数值分析课程课后习题答案(李庆扬等)

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x(27.982-A/783)=…+n2W/(yo)=^*(^)-(27.982-7783)=7783-27.982,iO

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7(X-Xo)(X-X|)(X-X3)max|/2(x)|max-------------!-----:——.VQ—A*—%%(x-x)(x-Xj)(x-/)2022(x—x)(x—x—h)(x—x—3h)000LMN=max(2/2)A(-/2)=—ymax\(x-x)(x-x-=(x-x-3/i)|000/(x)=(x-x)(x-x-h)(x-x-3A)0QQOᑣ=x—(3XQ+4/?)x"+(3x+8//?+3/J)x—(x+4/zxj+3h~)f\x)=3x*2-2(3X(,+4h)x+(3x+8xh+3h2),/0᩽XYZ[o_2(3x+4//)±74(3x+4/?)2-12(3x^+8xh+3h2)00o6,\]_(3x+4/i)±V7/?_4±V70--=X(\τfl3°34-y;l4—V^71--\;1—5—V71/z-3/(xH-------h)=------hx------hx--------h=—(14V7—20)/i',03333274+<4+V7,1+77,77—5,1b3f(xH-------/z)=------hx------hx------h=----(20+14J7)/?,n°333327dᯠ/Go+4,h)')=(y-x)*ᑣyz{/(>')=(y-x)kḄn▤~ᨽ⚗,>y=x,ᓽHp஺

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fkgk+i+f8ki-fkSkLpÖNk+Mkkk+=(Ai-f)gi+=(g*+i-g«)=Mkgk+i++kk+1.I12ஹpÖXg3=/.g“—/ogo—Zg"+M஺k=OA=OLpÖN]1yr,!ZfZk+2^+1⚚=E(fZk+gk+i⚚)k=ok=ok=oᦑp஺,å.!=Z1/(g&+i-g*)+g*+i(/*+i-/ᨴ=Z(g“J*+i/g*)=/"g"/og஺k=Ok=0w-Ii3>pÖqZ'x=4v஻èᡭ஺j=OJLI.?!LpÖNXx=Z(ê>Úᑜ)=-ê)’()஺j=oj=o14ஹf(x)=a+a,x+---+a_,xn''+%x"ᨵníbîï᪷x”/…ñpÖ0n»xVJO,0

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xnx,஺eF(x)"cf(xV)["°,⃁,x,=--------=--------'fl"—,)xfj(Xj-()f=o/=0[]1),ᵫoVf(Xj)=CL-------------=cf[x,x,---,x]Q1nj=°n(Xjf)i=0ᵫ„]v+(Xj)="n(x-x,.)>=on(x.-x,.)77ஹf<ᑅ016ஹ/(x)=/+/+3x+l,>/[2°,21,27],/[2°,21,---,28]=^—^=-=0o8!8![?]/[2°,2',-,27]=q=1,/[20,2',-,28]o17ஹ@ABCDEFᱯHIJ⚗L&*)=/">0"—M)2*—4+|)2/4!,(4,4+1),NᵫO>PᑖRBCDEFᱯHIḄT▲஺Q[?]VP30MP33,T▲஺জ)+—hmaxX஺27119ஹ>YZCᦪ\]^4CḄ_⚗`P(x),abcd+(0)=P'(0)=0,/1)=ᡠ1)=1,Pফ=1஺

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X,&=3X3x=3x—=2.145,nX“_X"_10.53-0.45800210009c5òòm—2—00o-2.862-þ01414m]2.7541ÿ23ó▣`0-2-0m2=2.413,m2,55òò4c332.0814m300-2-7742.14544000-27S(x)=^[ya(x)+m/3(x)]஺JJjij=025ஹ/(x)eC2[aᔣSQ)᪵ᩩᦪ1)[\f\x^dx-[[Sr(x)]2dx=[[f\x)-S\x)]2dx+2p7x)[/7x)-S\x)]dx2)/(%,.)=S(xJ(i=0,1,…,஻)!"#$%⁚'(a-x

15fs"(x)""(x)—S"(x)mx={S"(x)"'(x)—S'(x)]}<-j"'(x)-S'(x)]S"(x)dx=S\b)[fXb)-S\b)]-S\a)[fXa)@S'(஺)]-A^[f\x)-S\x)]dx=S"S)"'(b)—S'3)]—S'(a)"'ভ@S'(஺)]@A[f(x)-S(<=S"3)"'(b)-SQ)]-S஻ভ"'ভ@S'(a)]FGᦪHIJKL1ஹ(a)ᑭᵨPQRᣚTUPQ#VWḄY឵[ᚆ]⚗;(b)`/(x)=sinxᙠ0,^fg1h3Y឵[ᚆ]⚗ijUkliJmnḄopq᪍sᦪtᑖhvwxUyz஺[](a){x=a+(b-a)f,ᑣY឵[ᚆ]⚗#B„(/,%)=[\-]ᜐ(X),ᐸ!”(X)=[(b-a-xy-k஺(b){X=5f,ᑣY឵[ᚆ]⚗#(=f/(6(x),ᐸ!P(x)=>(9x)5k2஻2Bi(X)=£ᑘপ=/7/.»=sinOx^y-x^+sin^xx=+x=x3”(/x)=Z/(K)(X)7(){(/)2+ᔩ2+"Y-"O=sinOxf-+sin—x3x(--x)2+sin—x3x2(—~x)+sin—xx3(2J623223.71.23-732/஻ஹ33/%223ஹ3A/3.7123ஹ3=¡X(----X)-H----X(-----X)4-X=(----X~~TCX.^+X')H-----(—X-X)+X*22222422=¥X_§%(2_¨©2_J_(3ª_5)1842

162^g:(a)m<v"k(n\B«,x)=£f(-)Pk(x)=Ef(`)x\\-xy-kzk=0஻A-=o஻1kJ³஺*´_____0_____"(@µ¶஺·஻k\{n-ky.tf(^-l)!(n-l)-(^-l)!¸¹'")%)*(1º4=xx+(l-x)r'=x*=o᝕!(஻-1—᝕)½3ஹᙠᦪ¾¿À6Ḅ]⚗!g/(x)=sin4xᙠ0,2ÁḄᨬÃ@ÄHI]⚗஺®Wᵫsin4x,xe0,2Å0-lÆsin4x

17ஹsin——sinO?9Mᵫù=-----)61=/z(x)=cosx=---------------=—X?=arccos—22b-a71712~ᨬÃHI]⚗#,ஹ21τ220+arccos@y=-/(a)+/(x)+%(x—aX?)=-sin0+sin(arccos—)+—(x-----------———)22227T7T27ஹg/(x)=e*ᙠ0,1fḄᨬÃ@HI]⚗஺®Wᵫq='ম-f\x)=eX2=-—ᓃ~=6-1X,=ln(e-1),ᨬ2b-a1-0Ã@HI]⚗#ஹ//ஹ1Z஺+ᐗ2\1r0In(e-1)T/ý/0+ln(e—1)y=—f/(^)+/(-^2)1+a\(x------=~e+e+(e-l)(x-----------------------)oe100—1=@+(e-l)x——ln(e-1)=(e-l)xH------------ln(e-1)22228ஹ᝞ÿ⌱
r,p(x)=/+஻ᙠ—1,1ᨬrᔲᵫmaxp(x)=max+r)=1+r,minp(x)=min(x24-r)=rᨬ14-r=r,r=—L2ᵫ!ᳮ7ᙠ-1,1ᨬḄ$%&⚗()—1)=%2—gg=஺9ஹ,/(%)=/+3/-1,ᙠ0,101%ᨬ234&⚗(஺,ᡠ01%&⚗()7(᜜ᑣᵫ!ᳮ7/(%):(%)=T(x)=(8x4-8x2+1)=x4-x2+4Iτg2(ᐗ)=/(x)--x2+-)=(x4+3x3-1)-(x4-x2+-)=3%3+x2-Oo10ஹ

18T1Z“+1)=T„(z),re[-1,1],T*(x)=<11ஹJKL"(x)Nᙠ0,1PᩗP=S$ḄTU&⚗(஺Vx-x212ஹᙠ-1,1ᑭᵨZ[᩽ᓄ0/(X)=arctanxḄ1%4cᨬ234&⚗(஺2"-1ᵫ⚪eZ[⁚g)cos——k,l=1,2,3),8ᓽX=cos),p2=C0S^X3=COS-|^,X=cos(4,wU0yz஺)஺413ஹ,/(x)=eᙠ-1,1ḄZ[᩽ᓄ4cᨬ234&⚗()L“(x),}17-0ILᨵK஻1ᙠᦪᡃy4|(ᑘ()-L„(x)|

19/p1L(x)=x-3!+5!,¤)¸inx-LsO)]<,=0.0002,¹¥)5x5=—r+-x3-—x,ᡠ¨3%34&⚗()16554163(ஹº)383273sinx=x-----XH---X,¼¤)3!5!41638432-+—X—=7.986X10-4<0.005o7!1201616ஹ/(x)½¾Ḅ¿À᜻(Ꮤ)ÃᦪK°Än᜻ᦪᡈᏔᦪ/(x)Ḅᨬ234&⚗(£*(x)el᜻(Ꮤ)Ãᦪ஺/a)Ḅᨬ234&⚗(ᵫᑗÈÉÊ&⚗(yᑮḄËᵫᑗÈÉÊ&⚗(ḄឋÍ4ᓽy஺17ஹ0aஹbfax+6-sinx2dx)ᨬ¡1⚪Ñ6⚪Ḅ%34&⚗(¤ÒÈÓ஺kk2k3nᵫP\dx=—,pxdx=——Px2dx=——d=Psinxdx=1,a2Jl824fxsinxdx-<-xcosx)ij-Jr-cosxdx=1,ya=--(4—%)=0.664428b1ny7T2k3a1QT24]/?=—(^-3)=0.11487118ஹf(x),g(x)eC';a,bl,!Ö(a)(/,g)=f/'(x)g'(x)dx?(b)(7,g)=f/'(x)g'(x)dx+/(a)g(a)஺ÙÚÛᔲ᪀ᡂᑁß(a)¥)/(x)=On(/,/)=j"'(x)2dx=00/'(x)=0,àáâ°ᡂã,ᡠ¨°᪀ᡂᑁß஺(b)᪀ᡂᑁß஺19ஹᵨäåᐻ°ç((4.5)¢£(èḄ¡ᵨßᑖê[!ᳮ¢£ë…ì)l+xßᑖḄí¡ÈÓᐸïð஺

20[]=0.1961dY6]_¥)dx1,JZ~ZJJzAL111112,=(—a——)4----H----+—a+—=——-+—a>1326a26a2323a23}12q>0,wlj[\x-ax2\dx^[(ºù2)ú+[(ax?-x)dx=(g-ga)(?஻-g)=1஺ëᳮ-lWa<0fJx-ax2.x=i,^<,ax21dx>1,|a|41ßᑖ
yᨬ஺21ஹ,᜜=span{l,x},(p=.vpan{xl00,x101},ᑖþᙠÿᜐ
ᐗᐸ2/eQOJḄᨬᐸ஺ᵫfldx=l,'=(,)2dx+)3-=./0,1H---26,ᓽᙠ6
b=1xl00.xl0°Jx=—.”=-Lx'0'-x'°'dx^—ᵫI201b202203

21\x'm-x2dx=',\xw'-x2dx^—/0@)1031,104111U99x201x202.375.243201202a=103103X104,ᓽᙠH
211b1-98x202x203775148.202203..104.104x103(375.243-375.148)o22ஹ/LxM=Wᙠ-ᙠ
,rᙠᔾ=spa?r2,xM
Ḅᨬ஺[]ᵫ=[[-xdx+jxdx=1,£X2|X|JX=£--x3dx+ூW.---22152CZ7i--___35[a~\i128£X4|X|JX=j]-jr'dx+jx5dx=g/0222,210,2•b=------o3572128L)cJ)222105,579..3.ெ128_`ᨬa⚗c8LxM=£~+ᑏ/f!h4஺23ஹ““Lj=ᒹᔩ᯿ᔳ1opqrᑗtua⚗cvwxᨵ⌴{ᐵ}஻,(x)=2xu(x)-u_(x)onn}[vw]x=cos஺,ᑣ_/ஹ/ஹcsin[(n+l)arccosx]sin(narccosx)2x஻“(x)-1,-(x)=2x------==------------==—1JlrJl--.sin[(/?4-1)^]sin(஻e)2cosCsin[(஻+l)6]-sin(஻e)=2cos0---------------------=----------------------------osin0sin0sin0sin(+2)6+sin(஻e)-sin(஻e)sin(஻+2)..=--------------------------------------------------=-------------------=Un+\(%)sin0sin024ஹ/(x)=sin.xᙠ[-1,1]
ᢥa⚗cᑗtua⚗cᨬa⚗cᙳ஺[]ᢥ᯿ᑗtua⚗csin'=¡+£Ὢ(x),ᐸ£22k='C=2¤sin&/coskft/e,k=0,1,2,---.ᢥ᯿a⚗cnA2

22sinX=^aP(x),ᐸ£4=¨©[sing/^(x)dx._`kk2«=o212ª=g£sin,kk=.(—2cos])\=0.a,=—fsin—xdx=—[(-2xcos—)\-f-2cos—tZx]=—[(-4cos—)+4sin—1\]2L222=2222=j(-4cosg)+8sin.]=12sing-6cos.%=g£sin^-^(3x2-l)Jx=0.7x1%=51sin3,—(5x3—3x)dx7iJixx——{]-2x■—(51—3x)cos—]L]£—2cos-----(15x~-3)dx}<2t2212271AY=—f-4cos—+[cos—(15x2-3)dx]22^2=-{-4cos-+[2(15x2-3)sin-]',-f2sin--30xdx)222•1-'2=—[^cos—+48sin--60fxsin-Jx]222J-12711JYx=—{-4cos—+48sin—+60[(2xcos—)\2cos—dx]}222212=—[-4cos—+48sin—+60(4cos--8sin—)122222=—(256cos--432sin—)=896cos--1512sin—22222_`ᨬa⚗c3xsin«=6(x)=(x)+43A(%)2k=o=(12sin--6cos—)x4-(896cos--1512sin—)—(5x3-3x)஺22222=(2240cos1-3780sing)x3+(2280sin1-l340cos|)x25ஹ¬/(x)=arccosxᙠ-1,1
ᡂᑗtu®ᦪ஺ᢥ᯿ᑗtua⚗carccosx=*+£Q7.(x),ᐸ£2y

23=2farccos
cosdcos᝕6=2£OcoskOdO=sinsinkOdO]21?7=Lcosk஺M±=[cosLr-l]=[
-1A-1]nk-kKkF8248I_`arccosx=XL[
TM"-Z,,প஺26ஹᵨᨬ´qµ¶·᝞¹=஺+¶2Ḅº»¼cx½¾ᑡᦪÀÁÂᔠ,ᙳ஺Ä1925313844%19.032.349.073.397.85[]ᵫ&=
/LÅJ5MM=Z%=19.0+32.3+49.0+73.3+97.8=271.4஺/=15d=L᜛2LᓰMJLx,M=Z2f=l=19.0xl92+32.3x25?+49.0x312+73.3x382+97.8x442஺=6859+20187.5+47089+105845.2+189340.8=369321.55È3]aMMLXM=Z1=5,/=15LÉ
j42a•=ZX.=192+252+312+382+442/=1=361+625+961+1444+1936=53275LWLÄM82LMM=£%±=194+254+314+384+444i=\=130321+390625+923521+2085136+3748096=727769955327a271.4஺=4.578ᦑ¶Ì253277277699b369321.5b=0.047ᙳEᓛM&Î=Ïb+bxf=6.477025+2.732409+0.555025+0.729316+4.9729=15.46667527ஹÐÑᱥÓḄÔÕÖ×2ؾᦪÀ:ÚÛtLÜM00.91.93.03.95.0ÝÞsLßM010305080110

24àÔÕÖ×qa⚗c஻x)=o+bx+cx2,ᑣᵫ64=L᜛|LM,/L4MM=áᐘ=0+10+30+50+80+110=280o/=1.64=L஺2L£M/L£MM=áÈÄ/=1=0x0+10x0.9+30x1.9+50x3+80x3.9+110x5,=9+57+150+312+550=107864=L᜛3LãM/LÅMM=áு/./=1=0xLM2+10x0.92+30X1.92+50x32+80X3.92+110X52஺=8.1+108.3+450+1216.8+2750=4533.26åL᜛1LᓛM3LÅ.MM=>=6/1=16L᜛LÅM3L%MMqL᜛2LÅM,᜛|LxjM=2Å=0+0.9+1.9+3+3.9+5=14.7,/=1L᜛IçM,᜜LÅMM=L᜛3LÄM,஺\LÅMM=L஺2çM஺2L⚗MM622==
2+2+192+3?+3.9+5=0.814-3.61+9+15.21+25=53.6309,=16L%LéM,஺3LᓃMM=L஺3LÅM%LÅMM=2ë3=h+8᜛+1-᜛+33+3.93+53»=|=0.729+6.859+27+59.319+125=218.9076LHLX,M,᜛3LX,MM=ZX±=°4+0.94+1.94+34+3.94+54i=l=0.6561+13.0321+81+231.3441+625=951.0323614.753.63-a-280a=-0.5837ᦑ¶Ì14.753.63218.907b10782•b=11.0814o53.63218.907951.0323c4533.2c=2.2488ᦑÔÕÖ×/LxM=-0.5837+11.0814%+2.2488-஺28-31ᶍ஺

25pîïᦪðñᑖ½ᦪðóᑖ1ஹôõ¾ᑡñ¼c£Ḅöõ÷ᦪᐸøᦪùúûüýᢣwᡠ᪀⌼ḄᡠᐹᨵḄᦪ஺1)ffMdx=+A/(O)+AJ(h)oJ-hᑖ/(x)=l,x,x2ᐭᑮ:A_i+4+4=[jdx=2/jA.=—ht6+A=2h3(-h)+Aa-0+Alh=[xdx=0,ᓽ=A/?)+A஺♦0+A,/!=L”"'=0ᓽ4A_1=AAT(-/?)2+4)•஺2+A"=^x2dx=y//3A“-i+A■=~16,h

263)[jMdx=[/(-1)+2/C)+3/(D)1/3ᑖ/(%)=x,x2ᐭᑮG(-1+2ᓛ+3/)/3=fxdx=02x,+3X=12[(-1)2+2ᶭ+3L/3=M/=|‘ᓽ2Q+=12-3722+3V2X]=----------------X.=-------i+L/iU“71-272x=-------273]/33Hric8-36^+108-54_.1+672+24+16V2nb"#$/(x)=/%=[-l+2x----------------------+3--------------------]3433438+36d+108+54e]3J6^+24-16g=[-l+2x343343-36+114_0=343678ᨬ:ᐹᨵ2;ᦪ஺4)ff\xydxhM/(0)+/(A)/2+j"'(0)-/(m஺ᑖ/(x)=/ᐭᑮGn(0+//)/2+j(>2/0=஻3,ᡠo஺=\,!"#$/(x)=Y%n(0+/)/2+rs2(>36)=t$/(x)=/%஻(0+n4)/2+1~"2(_4஻3)=1w5ᡠo8ᨬ:1265ᐹᨵ3;ᦪ஺2ஹᑖᵨz{|}~ᑡᑖG

27kh711787=-[/(«)+2£f(x)+f(b)]=-[-+2^-k,k=\1஺4=]4+01178A▊1+2+)256+k211=84242401256ஹ1ஹஹ…=—[-+2(——+——+——+—+-—+——+——)+-]=0.111401642576526517281733055s=-[/(«)+4^/U,)+2)+/(&)]g°k=O2&=12᝕+1k716+2Z-8*/+m2k=\A4+716(2k+l)8k+2Z------------—«0.111571024+(2^+1)2256+5k=\#f—^)2dx,஻=10(ᶍ)x3)(4xdx,n=4#5=2G=7-14£6sin2wpdwp,஻=6ᶍ஺3ஹᱯ2.4ᐹᨵ5;ᦪ஺ᯠ⁚£#¤¥,,”§nᑖ/¨=1,k/,/,/,/,/424ᐭ§UG^^7+32+12+32+7=/?—a=jldx,b-a-“,3a+bஹ`a+bஹ“a+3bஹ——Da+32(——)+12(——)+32(——)+7b]90424b—a/?—-ci~0=——[7஺+32(஻+U+6(஺+஺)+7©=---=Jxdx

28b~a[la2+32(3a+b)2+I2(a+b)2+32(a+3b)2+7b2]90424b—Z7=90[7^2+2(9«2+6ah+h2)+3(a2+2ab+h2)+2(a2+6ah+9b2)+lh2]b—ci2cjcm2\b?—ap,°(30஺~+30஻஺+30/?~)==x^dx9030=b-a53/஺+38ஹ±r,3r——7«3+32(——3+12——)3+32(——)3+7&390424="஽7/+´(27/+27+9j+/)+?(/+3A+3j+µ9022+g(/+%2஻+27·2+27/)+7µb-a.45345,45,45,.b-a....,,,.=----(——aH---a~b2-\-----ab~2H-b)=3------(a+b)(a~2-ab+b~2+ab)9022224=3=fx"4J/ᔢ஽7a&+32(^,-^)4+12(^-^)4+32(^^)4+7b4J90424=^^-[7a4+-(81a4+108a3/7+54a2/?2+12a&3+b4)9083i+-(a4+4a3b+6a2b2+4ah}+b4)+-(a4+I2a3b+54a2b2+1080^+8W4)+764JbI/7-a=-^-(\SaA+\Sayb+lSa2b2+\Sab3+l8b4)=-^-(a4+a3b+a2h2+ab3+b4)b-CL□5cc/3o+/\s[/஺+ᓃஹ5-/஺+38ஹ5r,5r——7a5+32——)5+12(——)5+32(——)5+7ft5]90424=^^[7«5+—(243«5+405«4/7+210a3b2+90a2b3+I5ab4+b5)90323+-(a5+5tz4/7+10a3/>2+10a2/>3+5j+/)8+2(/+15a%+90//+270a2b+405a/243b5)+7/]+=+15a4b+\5a3b2+15a2/?3+15ab4+15/75)90b—a47,214ஹb'—a6(>=----(a+/?)(/+2a~/7~+b)=------=x^sdx661

29">"[7”6+32Á+”)6+12("+")6+32("+m)6+7஺6]90424=b~a[7a6+1(729t?+1458a%+1215a%2+540//+135//+18j+Â)901283+(a6+6a5b+\5a4b2+20a3b3+15a2b4+6ab5+b6)+1(a6+18a5/?+135a4/?2+540a3/?3+1215a2/?4+1458a65+729h6)+7b6]128b-a^2564051710_21953¥1710405,825,6ஹ(a+a5kb+a41h+ab+a2';b4+ab5+b)906432128161283264b1-o'=£x6dx6678ᨬ:ᐹᨵ5;ᦪ஺4ஹᵨ}~ᑖk-,dxÆÇÈÉ஺s=+4/1I+f(b)]=-^-[/(0)+4/1FI+/(DJ[]1(1+2.42612+0.36788)«0.63233Rs(7)=-——e-S67|8C=-=3.472x10-4180161'I180165ஹÎÏᑡÐÑÒ{G//(Ó=/3)3-஺)+M03-஺)24,2f(x)dx=f(b)(b—a)—(b-a)?1f(x)dx=f(--—)S-a)+f(b>a)*21224ᵫÖᑖL×ᳮᨵG/(x)=/(a)+/'(஻)(x-a),67ff(x)dx=£[/(«)+/'(஻)(x-a)]dx="(a)x+(x-a)2]*=/(a)(b-a)+^^3—a-ÙᵫÖᑖL×ᳮᨵGf(x)=f(b)+-b),67ffMdx={[/(&)+f'8)(x-b)]dx="S)x+Ú(x-bYt-(b)-a)-(b-a)?ᵫÖᑖL×ᳮᨵG/(Ó=/(Ú)+/'(Ú)0-Û)+ÜÝ(X—Þß6

30If(x)dx=1/(——)+f(ߟz-)(x>>—)+^—-^(x>——yldxDDDH7=r"/(/—஻^+b)ஹx+â1/j/(஻k+)8(ஹ/X—>஺+—á)22+^/'^(஻-()/x—>஺+—ᓃஹ)33M^஺222262=")(j)+ᓟ¥=—)…+å…6ஹz{(2.9)U}~(2.11)$஻->8%ᦈçᑮᑖj'/(x)dx஺ᵫ/—=>4Ðᓃ"(஻)=>ஹj1/஻è=>éêᔆবU1212VnJ\2nuîTfভè)=—ðqhòfভó"/ভèôI-S=n180ব180I2஻ᔆ2880/7ஹᵨõᓄz{ᑖ1/xdx,÷⌕ùᑖCúonᑖᡂüýÚᑖþÿ
£ᐭᵫ/—7“=—2=_ஹ£"£1/%=—ᘤ$,জ'()*12\2

3112஻,=-.஻ম)^\i-T\<^^L<,01஻n£8ஹᵨ456789:ᑖ2fe~xdx,⌕=IO-'஺ᵫT®=-f-T,JT,„_,যFR(h)=஺(H"ᒹ)'K஺(LM95mm4—1yZ/4—1⚓9ஹTUV⍝XYZ[ᙊ,[ᙊᕜ^Ḅ9`aXSc$aX[ᙊḄe^f)cXᙢᳫjHkV⍝jH[ᙊjHḄlm)nhpqᙢrlm)Hptᙢrlm)/?=6371`$pᙢᳫex)ᑣ”=27?+4+/7/2,c=wH-/0/2஺ᡃ~Y⚩⌼TUqᙢrlmh=439`$,tᙢrlmp2384`$)=TUV⍝Ḅᕜ^஺2R+H+h2x6371+2384+439ᵫa=7782.5,22H-h2384-439c=----=972.5'K22

3210ஹ
a஻sin&=+---஻sinᓛ(஻=3,6,12)Ḅ)ᵨn3!/5!/n᜜98=஻Ḅq஺
pT()(3)=3sin—=2.598,T(6)=6sin—=3,oT0(12)=12si=124(1-=3.1058,ᵫ'K,4—14141T(6)=-7^(3)--7(6)=-x2.598-1x3=2,464,l41411(12)=-7(6)--7^(12)=-x3--x3.1058=2.9647,r(12)=—Tje)--T(12)=—x2.464--x2.9647=2.43062஺2l1515151511ஹᵨᑡ789:ᑖ¡஺1)45678(2)¢rF£r¤¥`a3)¦:ᑖ§¨ᑖp©ᑖ)ᵨªᓄ¬r¤¥`a஺=Inyl®=ln3=1.0986஺12ஹᵨ¢r`a¯£r`a==ᙠx=1.0,1.1¯1.2ᜐḄ²ᦪ)(1+X)µ)Ḅᵫ⊤·¸:X1.01.11.21.31.4/(x)0.25000.22680.20660.18900.17361º2ᵫ¢r`a»%)=#3½஺)+")-/5)+º¾),1h2/'6)=¿À%)+஻/)Á/”©)

331h2½=2Ãஹ஺Y"§+3Ä+3…'()(x0)=*[ߟ3x0.25+4x0.2268-0.2066]=-0.247,0.12-240I2p|M(x0)|=-----x----------24=0.083(1+43)=^-^-[-0.25+0.2066]=-0.217,p0.12-240I2-X-----------<--x24=0.04,6(1+ᔉ6f\x)=[0.25-4x0.2268+3x0.2066]=0.18720.12-240I2pÇ2|-----X---------7<—x24=0.08o3(1+P3ᵫ£r`a'(/'(/)=~1—[-25x0.25+48x0.2268-36x0.2066+16x0.189-3x0.1736]12x0.1=*[-6.25+10.8864-7.4376+3.024-0.5208]=-0.2483/Vi)=ߟ1—[-3x0.25-10x0.2268+18x0.2066-6x0.189+0.1736]12x0.1=At-°-75_2.268+3.7188-1.134+0.1736]=-0.2163f\x)=---[0.25-8x0.2268+8x0.189-0.1736]212x0.1o=)[0.25-1.8144+1.512-0.1736]=-0.1883

34£ÈÉÊᑖ7Ëᦪ81ஹÌÍÎ⚪y'=«x+஺)y(0)=0ᑖв¸ÑÒ78¯ᦋÔḄÑÒ78ḄqḄ⊤Õa)kÖ×y=ga/+bxØ஺ᵫÑÒ`a'(y.+i=y„+h(ax+b),ᓽy,-y„-h(ax+b),01ni+ln%+iY%)=Zº("+°)=£'Û%)+Ḅ)+b]k=0k=0,ᓽ=y^[ahx+kah2)+bh\=ah[n+l)x+"("+Da/J+(஻+l)bh(}0k=O2y“=,+஻bh,Ýp>0=0,x=0,ᡠÛ=)஺ß)0,+nbhoàᵫx“=nh,'(py(/xn)ஹ-y„=-1ax2+b,x-[rߟn(n--—1)ah,-2+nb,,h,

35--an2h2+bnh--~~ah2-nbh--222y\=y„+h(flx+b)n+n_hᵫᦋÔḄÑÒ`a'()y„i=y+-[(ax+b)+(ax+/?)],+nnn+lahஹ)=y„+—(zXn+XnJ+bh+ᓽ%+1Yᓅ=T(xn+X"+l)+â)01%+1Y%=£[g(x*+x)+bh]=Y[^-[x+(2k+l)h]+bh}k+]j0k=02k=\2ah{n+1)(1+2n+1)(ZJ+1)ah2....,=----------2------------—+(n+l)bh,ᓽah(n+1)(n+1)2\,=---------x+——-——ah+("+i)bh0>'n+l=>0+~~X0+~Ya^+nbl1>Ýp>0=°)X()=஺)ᡠÛ2%+iah?+nbhoàᵫä=஻஻)'(p

36y(x஻)Y+ᓃx“Y'ah2+nhh=^an2h2+hnh-ah2-nbh=0o2ஹᵨᦋÔḄÑÒ78=ÍÎ⚪ᔆ=x+"00=1)=0஺'Ky”+]=1.105xy“+0.05x.+]+0.055í“,010î=1.105x1+0.05x0.1+0.005x0=1.11y=1.105x1.11+0.05x0.2+0.055x0.1=1.22655+0.01+0.0055=1.242052=1.105x1.24205+0.05x0.3+0.055x0.2=1.37246525+0.015+0.011=1.39846525'y=1.105x1.39846525+0.05x0.4+0.055x0.3.4=1.545303825+0.02+0.0165=1.581804101251y=1.105x1.58180410125+0.05x0.5+0.055x0.45=1.74789353188125+0.025+0.022=1.79489353188125’ï=L105x1.79489353188125+0.05x0.6+0.055x0.5=1.98335735272878125+0.03+0.0275=2.04085735272878125'X=1.105x2.04085735272878125+0.05x0.7+0.055x0.6=2.25514737476530328125+0.035+0.033=2.32314737476530328125'%=1.105x2.32314737476530328125+0.05x0.8+0.055x0.7=2.56707784911566012578125+0.04+0.0385=2.64557784911566012578125y=1.105x2.64557784911566012578125+0.05x0.9+0.055x0.89=2.92336352327260443898828125+0.045+0.0443.01236352327260443898828125

37y=1.105x3.01236352327260443898828125+0.05x1+0.055x0.9I0=3.32866169321644890508205078125+0.05+0.0495஺=3.428161693216448905082050781253ஹᵨᦋÔḄÑÒ78ð=x-+x-)',çè^º=0é9),©5),kÖ×b(o)=oy=-e~x+x2-x+lØ஺ᵫᦋÔḄÑÒ`a'(ñ+1=y“+஻a®+ìY%)')'"+|=y“+òó£+ôYK+x+i+õ+1+஻(ᱏ+X"Y÷)øÝᵫX஺=°),,,h2ஹ஻/2ஹ=(1Y஻+ù)xᐜ+-■--(X”2+x,,)+-(ü+1+x“+i)ý=0,h=0A,'Ky.+=0.905y,+0.045(ஹ+x,)+0.05(x®+i+x,+i),01y,=0.905x0+0.045x(02+0)+0.05x(0.12+0.1)=0.0055p=0.905x0.0055+0.045x(0.12+0.1)+0.05x(0.22+0.2)=0.0049775+0.00495+0.012=0.0219275%=0.905x0.0219275+0.045x(0.22+0.2)+0.05x(0.32+0.3)=0.0198443875+0.0108+0.0195=0.0501443875L=0.905x0.0501443875+0.045x(0.32+0.3)+0.05x(0.42+0.4).=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=0.144992256972187554ஹᵨþÿ
⚪+>=°,ᐸy(O)=l12+3஻T0ᦈ⚪Ḅ"#y=e~xo$%ᵫ'()*+,y„=y„+|(-y„-x,i)./(l+g)y“+i=0-^)y„»ᓽ+l+y“+i=./23ᵫ)'o=i+,'Kr°2+஻12+஻

382nhH+l4Alimy„=lim=lim1-=lim1-%TO/J-»0{2+h2012+hJ2012h5ஹᑭᵨ89
:;<ᑖe,2dtᙠ?x=0.5,1,1.5,2Ḅ஺f/_X2$%A>=Bᑣᔆ=e,./AB=0.5,ᑭᵨ89
Eᑮ:H>-(0)=0y=y„+hf(x,y,,)=y+0.5/,3ᵫ1=0,EᑮIn+inn)>i=+0.5xe0'=0+0.5xl=0.5J=K+0.5xe஺'=o.5+O.5xe025=1.1420127J%=+0.5xJ=1.1420127+0.5e=2.5011536Jy=y+0.5xek52=2.5011536+0.5e225=7.2450215஺436ஹMB=0.2,ᵨN▤PᐺḄRS-Uᛞ
WXᑡ⚪Iy'=x+y,0

39hy=y+(K,+2K+2K+KJn+in23oh,ஹJihஹ,ஹஹ,hihhஹ,ஹஹz-K{(x«+y„)+2[+(1+)(x„+y„)]+2[(+)+(1++)(x„++)]AOZ22424஻h\,ஹ,h2/+(%+2+4)+(1+4+2+4)(£+w)}hh2h2=%+y[*“+y“)+/7+(2+/?)(x“+>“)+(஻+)+(2+/?+)(x“+y”)oZZh2h3h2/+(B+2+4)+(1+஻+2+)(x„+y„)]4=y+A(3h+h2+)+(6+3A+/Z2+)(x„+y„)]no443ᵫ஻=0.2+,"=y1+30[0,642*6642(X.+y")]=y“+0.0214+0.2214(%+y“)=0.2214%+1.2214y“+0.0214./ᵫ=0,%=1+EIy,=0.2214x0+1.2214x1+0.0214=1.2428J=0.2214X0.2+1.2214x1.2428+0.0214=0.04428+1.51795592=1.58363592Jy=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°#y=2e'-x-l஺y'=3y/(I+x),0

40[]K|=/“K=f+thDf+᱆Dᡭ“+…,2nn=/,+(17)/7+«—,ᔆ஺%+…ᡠhy஻+i=ᓅ+§(2+K3)h7C/(th)-2rrix>r^r[(1-t)h]~7r1=y„+-{f/r„+thDfn+-^-D~f+-••+/„+(1-OW„+-------D-f+-••}nnhrcCInr(2/'—2t+v)h~2r-)=%+-[2/„+hDf+-----------D-f+-••]nn..B2c,(2¤-2t+l)h3c,=y„+/¥"+¦஺“+-----4+-,h2„h3”+1=y>,+஻ᓃ+?y”“+…/26¨©ªᦪ+,ᡠ«RS-Uᛞ)=%+¬+—Df„+—(D2f+fDf)+-••yn26*▤Ḅ஺8ஹXᑡ®¯RS-Uᛞ
°▤Ḅ:hஹh>"+i=y”+1(5+3)=%+6±2²+3³+4³´K\=/(x.y.)&=/(x“,y”)(1)■=/(x“+1,)'“+I&)(2),hh^=/U„+-y+-^)n2233^=/U„+-^y„+-^2)K3=f(xn+-h,ytt+-hK2).JD%ᵨ=+y(4&+4ᔩ+4¼)&=/(x,,y.)$%ᙠ°▤RS-Uᛞ)*½K=f(x+ph,y+phKJ2nn&=f(Xn+qh,y,+qh(rK[+sK))21317(1)M4=—4=0,4=—,p=—,q=—,r=0,5=1oᓽᡠ«
,4433

41r+s=14+4+4=i/,1¿ÀÁ4P+4᜛=¦/ᐹᨵ°▤஺Zp-+4q~=~4Pqs=%21413(2)M4=—4=-,4=—,p=—,q=—,r=0,5=1oᓽᡠ«
,93924r+5=14+4+4=1¿ÀÁÆ42P+4q=J/ᐹᨵ°▤஺4P*+4/=19ஹᑖÇᵨ▤È*ÉÊË
Ì▤◚*ÉÊË
Xᑡ⚪:y=l-y,y(0)=0,M஻=0.2,=0,%=0.181:;y(1.0),Î"#y=l-e-Ϩ©஺$%ᵫy=0.2+,Ðᵨ▤È*ÉÊË
h%+1=ᓅ+5(3/„-fn-\)=y„+o.l$3(l-y„)-(l-)%஺./=y“+0.1(2-3y„+y„_,)=0.7y„+0Ay_+0.2ntB=0.7%+0.ly+0.2=0.7x0.181+0.1x0+0.2=0.3267,0y=0.7y+0.1^+0.2=0.7x0.3267+0.1x0.181+0.232=0.22869+0.0181+0.2=0.44679y=0.7ᡭ+0.ly+0.2=0.7x0.44679+0.1x0.3267+0.242=0.312753+0.03267+0.2=0.545423%=0.7%+0”3+0-2=0.7x0.545423+0.1x0.44679+0.2=0.3817961+0.044679+0.2=0.6264751

42Ðᵨ▤◚*ÉÊË
%+1=+g(3,w/„-1)=K+O-l[(l-X,)+(l-y„i)]=ᓅ+01(2-y-y),+nn+iᓽ92L0+1=09y“+0.2,./y„=JJK+—°ᦑ+l92923629R+---—n72QOJO/O/.11~11■11w11929249691Bw+X0.3299+—=-—n45117/J4U6.,11Õ11~11111192_2=6065624=0.55142+x0.451736+—-HH11119292_6,96278_y5P4+x0.55142+—=——U.UJ47஺o11~111111#1-e-i=0.6321஺1h10ஹy'=/(x,y)ḄXᑡÖᑖ)*y=-(y„+y„_,)+-(4><-yJ,+)n+1I+1▤ḄW×ØÙÚÖḄ✌⚗஺B203$%y,=+Ý+<+(<+…1+12஺h-h2=y„~hy+~y«'—y+--->y“+i=y"+஻/+Þ4+…,nnh2y"=ßwḄI+¦à+…ᡠ1h-(y“+y„-\)+-(4),“+i-y+3y“_i)n=ீ(y“+x,-hyf+gyI-jyI+…)n226zh2h2w—2+—[4(y",+hy*+—y„+,••)-y„+3(/,-hy*+-ym-\—)]./¨©ªᦪ+n1h2஻3,7A2=5(2y“-hyr+—y^,-—y1^+••')+~(6y+hy^+-—y^+---)nnZ2o4Z,%2â3=%+ã+yK~24~y"EÖᑖ)*ᐹᨵ▤¿ØÙÚÖ✌⚗wäwå-)I=--Ko624811ஹæ×ᐹᨵXᑡ(*Ḅ°▤
I%+i=gy“+%y“T+%ç-2+%èß+èß-1+%%-2)஺

43MA3[]y“+i=y+hy+—y*+—+~Ê’+…nnZO24c,,,(2/7)2”(2/7)3(2B)4y“-2=y“-2/7)“+——y„w——y„+——y\+•••26244/,37/,4=%-2/iyI+2ryI--—y^+—y^)+•••y»-2=yI-2/7),I+ë+-=yI-2hy[+2h2y^-^~y*4,+•••2o3“0”+%y“T+஺2ç-2+᪍%ß+dîT+ïð-2)B2h3//=floK+ajy“-hy'n+-yn--yn+—yn(i)+•••]ZOZ44/,37/47+×[%-2ô+2஻2yI--yyI+-y-y£>+-••]3஻2hᡠ+/?{%<+4UI+õà+°ö4'+…]2o+%H-2hy+2h2y"-yf)+…]},B.஻=(÷+4+஻2)ç+(w-2%+஺()+4+b)hy+(+4஺2-2஺]-4/?)—y2n2/:+(-%—8%+3஽+12%)-^-yI+(/+16%+44-32/?)--y^4)+…2624஺0+Q]+஺2=1./ù)*ᐹᨵ°▤ᑣKúᨵII2"d+&+I2=1஺6/1+4%—2è—4/—1-%—8%+3b]+12b2=112ஹüXᑡýᓄw▤ýÿ1)y'-3)/+2y=0,y(0)=1,y[0)=1yf=ny(0)=1[]y'=pᑣp'-3p+2y=0,p(0)=l,ᨵ‘><P=3p—2y[p(0)=l

44!="ᑣ#$%⚪'(=2)y*0+=",0"-.'y*x+=e,2)/-0.1(l-y2)/+y=0,y(0)=1,y'(0)=0஺-y=P",y'=p,3ூJp'—0.1(l-y2)p+y=0,p(0)=0,ᨵீ,ஹP=0.1(l-y)p-yy(0)=1p(0)=03)x"«)=-,y"஺)=-+y2,x(0)=0.4,x'(0)=0,y(0)=0,y'(0)=2஺rr(`X=py'=q",£(f)=p,y'(x)=q,3=q'=,ᨵ3rx(0)=0.4'M஺p(o)=oq(0)=2y"+y=013ஹCD=0.25,ᵨGᑖIJ$%⚪y(0)=0,yপ=1.68",Nᯠ஻=4,y=y2?+yi(”=1,2,3),RS=0,%=1.68,Uᐭy-2y(=-h-y'+☢-2)ᨴ=02xWXiI«%—2)2+%=[\2%ᓽ<'+(r-2)\+%=0,1.68-2%+'=-]^(h~_2)%+%———1.68'6-210!%ஹ1h2-21%0ᵫ/?=0.25gh,ஹ01/12-2^>3c1g

45ஹ311016%=0.494381W<%=095786஺311-^3)'=136148016>14ஹklmy"=/(x,y)gnoGᑖ]pq+]=2y“-y“_]+/?2/(x”,y”)sᵨt['"_12]pu#$%⚪)'=vwxyឤ{|}.y(x)=~y(0)=y(l)=02'-2h1!]Cஹ[]ᵫGᑖpgnolm1—2஻J^=1o<1-2%D)_])v>15ஹC/?=0.2,ᵨGᑖlIJ$%⚪](1+f'-3y=6-3஺ly(0)-/(0)=l,yপ=2",Nᯠ஻=5,ᑘ=2<=+|2+,-1R4="+1%-,(஻=I,2,3,4)h2hUᐭWᑮ(1+x)ᐗ+121+y“T_/-T_3%=6x,_3,ᓽh2h(2+2[᝞,lᔣ[(4+4/+6h2)y+(2+hx+2ஹ=6h2(2x-1)nnnᵫVo—"*=1gW(%+l)>o-=/“ᵫ\=஺.2Wlm':h12-1000<0,2ஹᡭ=1.014872.12-4.42.0400-0.144%=1.0178502.4-4.882.240\=-0.048,gW'=1.07010஺002.84-5.682.6y30.048%=1.21930003.44-6.8ஹ—6.096))4=1.513297஺4,

46lmu᪷1ஹᵨᑖIulm——x—l=OḄ᪷⌕u¡G<0.05஺",)(Ḅ=¢2—£[1,ᑣ஻0)=[1,/ফ=1,ᡠᨵ᪷¦§'(0,2)¨'/প=[1,ᡠᨵ᪷¦§'(1,2)/(1.5)=1.52-1.5-1=-0.25,ᡠᨵ᪷¦§'(1.5,2)/(1.75)=1.752-1.75-1=—>0,ᡠᨵ᪷¦§'(1.5,1.75)16/(1.625)=1.6252-1.625-1=—>0,ᡠᨵ᪷¦§'(1.5,1.625)64/(12)=(12)2_12_1=_©<0,ᡠᨵ᪷¦§'112,1.625161616256116Cx*='(12+12)=12=1.59375,2168321a1t«¬-.Ḅ®¯<,(1.625-1=)=-!-<0.05஺216322ஹᵨ±²u᪷Iu/(x)=l-xsinx=0ᙠ¦§"0,1,Ḅ[¶᪷·ᑮ¸¹᪷⊈»¼-½|/(x/<0.005¾¿xy஺À3ஹ'ulm=0ᙠ/=1.5▬¸Ḅ[¶᪷ÂÃlmᦋᑏᡂÇᑡ{ÉÊpËnoÌÍḄÎU]p1)x=1+1/x2,ÎU]pÏ+1=l+1/x2)x3=l+x2,ÎU]px=R1+XA+13)x2=—-—,ÎU]px*+,=1/Jx*-14)x2=x3-1,ÎU]px=yjxl-1ok+isᑖ᪆ÒÓÎU]pḄᦈÕឋË⌱C[Ó]puØᐹᨵÚÛᨵᦔᦪÞḄ¸¹$஺",1)Â1()=1+4ᑣ8'(x)=g,|"(1.5)|=|—^yl=—<1.ᡠxxI1.5I27ÎUlIßàᦈÕ஺_____2_22)Â᜛0)=3+2ᑣ᜛'(x)=§x(l+x2)3,|/(1.5)|=|x1.5(1+1.52p=3^<1,ᡠÎUlIßàᦈÕ஺

4711_r1_£j—3)Â᜛(x)=.i----3Iã(p\x)-——(x-1)2,ä'(1.5)|=——x(0.5)2=V2>1,Vx-122ᡠÎUlIåᦣ஺___________o__4)Âç1᜛'஺)=5/(13-1)2,41Q--==>1,ᡠÎUlIåᦣ஺|^(1.5)|=-xl.5(-)2ZoV384ஹ±éue'+lOx-2=0Ḅ᪷ᑮêÛëᦪᡠ◤Ḅxyí1)ᙠ¦§"0,1,ᑁᵨᑖI2)ᵨÎUIï,=(2-*)/10,C#$/=0஺",1)ðᵨᑖI஻x)=e+10x—2,3Iã/(0)=-1,/প=e+8,ᨵ᪷¦§'"0,1,/(0.5)=Z5+3>0,ᨵ᪷¦§'"0,0.5,)(0.25)=eg+0.5>0,ᨵ᪷¦§'"0,0.25,/(0.125)=e°125-0.75>0,ᨵ᪷¦§'"0,0.125,/(—)=e^-—=-0.5605<0,ᨵ᪷¦§'1681168Jr3c[/(ò)=eó[ô=0.03578>0,ᨵ᪷¦§'—321616325--õ<0,/(—)=^Mᨵ᪷¦§'[9A-6432[6432J11U73c113÷(7^)='"*[ᨵ᪷¦§'-IZoo4IZo3223ø=141ú_23_3__/(ù-——<0,ᨵ᪷¦§'256128.256532.47277ú'2347~e512_/(—)=——>0,ᨵ᪷¦§'5512256_256512.93559~2393-_z,1024/(-c----->0,ᨵ᪷¦§'1024512_2561024_

481,2393ஹ1X*[*1-----+©-=0.090332,ᐳᑖ10þ஺2256102420482)ðᵨÎUIXE=<ᑣX,==0.1,X,==0.0894829,102102஺஺894829_0.09C639I2x=----------=0.0906391,ÿ=---------=00905126,310410ᓽx*=X4=0.0905126ᐳ4஺5ஹᦪ/(x),ᑗx,/'(X)"ᙠ$0ீ&W/'(X)WM,)*+-0<2<2/AfᑁḄ34ᦪ5,67x&+:=;-<(x*)ᙳᦈ>+f(x)Ḅ᪷x*஺@)*:ᵫx«+i=-"®)FGHIe(x)=x-»(x),ᑣd(x)=l-%>'(%),QR2S0"(x)>-1,ᓽ/(ᑘ<1,[\]^ᦈ>஺6ஹ_Gx=p(x)ᙠab@a,b:ᑁeᨵ᪷,\gak>l,(1)lm᝞opx=8(x)ᓄS〉+Ḅ]^tফpx=tanxᓄS〉+Ḅ]^Hxyx=4.5(z{)▬}Ḅ᪷஺@~:px=Q(x)ᦪHᑮx="(x),\@/('=—H[\᜛(X)/:@=-J-ஹW<1,ᦑ^X«+|="6ᦈ>஺Ipx=tanx,ᑣwp\x=sec2x,[\'4.5|=sec24.5=22.5,p^ᦋS=arctan%h,wp\x=—H[\'4.5|=——----0.047,1+x1+4.5]^ᦈ>஺%=4.5,7=arctanx=4.49372,x=x=arctanx,=4.493424஺027ஹᵨᑡy/=/-3.1=0ᙠ/=2▬}Ḅ᪷஺᪷Ḅ¡¢/=1.87938524…H⌕y¥¦§¨¡ᑮ©ªᨵᦔᦪ¬஺1)ᵨ®;2)ᵨ°±H/=2,²=1.93)ᵨ³ᱥµH5=I,%=3,X=22/4=xxl-3x-\_2xl+\k@~:1x=xk+lkfgk3x1-33x1-3

49=1.888889,"Jு:¹"87945,º»஺2X23+117x,=.13x22-393(y)2-35616/K)½*+1=x¾2),XQ=2,xl341+XJ)+1(x-3x*-1)-(x_|-3x*_1-1)("1.9x2x(1.9+2)+l15.821582Xj=1.9,x=1.88109421.92+1.9X2+22-38.4184115821c/1582iÃ\1xl.9x(----+1.9)+1Y=84184131582)2+—xl.9+1.92-3,º»஺w84129-558143."42+8412"Å…794U/a)3)xk+iHᐸÈa)±^a)2-^f(x)f[x,x.ix_]kkkk2co=f[x,x_1]+f[x,,x_](x-Xj,..1),X஺=1,X|=3,2=2,ᦑkkkk2t/a)஻/)=11^=1஺,/஺0)=-3H/a)=17,/(x)=l,/[x(),x=2X]/3-1/(X)-/(X,)_1-17216,Ì2H/]=2-3f[Xix]-flx^x^_16-102f[x,x,x]==6,0=16+6(2-3)=10,012x—x2-12011X3=2=2-=1.9465745,ᶍ஺1O+71O2-4x1x610+V768ஹᑖÑᵨᑖÒ®yx-tanx=OḄᨬÔÕ᪷஺[~]Ö×Ø6⚪Hx*=4.493424஺9ஹẆÛyÜḄ®^=L(x*+2),x>0,)*ᑗA=1,2,024x2&$ÞᑡX],/,…ß⌴áḄ஺k

50@)*:âᯠHX,>0,QRSXi-6='(4+£)å='®æ0,ᡠX242X@-2x>4a,k-1,2,--•,Xx-x=-(x.+-)-x.=-ߟ—<0,ᡠXÞᑡß⌴kt+1kAA2Xk2xkáḄ஺10ஹ+/(x)=0Ḅ®^x*+|=xé-/(4)//'(&),)*R=(4-x1)?ᦈ>ᑮë"(x*)/(21(x*)),ìx*S"x)=஺Ḅk᪷஺t11ஹlíᑡᦪîï®Ḅᦈ>ឋÒᦈ>ñ{஺ஹ[Vx,x>0ஹx>0I)/(x)=L2)/(%)=L஺[-J-x,x<0[ߟV?,x<0[~]1)ᵫp(x)=x-Jì=--^-=-òFG“(x)=-l,ᦑ®ôᦈ>஺f(x)12G-gxFG"(x)=-3஺0,ᦑ®▤ᦈ>஺2)ᵫõ(x)12ஹøᵨ®+7/4=0,ùúyû᪷üḄ^Hxîïᐸᦈ>ឋ஺[~ߟHᑣ…~-a2xl+a2a-----o-=-----o—=—XkH------7o3ý3xf33xf13ஹøᵨ®+7/(x)=l-þ=0,ùúy&Ḅ^HxyVTEḄx஺g(x)=x?-a8o14ஹᵨ/(x)=x"-a=0#/(x)=1-3=0,ᑖ'()*CḄ,-./01*linMV^-Xhi)/(:;4<஺?;Q_(஻;1)ᨴ+an-1a----Xk+……₠bnx'^'EIn

51,r(஻T)AI—7a----------x---------k..'\la-xnnx=hm———k+l=hm---------------------—=hm——-------j("Na_Xk)2ia-Xk)2i_2&a_Xk)nxr-n(n-1)%*1-1].(n-1)=lim----------------------------=hm------=--------------28_2n[n'Vaxr'~(n+l)xG]`᝞-(„I4]a+_(H-1)_1-n2[n\[a-(A?4-1)V^]2ᢚ1-—ττ_Y/(^)_£xf-ax_(H+l)ax,-xfxRxxRxkk]-k~F~~-k------7~k+f(Xk)/ananaG(n+l)ax
l.im.-Ma----x-M-=lim-----------~~-na----------=limna'^a-(஻+l)axk+x”i(Ja_X*)2kT8(Na-Xk)25na^yfa-x)2k_-(n+V)a+(//+l)x^_(஻+l)(x?-a)_(஻+l)஻xGi1-2na(Va-xj-2na(yJa-x)…2nak/i-l(n4-Y)ann4-12a2,4a15ஹKL,-./+%)NOPQḄR▤஺ᎷUVx°ᐙᑖ☠3x+akYx*,*lim(&-/+])/(&—Z£\஺4&(x_+3a)..yfa-xk+l..3x?+a_.c'(3XG+a)-x*(xG+3a)limߟ———-=lim-------=------------[]j(Va-xj'3—(7a-x,)3i°°(Va-x>(3xG+a)k(V^-Xk)31_1=lim=lim——᝕;>8(V^-x)3(3xj+d)82)x-+a(3(7a)2+a4ak

52defgឋiḄjk2ஹ(a)mANop▣rs00,tuvwxy;z:0A{ᓄ}KL&Nop▣஺0.6428X,+0.3475X-0.8466X=0.412723(b)ᵨvwxyopi_<0.3475X1+1.8423x2+0.4759/=L7321«-0.8466X,+0.4759X+1.2147X=-0.862123KL(a)QḄᐗ=஺;᝞(i,/=2,%,஻)0}ANopQUU,Cl..▣0%=%,.0i,j=1,2,,/!,ᡠa;=%-a1---=ᓽA,Nop▣஺(b)ᶍ஺4ஹmA}n▤᜻▣rᨵᑖ/A=LU,ᐸLNᓫR▣0U}R▣0*KAḄᡠᨵ¡¢£¤/ᙳ¦}§஺(I()A(Ji1lஹKL¨L©Uᑖᙽ0L=M,U=ᦈ”3),ᐸ}k▤ᓫR▣0Ugk▤R▣0ᑣAḄk▤¡¢£¤/}\LU\,®ᯠ᜻஺kxkkxk7ஹmANop°U▣0tuvwxy;z:0A{ᓄ}ᓽa',ᐸ0A2A=(%)“0&=(*),iGKL_(1)AḄoᐗ%>00=1,2,-,//)G(2)%Nop°U▣G(3)«*2)0o

53(2)A,Ḅᐗ*)=%-&&,(i,j=2,3,3,஻)0}ANop°U=ᡠÃ=%-=2=▣0ÅᓽA2Nop▣஺(3)}ᓽ>0,ᡠÃ☜)=%-3Ç=%—/W%஺awa\\(4)Ãᶍ஺-21-3-1310712ஹᵨvw-{Ê*AḄ⌮▣_-124-210-15[]_3_1_-21-3-1100஺-1-0002~2~223107010031070100—124-20010—124-2001010-150001-10-150001-Ì1311Í1-;;;;-000]_3222210002~2~2219130---8---10001-9-173-2002222—>—>02-2--2-01002-2--2--01022222222]_o-111-105-—0015001~2222L2222-j038-1100■■1038-1100"01—9-173--20001-9-173-200—>—87002540-7510001—05-2552500-4-31-10100-4-31101

5401642316423100100-—05;255~255255251312_19_1312_19010-00100525;525525;525TT187118711000001-05_2552552552531I13145000001—;2_5;585`178517.418_236100085858517336214130100851742517—>195380010——8517;851731450001—85;1785174182316"858517621413-1717425ᦑ/4T=O538——1785173145-85178517214ஹᵨᦋÑḄÒ᪷i-11s10723Õ᳝=—,x=-,x23T15ஹᑡ▣Ùᔲᑖ}LUÛᐸL}ᓫR▣0U}R▣ÜÝÞÙᑖ0ßàᑖNᔲá;஺}AḄ;ஹåஹR▤¡¢£¤/ᑖ'}1,0,TO,ᡠÃA¦Ùjkᑖ}R▣Ḅâã,çᣚé:êÃ஺}BḄ;ஹåஹR▤¡¢£¤/ᑖ'}1,0,0,ᡠÃB¦Ùᑖ}R▣Ḅâã஺}CḄ;ஹåஹR▤¡¢£¤/ᑖ'}1,5,1,ᡠÃCÙëᑖ}R▣Ḅ

55âã01rᑖNá;Ḅ஺16ஹìí)îᑖ⌱£ᐗRᑖ᪾ñ01rᵨ?i[]X]=p%=-1,%=G஺2318ஹmAG1”OPAḄéᦪ0ᑡᦪ02-ᦪôF-ᦪ஺0.10.3I=max{0.6+0.5,0.1+0.3}=1.1,ML=max{0.6+0.1,0.5+0.3}=0.80.60.10.60.50.370.33-}AZ0.50.30.10.30.330.34J1,τ/I-0.37-0.33°,2,2°0;Tõ==(A-0.37)(A-0.34)-0.332=»—0.7U+0.0169,0.33ö0.34.0.71±V0.712-0.13271±2V1218z=----------------------------=-----------------2200»÷ø2=ùax("4)=I"=0839஺|A"=70.62+0.52+0.12+0.32=VOJI=0.8426஺19ஹ*K:(a)(b)^||<<||A||<||A||2fo(a)IWL=ûಘ*Hi«max|x,.|=+L஺/=]cný¾=ZW20ஹmPeR"X"r᜻0mþ}R";ᔣᦪ||=ᑘ஺IWI,R"ᔣḄᦪ஺ᯠH=o,|=▂==ஹpIk+/II஺=||!"+$%||=+&I$I▬I+1%|=|(+1(,*+R"

56ᔣḄᦪ஺21ஹ.Ae1ஹ"3456|7=!Ax,x%"|9R"ᔣḄᦪ஺1;3A456ᡠ=kL=!AX,X%2=7.xrAx>0,2___________||cx||=wAcx,cx2=>Jc2xTAx=|c|VxrAx=|c|||x||,4AIk+஽IL=!+x%5+x%%=!X|+XTA!XJ+x%2222=xLAX1+XLAX2+xOAX+XOA=2,*+P.R"ᔣḄ+ᓅ@A+B஺=+⊈=+ᑣᨵ=w2஺{a+a2y=஺ᑣ0=(<2,x+ay,ax+ay)=+R+2%,ஹ+¡|O2i2ᓽa/Mb+a21yl2=஺=¢L+2«[2R|21yli2+¥=(▂¦+▂)2ᓽ©ᙠᐰ3¬Ḅ,஺2,*+X}yឋᐵ஺24ஹᑖ¯°±R2²!³´%Sஹ,={xl|x|„=l,xe}"=1,2,8%஺

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58IK'dl_;3m/x/-----I\-max1tý-TMᡠ஺IWI||AAX||þý'ÿ|min---஺M29ஹA᜻▣1|ᑺ|<1,$(A+9)t)ᙠᨵ,-᎔cond.A05||A-1-.A+^0-1||<_________M1—co஻d.A0WMl9:;<A+==A(/+AT@ABCDBEᑜ<1,ᡠᵫHᳮ18KL,/+A”N᜻ONA+P᜻ᐸ⌮)ᙠ஺.A+S0.x+a0=Ax,WJ&=A+^Y'Ax-x=A+^Ay'-A-'Ax,WᵫA+=0X=—.□0xKᙠ=-=+A-ZtA-1.[0x,K--.4+a]=./+ᑁ=0-_`ߟONIA-1-.A+&0TD;./+/T=0TAT.ᡧ0AT||de+A-W-1|A“LMh^MTqFjJfmn.A+Ḅ1p|qIHMᗞi0u30ஹ▣xnyznᦪᡂ4=2}/,:~=±gc°஻d.A08ᨵᨬ஺2-|J-19:;ᵫ4=KL~4Ho▣A᜻A-1=Z,ON-11--2L2J

59concK.A)^=A~]A=max<+L-+2>max{24+4,1+1}4A=(1k2>max{3q,2}W~|21>,max{3|A|,2}=2,ON3~Ngmax{,2}=3ONcond(A)„=(+2).max4,2}=(+2)-3=3+6q>7஺A7?ᡠco஻d(A)g=7ᨬ=§,ᓽ4=±§஺31ஹAH▣ᐸᑖA=LO/Z=W'W,ᐸEW=஺⋭஻$(a)cond(A)=[cond(W)]2(b)cond(A)=cond(W)cond(WT)22222G[:]ᵫA==W,WKLA(A)=A2(W),A(WT)=A(W),஻(WT)T)=஻(WT)T)=஻WT),ON“4-1)=§(¨1),ᦑ|A*=|«£,ii4=M^KI=M>kT)-1ll2=k-1L22(a)cஹo஻d(A)2=D"|¯=|ᓺᓅ|ᖹ³´2=[co஻d(W)2µয,஺·¸)2=m|21AhMᓱ|ᖹ஺=(||wT|jh<)(||(WT)T|2Ml2)=CO஻d(W)2CO஻d(W7)2°32>4=-½AḄᩩ¿ᦪco஻d(A)ஹ,0=2,8)஺999o10099-9899[]ᵫA=KL,A-',ON9998-99-100-9899T-9899'19405-19602(d)=99-100(99-100-1960219801

602-1940519602ᵫ(AT)T(AT)D=§-39206/1+1=0,196024—19801A/JlOO9Á00991980119602[9998199981960219405/L-19801-19602ᵫk/_A“|==§n392064+1=0,-196024—19405K||A||,=[A]L=Jl9603+N4277608,ONco஻d(A)2=|A1|&A|,=19603+J384277608஺39206஺ÂnÃ=199,ML=199,ONco஻d(A)8=|A[UK=199X199=39601஺33ஹ:}᝞ÅAÆÇ▣ᑣco஻d(A)2=l஺9:;ÉAÆÇ▣ᑣAT=",ON"A=/,(A-')TA-'=AA-'=I,ᦑ1Ê=|A-1|=bco஻d(A)2=-ᑤ2=1஺234ஹ4Ì^᱄ÎᓽRa▣Ḅ½Ðᦪ:cond(AB)

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⚗=-4,/=3,/=2(b)ᵨ:=£)-'(£+t/)x(x)+D-'bx'1ஹ]ஹ(21)0--&'ஹ5555’02r’-12ஹ5]_2-102x(k)+20—_--0-”)+54442ஹ2-30,ஹ3,31113+<10,ஹW,ஹ10,1510Jᵨ./-0123X(*+D=(O_£)-ஹ>Ux@+(D-L)-'bT400"02r400-12ஹ-1400020+-140202-3900°,2-3N31000055'021'-12)1\_10002xয+020204204131ஹ0007313,4040io>-40P/ஹ2\_'_1Zஹ055111220”+1020y11210208>?@3ᓽIK=ML>i>Fᦪ/+A++…+A*+…Jᦈ2Q஺&?@SᯠH=|A|L=2>1,VWA?=YYYY=(),ᡠ[Ak=0(A:>2),FᦪḄ]^/+A=

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6310-0.4-0.4ஹ'0-0.4-0.4ABo=£>T(L+U)=1-0.40-0.8-0.40—0.8ᵫJ-0.4-0.80,ஹ-0.4-0.80,20.40.4|A/-5|=0.4A0.8=(2-0.8)(22+0.82-0.32)0¯,0.40.8A=(A-0.8)(A+0.4-7048)(/1+0.4+7(148)=0/?(5)=0.4+V0.48>1,sP°ᦈQ஺0-1’100ஹ’0-0.4j0.4ஹG=(O-L)"=0.41000-0.810.40.81,ஹo00)ஹ>±"100Yo-0.4-0.4ஹro-0.4-0.4ஹ=-0.41000-0.8=00.16-0.64[0.4-0.810070.160.8,A0.40.4|஻-G|=0A-0.160.64=4(²-0.962+0.1152)=¯,0-0.164—0.8=2(2-0.48+VO.1152)(2-0.48-Jo.1152)=0/?(G)=0.48+JO.1152<1,sP./-³12ᦈQ஺’12-2ஹ(b)ᵫ¬ᦪ▣A=111¯,321,'1Y0-22"0-22ஹB=D-'(L+U)=1-10-1-10-1,ᵫ(}4-2-2kߟ2—20A2-2\AI-B{\=1A1=ᐕ=0¯,/?(µ)=0,sPᦈQ஺224

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