(ÞḄßà஺»áᙠâ᦮ᦪm,ÝM/(x)=(x-x*)"g(x),ᨴ0<|g(x*)|<+8,ᑣ}x'b/(x)=0Ḅmê᪷஺ë஻?=1íhx*Z}bᓫ᪷híX*îï஻x*)=0,/V)*0osḄឋ01/(x)=0,ᵨñò0=MᑮḄó"ôÇḄhõ᝞e--x=0஺ឋ01ḄẆ÷01/(x)=0ᙠøùḄᩩûüh᝞ýᑭᵨÿ
ᑮx*Ḅx,Ḅ£ு0,1!"Xᐵ%£&'Ḅ஺%ᐹ*Ḅ+⚪✌ᐜ⌕0ᦪ/(X)5678ḄẆ:ᑨ<=Ḅ᪷Ḅ?ᦪ@ᜧᭆCDEFGHᙢ⌱Kᨵ᪷MN஺᝞P⌱QHRS6TḄ᪷⌲?ᑖWX=YZḄᨵ᪷MN஺[ᑖ\Ḅᱯ^&_/(`)=0ᨵᓫ᪷!ᐹᨵᦈdeḄᱯ^஺ᯠgᨵh᪷ᡈj᪷Ḅkl[ᑖ\mnᨵ!ᜫᦔ஺1ஹᵨ[ᑖ\s/tஹ_1=0Ḅv᪷⌕swx<0.05஺m^f(x)=x2-x-l,ᑣ/(0)=-1,42)=1,ᡠ6ᨵ᪷MN(0,2)

57/প=-1,ᡠ6ᨵ᪷MN(1,2)/(1.5)=1—1.5—1=-0.25,ᡠ6ᨵ᪷MN(1.5,2)/(1.75)=1.752-1.75-1=—>0,ᡠ6ᨵ᪷MN(1.5,1.75)16/(1.625)=1.6252-1.625—1='>0,ᡠ6ᨵ᪷MN(1.5,1.625)/(I—)=(1—-)2-1-^-1=--—<0,ᡠ6ᨵ᪷MNfl—,1.625^1161616256116J1Q51QQX*=—(13+1_)=1t=1.59375,2168321a1!'ḄW<-(1.625-1—)=—<0.05o216322ஹᵨs᪷\s/(x)=l-xsinx=0ᙠMN0,1Ḅt?᪷¡ᑮ᪷⊈|/(/)|<0-005¤¥¦
஺?3ஹs¨3t¨2_1=஺ᙠx0=L5▬Ḅt?᪷«¬ᦋᑏᡂ°ᑡ²³´nµ¶·YZḄ¸¹mnº1)x=l+l/*2,¸¹mn`*+=l+l/x2)X3=l+x2,¸¹mn=#1+3)/=—!t¸¹mn4+1=1/Jx*-14)x2=x3-1,¸¹mnx=Jx-1ok+lx—\¾ᑖ᪆ÀÁ¸¹mnḄᦈdឋµ⌱QtÁmns=ᐹᨵÃCᨵᦔᦪÄḄ஺1)«9(X)=l+~,Æ=—ÇÈgÉ(1.5)|=-y=Ë<1,ᡠ6¸¹\ÌÍᦈd஺_____°_22)«᜛(Ð)=Ñ[Òᑣ஺'(X)=§(1+X2)3,ÈgW(1.5)|=|x1.5(1+1.52Õ=Ö◤<1,ᡠ6¸¹\ÌÍᦈd஺11_21_2_3)«(p(x)=,ᑣ(p\x)-—(X—1)2,Wu|^?r(1.5)|=—x(0.5)2=V2>1,Vx-122ᡠ6¸¹\Ûᦣ஺4)«=ᑣd(x)=5`2(/-1)2,Èg

583io=>1,ᡠ6¸¹\Ûᦣ஺|^(1.5)|--xl.5(—)22oV384ஹGs/+10¨-2=0Ḅ᪷ᑮÞCßᦪᡠ◤Ḅ¦
à:1)ᙠMN0,1ᑁᵨ[ᑖ\2)ᵨ¸¹\=(2-e%)/10,Q7%=0஺1)ᵨ[ᑖ\å/(x)=e*+10x—2,ᑣZ(O)=-1,/প=e+8,ᨵ᪷MN0,1/(0.5)=e°s+3>0,ᨵ᪷MN0,0.5/(0.25)=e025+0.5>0,ᨵ᪷MN0,0.25/(O.125)=e0125-0.75>0,ᨵ᪷MN0,0.1251~13Q1O-0.5605<0,ᨵ᪷MN—C-----------81683-1717/J=e32-LL0.03578>0,ᨵ᪷MNt,t321616325-39/J=e64_[<0,ᨵ᪷MN—64326432111173/(—)=£>128--<0,ᨵ᪷MN—12864…1283223—141/(஽)=e256--<0,ᨵ᪷MN—256128256324747227777|êë1-7-I'-i42347/(—)=e512----->0,ì᪷MN----,---5122…56256512/(W9L3)=஻955599îï42393024----->0,ᨵ᪷MN——,-----10245…1225610241QC”g*1/2393ÈgX=—(-------F)=-^=0.090332,ᐳ[ᑖ10ó஺2256102420482—2t஺°2)ᵨ¸¹\ᑣ=±±=0.12-e=0.0894829,101010

5900906391008948292—Px,==0.0906391,x=-..............=0.0905126,3104410ᓽX*=¨4=0.0905126,ᐳ¸¹4ó஺5ஹ0ᦪ/(x),«tᑗx,/'(x)÷ᙠø0e'(x)>-1,ᓽ'ম<1,ᦈ஺6ஹ#x=e(x)ᙠ%&'஻ಘᑁ*ᨵ᪷-.aA->1,/0᝞23x=°(x)ᓄ〉6Ḅ8ᓄ〉6Ḅ-9:x=4.5(;<)▬>Ḅ᪷஺'?@3x=9(x)ABCDEᦪ-Gᑮx=eT(x),
/T(x)'=——9(x)|'/(ᑘ'=I—<-<1-ᦑNa”=6'(xQᦈ஺(P(x)k᜛(O)=tanx,ᑣ(p'(x)=sec2x,P(4.5)|=sec24.5=22.5,3NᦋRZ+i=arctan,S
-(p\x)=—U-,'(4.5)|=——=0.047,1+x1+4.5ᦈ஺C/=4.5,X=arctanx=4.49372,x'=x=arctanx=4.493424஺027ஹᵨWᑡYZ:஻x)=1—3x-l=0ᙠx0=2▬>Ḅ᪷஺᪷Ḅ[\]x*=1.87938524…-⌕:`abc[\ᑮdeᨵᦔᦪg஺1)ᵨhiZ;2)ᵨklZ,C%=2,x=1.9n3)ᵨoᱥqZ,Cx=l,x,=3,X=2xQ2/(x*)__xn-3x*7=2xn+1'?@1)x=xrx=2,k+ikf'(x)~k__3x"3-3x”30k2(U)“2x23+11710555=1.888889,X=1.87945,st஺3x22—39^7^5616

60Hwf)%=/2)XQ=2,x*—3x«—1/_\_Z-J(Z+4-1)+1-+3M+ᡈ31.9x2x(1.9+2)+l15.821582x=1.9,x1.881094}21.92+1.9x2+22-38.418411582,J582,cஹ,----xl.9x(----+1.9)+1841841-15821582_X19+1923,st஺8418419558143.42+84121026542442,…----n---------------------------=-----------=1.87941115822+1582xl.9x841+0.61x84/5462043213)Xi=x*------1,…ᐸco=f[x,]+f[x,x_,X_](x-x_j),o=1,1=3,2=2,ᦑkkktk2kk/=1,஺]=O2=5=]0,/(x0)=—3-/5)=17,x,-x3-10./•(x)-/(x,)__1-172ᨴ2-1%2—%]2—3஻/--ᓰ]=&¡U"£*J==6,69=16+6(2-3)=10,x-x2-120X=2---------,1=2-----?-==1.9465745,TB&o310+V102-4x1x610+V768ஹᑖ©ᵨUᑖZªhiZ:x-tanx=0Ḅᨬ¯᪷஺'?@°±²6⚪-x*=4.493424஺9>Ẇ¶:·ḄhiNx*+1+¸¹-x>0,º»¼ᑗ=1,2,…-024x>4a¾¿ᑡ,4,…À⌴ÂḄ஺k'º»@Ãᯠ->0,/+1_&=¹Å4+ƹ_Ç=Å/ȹ220,ᡠ242xk12x>4a,k=1,2,---,x*+@-É=Å4+¸¹4ߟ<0,ᡠ¿ᑡÀ⌴k2Xk2xk

61ÂḄ஺10ஹ¼6/(x)=0ḄhiNXg=4-/(x*)//'(x*),º»=(/XJ)/(XJr.2)2ᦈÍIJ——"(x*)/(2/'(x*))-SÏX*/(x)=0Ḅ᪷஺811ஹ/ÐWᑡEᦪÑÒhiZḄᦈឋªᦈÔ<஺x>0x<0'?@1)ᵫ᜛(x)=x-£×=%-Øஹ=-X”(=-1,ᦑhiZÚᦈ஺2^l~x./ஹf(x)Mx2=-OXd(x)=-Lw0,ᦑhiZ▤ᦈ஺2)ᵫ9(x)=x-----=x------ffM2422—x312ஹßᵨhiZ6Yà/4=(),áâ:ãY᪷·ḄN-9ÑÒᐸᦈឋ஺f(x)_xl-a_2xl+a_2a'?@/(x)=x3-aäij஽-I=xk9kfg=Xk-3xn=3æ=@ᓰ+ç13ஹßᵨhiZ6Yà/(x)=l-==0,áâ:¯ḄN-9:vn?ḄX]஺'?@g(x)=x2-a,äUx=x-=~-=X"+"=—x+-^—oêk+lkxk(p\x)2x2x22xkkkk±ë8o14ஹßᵨhiZ6Yà/(x)=x"-a=0ª/(x)=l-==0,ᑖ©áâ:᪗ḄN-9:-x)/(ypa-x)2஺k+xkf(x)_xn-a_1)ᐸ+a_n-ia'?@%=/kf'(Xk)knx^{nk

62‘_Xk+llimï஻Uðᓃòlim&T00î-4)2is-2(Va-x)«Xj'k-n(«-1)%^*1,.(n-1)lim--------------------=lim----m----------is-2n[n'4ax'^-(n+1)x(]2[n\a-(n+l)x.]A(n-1)_1-n2[n'4a-(n+l)Va]2f(x)x[x'^-ax(஻+l)ax*-x]kk----=X*-------=x-----------=---------------kf(x*)_LnananxVl„/~(»+^)axk-xk+'..'yfa-Xna'4a-(n+1)ax+Xj+Ik+lnaklimߟ——=lim------~—------=lim----------is(4a—x*y18(Va-xj2ina(\a-xj2..-(஻+l)a+(஻+l)xf(n+l)(Xj-a)(n+\)nx'^-lim---------=-------=lim------------=hm----------஺J8_2na^a-x)k^-2na('\la-x)…2nakkn-1_(n+l)an+12a᝞15ஹº»N4õ=%(Xd+3”)À`a8Ḅö▤YZ஺Ꮇøù]ᐙᑖ☠3x+Qk>x*,:lim(Va-x)/(Va-x)2k+xko&T8ýx”(xn+3a)y[a-x...3xr+aVa(3x?+a)-x,(x?+3a)lim—,=——=lim----j=---=lim-------------------[?]"8(Ç4)3loo-Xk)10°(-%)3(3%+஻)Olim(7"—=lim/—11j8(7^-4)3(3x+a)J83x+a3(V«)2+a4a⊡ᐙ⚪1ஹᑨ!"ᑡ$%ᨵ'()᪷+,ᢣ.ᐸᨵ᪷01:1)1-6x—5=02)x=2—C[9]1);/(X)=X3—6X—5,ᑣ/'(X)=3X2-6,=>G0H+fr(x)>0,/(x)AICᦪ஺KLA/(-M)=4N-5ு0,/(V2)=-4V2-5<0,/(-2)=-1,/ব=4,ᡠTUV/(x)=0ᨵW(᪷+ᨵ

63᪷01ᑖiAj-2,-মj-l,0mn342mop$%ᦋᑏA2-x=e-++tCᦪujxm=2-xvḄxy+ᵫxyUV{(Cᦪᨵ{(|}+ᐸ~ᙶ᪗01j-2,-1mvj1,2m,Lᡠ$%ᨵ{(᪷஺2ஹ4=3++᝕=01,2,…Ḅᑡx021ᙳᦈ஺2Xk;/jXm=^+LᑣdjXm='--yo2x2x=xNl@+^jxm=-+->2J^=V2>l,,m|=¡-5p<1,ᵫr2xv2x12xI2Ḅᑡᦈ$%x=-+-Ḅ¥¦G᪷X*=2x3ஹᑭᵨ〉=Ḅlim,2+ᦈª+&=2஺k-KCs---------------/kX=0f-oὃ⇋,-----°I_ᵨ=±+4+1=J2+%k=0,1,2,…%2=+...+—J2+J2+••,+o³9(x)=J2+X°Ij(p'(x)=—Jo=XE[0,2]@,X)e[0(0)4(2)]=¶,2]u[0,2],,LḄᑡᦈ$%x=V2+7ᙠ0,2ᑁḄ¥¦᪷X*=2஺4ஹ;aAG᦮ᦪ+»¼½¦(¾’ḄÀÁÂ+⌕¾ᙠÂÄÅÆᨵa◀ÈÉÊ+,ὃ⇋ÂḄᦈឋ஺9ὃ⇋$%/jÌ=L-஺=0,ᑣLATÍ$%Ḅ᪷஺:jÌ=-3,ᵨÀÁxax1----ciÂx=x_/0m=Xk¦⚗=Xk<2-aXk=,k=0,1,2,…஺Cᦪk+ikf

64Mx)=x(2-ax)ÄÅÆᨵ◀ÈÉÊ஺ᵫl-ax*+i=1-ax(2-ax)=(1-ax)2,k=0,1,2,…⌴ÑÒᑮkkk\-ax=(l-ax)2",ᦇ=0,1,2,…+9Ò/=ᓃ1—(1—%)"௃+×=0,1,2,…+k+}0a1&2limx=—<=>lim(l-6tx)2=0<=>-1<{-ax^<1o0

65ÙÚÛ9Üឋ$%ÝḄÞß$È2ஹ(a);Aàá▣ãä0,åæçèéêȦë+AìᓄA""0'oA_2&àáî▣஺O.6428X1+0.3475^2-0.8466x=0.41273(b)ᵨçèéêÈ9á$%Ýð<0.3475X,+1.8423X+0.4759X=1.7321஺23-0.8466x,+0.4759ñ2+L21479=-0.8621(a)A2ÄḄᐗóôõöd/=2,÷-,஻)+KLAAàá%▣+ôõ%=஻ᡝ+=…+"+ᡠa%=%—=—j_=ᕖ+ᓽ&awawàáî▣஺(b)ᶍ஺4ஹ;AAn▤ý᜻ÿ▣ᨵᑖA=LU,ᐸLᓫ▣U▣AḄᡠᨵᙳ!"஺(1oஹ(11U\&'()L*UᑖᙽL=M,I**g),ᐸu=ஹL(”-k)xk^(n-k)x(n-k))ஹ°(“-/:)B4(n-k)x(n-k))12.k▤ᓫ▣Ugk▤▣ᑣAḄk▤\LU\,7ᯠ9᜻;஺kxkkxk7ஹ=A>?@A▣BCDEFGHIJKALᓄᓽOᐸ0A2A-(aij)>&=ভRn'S(1)AḄ>ᐗW%>0(/-=1,2,•••,»)R(2)4>?@A▣R(3)`)<%(i=2,3,…,஻)R(4)AḄe>fᨬᜧḄᐗWiᙠ>kR(5)maxa'2)ᡠᨵk,|,}<1஺&'((1)~⚗=(0,0,…,0,1,0,…,0),i=l,2,…,஻ᑣA>?@Ai▣ᡠᨵ7x7Ax>0o

66(2)42ḄᐗW஺a,j=2,3ஹ஻)A>?@A«ii▣,%=%,i,j=1,2,,ᡠa/=%—""""=a/-ᓽ"=ᗔ,«nᓽ>?▣஺2(3)ு0,ᡠᑐ=4I2=0"Iᒹ4%஺«11«!1(4)ᶍ஺-21-3-1-310712ஹᵨDE-LHAḄ⌮▣S-124-210-15312OOOOOO----22223OOOOOOOO242OOO242OOOOOOOO5OOO1311OOO2-2--2-2-_31-00019132~2~22O8OO--2-2-2-201-9--173-2001111211->21O2-2---OO02--2--010222222221111O一151OO05---001-2-2-2--2~2222O38OOO38OOO2OOO92OO-一871±OO257OOO-一一-O4055OO43O2525-OO4311O-

671642316423100010052552552552513121913121901n0010525525-525—525T87118711c0c1—0001-0525525525525c17314I31450c0-1000525525JI85-178517.-,ஹ,ஹ4182316]1000--858585173362141301()0——ஹ851742517195380c10-8517851731450c01——-851785174182316'8585851733621413851742517ᦑI=o1953885178517314585178517-2-1000-1-12-100013ஹᵨH>Ax=b,ᐸA=0-12-10,b=000-12-10000-120

68&(11125ᡠ᜛5=£=4=£63=!=2=£¡0323-214ஹᵨᦋ£Ḅ¤᪷H-11&(—2319'9V15ஹᑡ▣§ᔲᑖLU¬ᐸLᓫ▣U▣®¯§ᑖ©ªᑖᔲ«I஺123111126A=2418=221C=251546733161546&(AḄIஹ°ஹ▤ᑖ±1,0,-10,ᡠA!§²³ᑖ▣Ḅ´µ¶ᣚ¸K¹஺BḄIஹ°ஹ▤ᑖ±1,0,0,ᡠB!§ᑖ▣Ḅ

69´µ஺CḄIஹ°ஹ▤ᑖ±1,5,1,ᡠC§»ᑖ▣Ḅ´µ¼ᑖ«IḄ஺16ஹ½¾x¿ᑖ⌱ᐗWᑖH᪾¼ᵨÃH18ஹ=4=''ÄÅAḄ¸ᦪᑡᦪ2-ᦪÈF-ᦪ஺0.10.3&=max{0.6+0.5,0.1+0.3}=LI,||A|,=max{0.6+0.1,0.5+0.3}=0.8,0.60.10.60.50.370.33-“A0.330.34J'0.50.32_n37-033R—AZ|==(2-0.37)(2-0.34)-0.332=22-0.7U+0.0169,0.330.34,0.71±A/0.712-0.132711271218z=--------------------------=----------------2200vÉ114==0.839஺ML=V0.62+0.52+0.12+0.32=V0?7T=0.8426஺19ஹS(a)(B);MIFÊËÊÌ஺yjn(a)IWL=Í5KIM=Zk14஻max|x,.|=஻|Ï஺i=lÐMS=,?ig20ஹ=Ñe/T"9᜻;={R"IᔣÓᦪAÔ|Õ=Öᑘ஺½'|ØÙᔣÓḄIÚᦪ஺&'(7ᯠÛ=|ÜÝ0Þ=||M=\CM=ßIpஹ

70X1+x,=P?@AAÔIkL=¬Ax,x"½'|.ÙᔣÓḄIÚᦪ஺[']A>?@AᡠHA=¬Ar,é'=>0,Üh=ACXCX
2=yc2xTAx=|c|VxrAx=ËÏ9Iki+஽IS=¬4¬ᓛ+%2¬X]+=¬X]+X2y4ᓛ+X2=x[Ax+x[Ax+xRAX]+x[AXvÉ|||H"ᔣÓḄ]22><ü¬ý{Ñ=%max|x,.|=%|xþ,Élimÿ=1,ᡠᵫᜳឋlimj=kL஺23ஹxyឋ!ᐵ/”0&'ᨵ)++,=-||2+/2஺[]xyឋ!ᐵ2y20&345y=cx,cN0,ᑣ-+9=:x+JO':x+y+=/x+/y+y0+yTy=|x|>+||y|>+2xTy=IWI2+H2+2/cx=IWI2+c211cxe+2cxx=WI2+CD+ZWI>FG=:i+c+2M=:M+cM+2=:M+I+2|X+>1TM2+N2஺M1b+ᑗ2=P2+/2,ᑣᨵQ=D2/12A஺ST4x+a2y=0,ᑣ0=@x+5%x+%y+=W|Z+2[+▐]ᓽ-M1=_Z+2`a||bI+acJ>=:%|b+%/dᓽeᙠ3ᐰhiḄ`,஺2,FGxyឋ!ᐵ஺

7124ஹᑖlmnop(rs)S,,={xIWL=l,xew}(v=l,2,oo)□|}~=£hpo(1,0),(0,1),(-1,0),(0,-1)h⚔Ḅஹh1=1Ḅ஺12=12ᓃ2hᙊoh1Ḅᙊ஺|x|-max|x,.|hpo(1,1),(—1,1)(——1),(1,—1)h⚔Ḅஹh2yḄ஺25ஹT||R"(ᡈC")ḄQᦪGPQ᜻(ᡈ¡)¢▣¤¥ᦪ-|=¦§|,Ml=|PAPᧅ26ஹ5DஹஹMl,hª¢▣«¬ᦪeᙠᦪ®£ு0,°±QᑗAc²³"´<||A||,4c2MI,0|~ᵫᦪḄ¶·ឋeᙠᦪG஺2,°¹GHs(W,2H,ᑣᨵaM´<\\Axi7228ஹ5AhÏ᜻¢▣ÇÚ=minÜIk'llv*°MA/IM1|~ChÞ||=ᘵT,-----J?=max,ᡠ¹஺Hl.°MW-minCá||||v29ஹ5AhÏ᜻¢▣,|k|᎔|<1,Ç(A+<54)-,eᙠᨵäåcond(A)|A&(A+M)1|D<---------TTI-cond(A)IMHI|~ChA+□=A(/+AT▢èᑁêPA1I<1,ᡠᵫ¤ᳮ18,/+ATìÏ᜻FGA+&LÏ᜻ᐸ⌮eᙠ஺5(A+(54)(x+ð)=Ax,ᑣ&=(A+M)TAx-x=[(A+(54)T-]Ax,ñᵫ(A+SA)Sx=—34)x¹]=-(/+A-'3AY'A-1{8A)x¹A-1-(A+3AY'=(I+A-'3Ay'A-'(^A-',FG+AA^\1A-A-1-(A+t=(//硼AATN一<一/+A-A-硼A-2o30ஹ¢▣óQôÓQᦪᡂhA=~~,×=±:&M“d(A)8ᨵᨬcÍ஺224j|~ᵫ4=&¢▣AÏ᜻"FG111ú

73cond(A)^=A~]A1+,1,—1+2>-max{22+/1,1+1}=max<8822=(|+2).max{3|2|,2}ñû6&,o|,maxü,2}=2FG(|j|+2)-max{3ý,2}>(1+2)-2=7ocond(A)xI4&maxᑭ42}=3ûFGco஻d(A)8=(|j|+2)-max{3|/l|,2)=(1+2)-3ᑄ=3+6ᑄ>7஺ᡠco஻d(A)8=7"ᨬ$,%"&2ᓽ4=±±2஺3331ஹ+A,-./01▣3ᐸᑖ6,A=LOZZ,ᐸ:;=஺"2ᔆ>?(a)cond(A)=[cond(W)]2d(b)cond(A)=cond(W)cond(W1)o22222[?B]ᵫE=F஺1/GW,WIJ2(A)=22(tV),=4((WT)T)="(WTN)="wT),PQA(A1)=R(WT),ᦑT(A||,=||W"$14TM%Kl=lU1VN12TM%,(a)co஻d(A)2=W|XY=||w1|w|=[||W-|||H]2=[^(IV)12222যc,஺஻[4)2=|4F|Y=||\X>||]஺r=(k-1||M2)(ll('vTrllkT||)=condOV)cond(W)°222221009932ஹ+A`aAḄᩩdᦪcond(A)(v=2,8)஺r999810099-9899[6]ᵫA=IJ,PQ999899-100-9899-989919405-19602(A-1)r(A-1)=99-100199-100-1960219801

741/1-1940519602ᵫijk-l")|==22—392064+1=0,196022-1980110099T1009919801196029998J|_999819602194052-19801-19602ᵫ◍-ATA\==22-392062+1=0,-196022-19405ITno=J,="19603+p4277608,PQco஻d(A)2=|AT|,M=19603+)384277608஺39206஺=199M|,=199PQco஻d(A)8=JA|,=199x19939601o33ஹ?Bq᝞sAt/u▣ᑣco"d(A)2=1஺w?BxyAt/u▣ᑣAT=",PQAzA=/,{-lEjqM=/ᦑ|2=|„=L”஻dভ2=~B|=1஺34ஹ+A,BeR"*"3M,᧽ஹ"1▣Ḅaᦪ?Bcond(AB)6:1\31-1ஹஹ<3-12ஹ(1)2-13x0](2)111x-422C-2(21-1"<-3>/’12-334ஹ’15ஹq23ஹ14ஹ-183-1--1X,L-15(3)128ভ0%2♦11116J4Iஹ3,/13,ஹ31—11kX4>2,7q'X1)21]’0ஹ(5)223x3o2ojC-32[6]q1)-1▣w1▣¡ᣚ,

75♦1-13](\X]=12-130-0-35-6ᦑ«¤2=2஺\1-21-5)10-10—2,,X3~0(2)-ᦪ1▣Ḅ¥1▣¡ᣚ,/ஹ/3-12-33-12-3(3-12-3ஹ¦41¦41111-4->0---3->0---3333321-1-3¦57C,ஹ11110-——-100——1331147,(3)-ᦪ1▣Ḅ¥1▣¡ᣚ,12314‘12314ஹ%1—101280128,ᦑX)=2o24113]ஹ00-5-15?X3-3(4)-ᦪ1▣Ḅ¥1▣¡ᣚ,’12-33415ஹ<12-334151()37s15222-183-1-1-15¦53219111160----4434<31-112>¦77¦7ᓛ=1<444]x=22,ᦑ«X'12-33415'12-33415/=337<15¦37\15¤4=0A0---5—222222T¦¦1129c¦112900——1100——113636¦¦735ccc91c00-—7000—01361337(5)-ᦪ1▣Ḅ¥1▣¡ᣚ,’1210]<121011210Xj=12233fo-213-0-213ᦑ,ᑍ2=-1஺-302)10-11X3=12ஹᵨᑡ«ᐗGauss>6ᑡ:

76/\/\’12-334ஹ´'15ஹ’123ஹ*’14ஹ-183-1-1XyZ-15(1)012X2=8(2)1111x633417□ஹ3111kX4>[2;/\(-3261'4ஹq-i1ஹ4(3)10-70=7(4)5-43X2—-12o15—15JkX3>qஹ211JI>ஹ"235ஹ(5](5)347x=60:J33;\x:'123ভ(24113ஹ24113X1=1[6]প0128-01280128ᦑ<=2஺º112412314J515%3=30022)’12-33415]<-183-1-1—15]-183-1-1-1512-33415—>1111611116131ஹ31-112)-112)’-183-1-1-i5]r-is3-1-1-15)7W537510-10332662-07171737171731o61818661818603_75621J710-1j526331'-183-1-1-15ஹ83-1-1T5)3_7*-1037510=126622662-)50A50o஺”850X2=2(2)00ᦑÃ2727927279X3=314ÀHo91=000000ÄV93JI251

77

7803ஹᵨ1▣ḄÅÆÇÈᑖ6>6:1ஹ஺1020ஹ11020ஹ010101101w6xᵫIJ>62431221010%0101E2,1ᨴஹ’5ஹH=51020ஹ’5ஹX]=101Ë3%=3,Í1013=1ITVITV121,17Ë=6216x3—2Ì”0107=42Eஹ4,A=24ஹᵨÎ᪷ÐCholeskyᑖ6Ô>6:Õ23ஹ,ஹÖஹ<422Ü'3ஹ(1)220X23(2)210163012E3,2122w6xᵫᦪ1▣Ḅ-./0ឋ,IÝ&=,ᐸ:L,ÇÈ▣஺$⌴6ஹஹ□323ஹn2A/3V6-V6(1)22u=-------333ஹ30ফV3-V6V3V3\/ஹ%Öஹ>6⌮á,3ITÃ,33V3-V6V37%%/\´=1,>6=yIT

793ஹஹá2’42222112Ýஹ\3ஹ3(2)21011330஺>613%=6ITVË2,21270¦17,101E>3)G,2>65ஹᵨᦋḄÎ᪷LOZᑖ6Ô>6:ஹஹ1ä"1010>61Ë16IT%6,53042173733ஹ11ஹ3Rஹ3yT1>612X22Ë3ITæX2=-1஺1X3>2å29=273>7

8011--1\1zr\2\22y31I1111o求解-6可得--y22222711y371o-o-72L217/3Já=314422(4%2,>6\_,10x29ËITx222221kX3>⁠,12>3722,26ஹᵨçè>6Ç-È:2X]+x2-32x1-x2=02X]+£=1X]+2^2———3—X]+——0X]+3X+x=223প49ফ4বV3%2—7%3+4%——10—xo+2ê3j4=0x2+x3+x4=22X3+5X4=2—F+2X4=52%3+%=0w6xëçè-ᐸ¥1▣¡ᣚ,ஹ21003"21003ஹ3912-30-30-302~203-74-1003-74-10x=04W0J°)I஺02527X3—1ìTᑮqr21003ஹ'21003ஹx2=-13_,93¦95i=20--30——0--3022-»2200-14-100-14-1ஹ00252,000130J

81\2-1000ஹ"2-1000ஹ12-1000--100->20-12-100-12-1000-125,ஹ%4=41°0—125,01ìTᑮqF=3(2)"2-1000ஹ\2-100x=22j3jï()jj1000--1002x\=124j4j00--100()j—10335ஹ00-125)000-514121001ஹr2loopro131020-10-—>220111201112ஹ00120,ò4G2ஹ00120?(3)"21001ஹ'21001ஹ,ìTᑮq■ò3=-153%2=1530-100-1022ᑁ=022->->7370U0-3100-1—5555oj714ஹ0012000------77ஹ+x=(3,—1,5,8N>IMHLö஺w6xW,=|3|+17+15|+|8|=17஺|÷=rnax{|3|,|-1|,|5|,|8|}=8஺H=732+(-1)2+52+82==3¡஺28ஹ?Bq1)|÷ùᡈ4Hxi8]2)||xL<||x||<7^11^02w?Bxi)M=ü,iæM=£iÃ஻þ=ÿL஺1=1llxll=maxlxJ=/(maxlx.l)2)11llo°i3"v1=HL4J஻(⌚2k|=Gmax|x,.|=

829ஹᑖ!"#ᑡ%▣ḄMbML*I/஺,-.(1)Ml=max{4+|-1|,|23|+6}=9,ML=max{4+|-3|,51|+6}=7,4-14-117-1878=ᵫ-36-36-18452-1718=22-622+441=0,11182-452=62±J622-4x441=3i±2>,2?@||A2=BCDE=731+27130=V26+V5o(2)RM=max{2+|-1|,1+4}=5,|H,=max{2+l,|—1|+4}=5,j_520-AZ|="=22-222+81=0,-N1122-17OᙶQRS=11±2T2?@Mb=AMmaxS")=g+2=V10+lo‘1111ஹ-11-1110ஹ"%▣஺=ḄW*⊈*Y஺2I—111J-1-1I,-.|஺|Z4,|Q|L=4,78Q7Q=4/,ᡠ]I஺1=2஺

83^_`-aឋcdeḄfghi"jklᢝᜧopq%▣ḄpqឋḄᨵᦔᦪu-hvᡃxaឋgᦪcdeᦪu-hḄ2yz{|⌕Ḅ~⚪஺ᵨfghḄᜐᙠ◤⌕᪆ᦪ%▣ḄzᐗcdḄ⚗*7@ᜧopq%▣*ᐹᨵஹd᪀ᓫḄ஺ᵫfgḄᦈ¡ឋᦈ¡¢£¤cdeḄ¥ᦪ%▣¦ᑗ¨ᐵ*7ªfgḄ⌱¬fgḄᦈ¡ឋᡂ8¯°Ḅ±²³⚪஺,´µ.fg=Bx(k)+fḄ¶ᙳᦈ¡¢£´µ8Rk(B)=m¸*Iok,´µ.fg=Bx(k)+fḄº»ᦈ¡¢£´µ8R(B)=limR(B)=-Inp(B)஺kuN¾¿Ḅv*º»ᦈ¡¢£¤ᡠᵨḄᦪÁᐵ஺7ª*ᨵÂÃĺ»ᦈ¡¢£Å8ᦈ¡¢£஺5xj+2x+Ç=-12?1>Écde<-X.+4X+2X=20,232x-3X+10x=3l23(a)ὃÍᵨÎÏÐfgh*ÑÒ-ÓÔÕfgh-ªcdeḄᦈ¡ឋÖ(b)ᵨÎÏÐfgh×ÑÒ-ÓÔÕfgh-ªcde*⌕"Ø5(A)2<.0~4ÂfgÚÛ஺"521ஹ,-.(a)ᵫ¥ᦪ%▣-1428ÜÝᓰ%▣Ïß*ᵨÎÏÐஹÑஹ2-310,Ò-ÓÔÕfgh"-ªcdeᙳᦈ¡஺,àá-8□=-4,/=3/3=2.(b)ᵨÎÏÐfgh:(*i)=D-\L+U)x(k)+D'hx+]ஹ]ஹ(21)0--åæஹ5555জ21ஹ'-12ஹ52-10220——--0-²)+544422-30331\71\713_1510J<10>ᵨÑÒ-ÓÔÕfgh:

84²+1)=(O2L)-'Ux*>+(D-L)-1b<500Y7o21ஹ00YY-12^-140002í+-14020-3e000,2-393,ஹஹ1000055’02r112ஹ1110002x(i,+020204204,003,13I131404010>-404010>/\ஹ21[120552511122”)+010205112102087JO7002ஹÉA,ðñòᓽMILML>1,ôᦪI+A+A2+---+Ak+…Ãᦈ20¡஺0000,ðñ.øᯠ|K=ML=2ு1,ü78ý=0,ᡠ]202010M=0þ^>2í,ôᦪḄuÿ/+A213ஹ⌱ḄA,ᑡ#,#,…ᦈ஺/IAḄ"#ᱯ%&'x)*Ḅᱯ%ᔣ,'ᑣ1-Anx=—x-^Q,./0஺n

85\ax+ax=b54678}i]i22t4ஹ2349:;<=ᑁ+a22X2="2?@--BC-/2Dᔆ”@G=1,2,…@஺----஺2ᑁ"""@a22JKᵫMN9:;

86a\\0—Q1200Y஺,L,U,b஺2200"஺210ᑣᵫ9:;<\0'x{k}=D-'[b+(L+U)x(k-')]=D-\L+U)x(k-l)+D-'bᓽ^\_9:;<'./ᦈḄᐙ⌕ᩩV0£)T(L+U)<1,/0-%-1«110-a1?a\\f«+஺)]=oᵫ-1a22.~a2\0&L0a222%_p2q]2a21%2a21஻"Z)T(L+U)=0\0᜛[0T(L+U)]=ᦑ0nAaiia22a22஺X]+0.4X+0.4X=1X14-2X-2X=123235ஹ234(a)«0.4xj+/+0.8*3=2{(b)X]+ᑍ2+~3=1{0.4.x,+0.8*2+/=3+2X2+x3=1ὃ234Ḅ^_9:-9:Ḅᦈឋ஺'10.40.4ஹ(a)ᵫᦪ▣A0.410.8\,0.40.8171Y0-0.4—0.4ஹ(0-0.4-0.4ஹB0=Z5T(L+U)=1-0.40-0.8-0.40-0.8'ᵫIA-0-4-0.80,-0.4-0.8o>/I0.40.44/-=0.420.8(2-0.8)(22+0.82-0.32)\,0.40.82(2-0.8)(2+0.4-V048)(2+0.4+7(X48)=0p(B)=O.4+VO48>1,./^\_9:ᦈ஺o

87(1ooY’0-0.4—0.4ஹG=(D-LY'U=0.41000-0.8ஹ0.40.81)\00/1,ᵫ[100Yo-0.4-0.4'fo-0.4-0.4"=-0.41000-0.8=00.16-0.64ஹ—0.4-0.81000.160.8,20.40.4|2/-G|=02-0.160.64=2(22-0.962+0.1152)=0-0.162-0.8\=2(2-0.48+70.1152)(2-0.48-Vo.1152)=0p(G)=0.48+70.1152<1./-9:ᦈ஺12-2](b)ᵫᦪ▣A111\,221Y0-22’0-22ஹ8஺=0"(L+U)=1-10-1-10-1ᵫ4-2-20J2-20,22-2|2/-B|=121=A3=0\,᜛()=0,./^\_9:ᦈ஺()222qooY7o-22ஹG=(D-L)7U=11000-132UI஺00,ᵫooYo-22]¢-22ஹ1000-1=02-30oj10-2¡஺4"2,22-2|2/-G|=02-23=£(ᑖ+8)=/1(/1—2")(/1+2¥')=0\,0-42+2p(G)=2¦>1,./-9:ᦈ஺6ஹJlimA*=AḄᐙ⌕ᩩV)§ᔣ,x¨ᨵlim=Ar஺ZK—>00jt->oo«§ᔣ,X,¨ᨵlimA^=Ax,ᑣ¬®xᓫ°ᔣ,4'ᓽ0

88lim4=A,±²³ᯠᡂ¶஺kT87ஹAr=A,ᐸ¸A¹º»'¼234Ḅ^_9:)ᔲ"»ᦈ¾ὃ¿⚪5(a)234஺"»'³ᯠ5(a)¸Ḅᦪ▣)¹º»▣'n^\_9:ᦈ஺111⚗"Â"ÂÃ51iix----&—x="?24344428ஹ234'111~~X\"Ã/+Æ=Ç442111----X+X^-Xi24(a)J234Ḅ^_9:Ḅ9:▣ḄÈÉÊ{(b)J234Ḅ-9:Ḅ9:▣ḄÈÉÊ{(c)ὃ234Ḅ^_9:-9:Ḅᦈឋ஺110"44j_011ߟ"44ᵫᦪ▣A\,j__j_104~4j__J_014~47I10004444q1_1100004444(a)=D-i(L+U)=,ᵫ1J_100004441_]_2000J4J4/1_12044I]_0244=Ë(£_{)(1+{)=0\,P(BJ={o/J__1A4~4J__1024~4

89-I/'1000ஹ11000100441]_]_G=(D-L)T1J=1000-4-4440000-014ஹ0000b\由/!]_r/XJo/0010ஹ44nO000044]_100=-1J]_44000=4441100-O0000841147ஹ0000701088>0~4~402__L_1M/-4]\=Í(4";)=0\᜛(G)=!஺G|=00A.——8800Bc@ÑA)ÒÓÔᓰÖ▣'×Ø9:¨ᦈ஺9ஹᵨSOR2234BᑖÝ®ÞßÑàá=1.03,஺=1,«y=1.1@4xj-x=12"ᓛ+4X-X=4{23-M+4å=-3æçX*஺⌕JèQ*-<5x10-6ê9:ëì'íîï"#6y&ç»9:ᦪ஺Bᶍ@஺5xj+2X+£=-12210ஹᵨSOR2234B®ᗂ=0.9@<-ò+4£+2£=20{⌕Jè2~1"3X+10x=323QGó-ôRs<10ஹê9:ëì஺

90‘521ஹ[]ᵫᦪ▣A=-1420=0.9,L=(D-coLY'((1-(y)D+coU),(aஹ2-310?f=0(O—ᡈ)ú\,-1‘500ஹ"0.5-1.8-0.9]=-0.94000.4-1.8J.8-2.710yஹ001,ý__9__2_ஹ0010-25-505'().5-1.8-0.9ஹ21o919981c0.4-1.8=200440010002000ஹ(01,-531271-53174795879120000400lojL40000100(JOO20()000Ja([ÿ8ஹ0‘5007T2]5J12)ὡ940bf=0.9-0.94320=0.9-020=,ஹ3J2004ஹ3J100()J.8-2.710>-531271177]74(20000400lOjUoooooJᵫx(*+1)=Lx(k}+/\0஺[æçx.=—4,4=3,û=2]w11ஹᨵAx=b,ᐸA!"#$%▣஺()*+0x(z)=x*)+°s—Ax"))3=0,1,2,…)567890<&<<=>?()@ᦈB(ᐸ0

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