数值分析第五版课后习题答案(李庆扬等)

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KḄLMᓫKOᢣQRS=TKᨵᦔᦪVWX$=1.1021,x$=0.031,x$=385.6,x$=56.430,x$=7x1.0஺x$=1.1021ᨵ5KᨵᦔᦪV$x$=0.0031ᨵ2KᨵᦔᦪV$x$=385.6ᨵ4KᨵᦔᦪV$x$=56.430ᨵ5KᨵᦔᦪV$x$=7x1.0ᨵ2KᨵᦔᦪV஺4ஹᑭᵨ_`(3.3)8ᑡᔜḄ▲ᐸcxW,x$,d;,x$ᙳ3⚪ᡠiḄᦪ஺(1)X$+X$+X$$e*(X$+x$+x$)=£l£(ᓃ)=£(xW)+£(x$)+£(x$)«op”.=-xl0-4+-xl0-3+-xl0-3=1.05x10-3222(2)xxx

1*/***ஹe(XXX)=2£(x$)=(X$X$)£(XW)+(x$x$)£(X$)+(x*x*)£(X$)123JA-l=(0.031x385.6)-xl0-4+(1.1021x385.6)-xl0-3+(1.1021x0.031)-xl0-3$222=0.59768x10-3+212.48488x10-3+0.01708255x1()-3=213.09964255x10^=0.21309964255(3)%$/x$஺e*(x$/xW)=££(x$)=-4£(x$)+7^7£(xW)4=1X4(u)=vx110-3°°3\xlxl056461+,X1X10-356.4302(56.430)22(56.430)2256.461xlxlO-3«0.88654xlO-5(56.430)2'25ஹz{ᳫ}~⌕▲LRᐕḄ=4£”(%(R*)3)ᵫ1%=£$(—(R*)3)=---------38*)3*G%(R*)3)=l%xg»(R*)3=W4%(/?*)3£/(R*)=4(A)x/(R*),3*+£*(/?)=l%xR*,ᦑ£$(8)=£(/)=l%x=——o3R33006ஹ_=28,ᢥ⌴_`ᓃ=ᓃ1-(஻=1,2,-
)z{ᑮ0V783«27.982(BKᨵᦔᦪV)Oz{¡⚗£ᨵᜧ¥ᓃ⊤§Ḅe*¨)=ᓃ-%,ᑣe*(y0)=O,ª«ᵫᓃ=ᓃt
ᯅ*27982=J
¯x°ᓃ
ᓃ=ᓃt
%

¯x(27.982-7783),ᓽe*(y„)=e*(%T)
¯x(27.982-7783)=e*(27.982-7783)=…*+/(/)=e*(4)
(27.982-77^)=7783-27.982,100

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Òdx?[]Ôr=dx=arctan(N+1)-arctanN,ÊNᐙᑖᜧλMᦪ×a=arctan(N+1),f3=arctanN,ᑣN+l=tana,N=tan0,*+iN2+N+\ÑV+l11ÔØLi+%2dx=a-p=arctan2N+N+\9ஹÚ¹ÛḄÜÝᜧÞ100cm,ßÏ᪵àáâᐸ☢~GH?1cä2?[]ᵫå((/*)2)=[([*)2][£*(/*)=2/*£*(/*)⌕£*((/*)2)=1,ᑣ*஻*ஹ£*(”*)2)_1ᓽÜÝßæç/=100±—2x10020020010ஹS=$g/Ꮇég=êëḄ+tḄàᨵ±0.1ìḄíîÊtïäÎSḄ(ïä+ᓾ×஺íîÔåয=ò)*,)=gw=(W*,£$(5)=õ=ö÷=ø2=Qᡠ·Dí஺S9(ᔉt5t11ஹúᑡû>“ýæç⌴ᐵÿy“=10y,i-1(஻=1,2,…)ᐝ=⊈a1.41(ᨵᦔᦪ)ᑮ0!ᨵ"ᜧ$%&'()*ᔩ$

3,-./0”23Ḅ567Z(y„)=y„-y„,ᑣᵫ<஺=>?J”=10%T-1y1411=C஺'EF£*(>0)=ᓣ1஺/L-%=IO(%T-O1)ᓽQ=10%.R12£"(>“)=1஺£*(T_.)=10"£*(T)VW£*(X0)=101°£*(Z)=10◘ᕆ10-2=9108,_`'(a)*஺12ஹ/=(c-1de⊈஺1.4,ᑭᵨhᑡjklm&nᑮḄopᨬr$~(3-2V2)3,——99-7072o(V2+1)6(3+2V2)3z._2/{=9|]ᡠ~£(V2+1)6e*(£)=|*(1.4)=M^XIOT=6.54xKT,<1*10-2,ᨵmᨵᦔᦪ;22=(3-2/)3,e*(£)=£'e*a.4)=6(3-2xl.4)2xxl()T=0.12xl()T<|xl0-1,ᨵᨵᦔᦪ.-1=(3+2e*(£)=A'e*(L4)=------——x1xItT4=2.65x10"<_1ஹ10"ᨵmᨵᦔᦪ33(3+2x14)422_.___t11£=99—70e*(£)=£e*(1.4)=70xjxl()T=35xl0-i<^xl0',ᨵᨵᦔᦪ஺13ஹ/(x)=ln(x-ylx2-1),/(30)Ḅ7஺ᵨᦪ⊤¢ᦪ!ᨵ"ᜧ$ᦋᵨ¤m¥¦jkIna-T7CT)=-ln(x+V7=I)ᦪ!ᨵ"ᜧ$,-._2,3()2_I==29.9833(ᨵᦔᦪ)^*(x)=-x10-4,ᡠ~2

41e*(/i)=(/§)*e*(x)=-.x-xlO(3O-\/3O2-1)2Xஹ10-4=0.2994x10-230-29.98332e*©32ªT©/2'ª,e*©xª-X10-42------!------x^x10-4=08336x10-630+29.98332x+1Olox=IO1014ஹ¬ᵨᐗ¯-(°12Ꮇ*²ᨵᦪ¢op³ᔲX1+L2=2E☠?1A101A10_7,-.·¸-2᳝=T—º2=C^஺»¼ᵨᦪ½nᑮ10'°-1210,°-1x=l,x=1,opE☠஺215ஹ¾F¿À☢Â=,Ã^!1஺ᐸÅc2ÇÈ0

5ØCÙÚ7¯©40-42ª1ஹ᪷Ü©2.2ª*ÝḄßℳáᑡkâ1X()X஺-cᓃ©XoX|JÏÐᓃ©xª³nç"⚗kéḄ1Z—1ä•æ1XX2…xn᪷³êë,…Éᓃ©XoX|,…=V,i©XoX|,…,X,Iª©X-Xo>-©X-X“Tª஺.m!’mR.m!ᓃ©XoX|,…,x“Txª=nn©x,rªn©xrª,ÏÐ.ᵫ°EnÏ஺j=o2ஹ»x=l,-1,2,/©xª=0-3,4,/©xªḄCçÚ7"⚗k஺(X—X)(X-X2)(x-XoXx-x?)(X-Xo)(X-X|)L(x)=%(X஺-x1)(x0-x2)(X|m/)(î-x2)(X2-Xo)(x2-X|)(x+l)(x—2)(x-1)(ï—2)(x-l)U+l),-.+4x=Ox+(-3)x(1+1)(1-2)(-1-1)(-1-2)(2-1)(2+1)--(x2-3x+2)+—(x2-1)=—x2+—x--236233ஹñÃfM=InxḄᦪ7⊤ᵨòឋÚ7cCçÚ7ln0.54Ḅ567஺X0.40.50.60.70.8Inx-0.916291-0.693147-0.510826-0.357765-0.223144,-.e4=0.5,%,=0.6,ᑣy=/(x)=/(0.5)=-0.693147y,=/(%,)=/(0.6)=-0.510826ᑣ00,ôஹX-X|,X-Xx-0.6xX-0.5L.(x)=y„------+y.-----Q-=-0.693147x----------0.5c1i0n8o2o6x--------1%m/Xi—/0.5-0.60.6-0.5,=6.93147(x-0.6)-5.10826(%-0.5)=1.8232U-1.604752VWL,(0.54)=1.82321x0.54-1.604752=0.9845334-1.604752=-0.6202186஺ex0=O4,$=0.5,x=0.6,ᑣ%=f(Xo)=/(0.4)=-0.916291,2=/(x,)=/(0.5)=-0.693147,y=/(x)=/(0.6)=-0.510826,÷Uy)22

6,<ஹ(x-x.Xx-xJ,(x-x)(x-x)(x-x)(%-%))020L,(x)=y()+y(+y2(x-X])(x-x)(x(-%)(%(-x)■(x-x)(x-xj00202202=-0.91629lx(x-S5)(x-0-6)+(ߟ0693147)X(ºm°4)஺-0-6)(0.4-0.5)(0.4-0.6)(0.5-0.4)(0.5-0.6)+(-0.510826)x(X-84)(X-0-5)(0.6-0.4)(0.6-0.5)=-45.81455x(%2-1.lx+0.3)+69.3147x(x2-x+0.24)-25.5413(r-0.9x+0.2)=-2.04115x2+4.068475x-2.217097VWL2(°-54)=-2.04115x0.542+4.068475x0.54-2.217097=-0.59519934+2.1969765-2.217097=-0.615319844ஹñÃcosx,0°4x490°Ḅᦪ⊤ûü=1'=(1/60)°,ᦪᐹᨵ5ᨵᦔᦪẆÿᵨ
ឋcosxḄ஺⁚/0—W)-----+(ᨴM()-----,de2!ZM/X,-Xocosj(x-x)(x-x,)+(y-y)X%l+(y1-%%,Je(xo)xj0002X|MX஺x-x0|R(X)K||COSaX-Xo)(x-Xj)|+|y-y1'+M-%]00QXr|1s-5<—5(x_XQ)(X_X))+—x10+—xlOx------2%)-x0-5=-x6.94xlQ-54-lxW5=3.47x10-57J-+-X102422144002225ஹᓰ=%()+l)k-1,2,3,max',(x)|஺

7pqM%0rpqMsrpqMsrmax|/9(x)|maxx0')=(y-x)k,ᑣ¦§¨/(>1)=(y-x)"Ḅn▤ª«ᨽA⚗C,(y=x,ᓽ±஺7^/(x)€´/(a)=/(b)=0,^-a)2max|/w(x)|0

8¹⊡ᐙ⚪3,ᐸ¼½/p¾=/3r=0ᓽ±஺8ஹᙠ-44x44ÀÁÂ/(x)="ḄÃÄ⁚*ᦪ⊤)ÅᵨÆÇe’Ḅ)⌕ÊËÌÍÎÏIO",ÐÊᵨ*ᦪ⊤ḄÑÒh#½AÔÕ[]ᵫ⚪234)xÊᵨ⁚/z,×)/=Ø+ÙÚÆÇ)ᑣÛ2(X)=/Ü(X-Xo)(X-Ø)(x-X)2Ý⚗)')k-U,-h)](x-x)[x-(x+/?)],^G(X,X)t]02oxfM=[x-(x-h)](x-x)[x-(x+h)]=x3-3xx2+(3x}-h2)x+(x,2-h2),]]]}ᑣ/(%)=3x2-6X]X+(3xßMà)dey()Ḅ᩽x=x±—h,ᦑx1I/.zJV3,V3V3.,2V3en3max/(x)=~~h•(1+—)h-(1--~)h=——h',eeq3339|/?(x)|<—max|/(x)|<——/z3=4h3,⌕ÊᐸÍÎÏ10ã,ᑣᨵ2616927å^7/34I஺-஺)ᓽ஻J24yxio-2æç^xlO”=0.472x10-2஺27e27.3899ஹÅy“=2",OéN¢ê”஺à“=(j)ë=ì(->íf=£(M௃)ï"}=0\JJj=0\JJ[]=(-1)H+(—»O+(T)2(ßò+2+(-1)(}òM+(T)(:ò°=2,,+4-4x2,,+3+6x2,,+2-4x2,,+|+2"=16x2"-32x2"+24x2"-8x2"+2"=2"

9=E4(—u(4,ஹᔢõ=24(—M,4jஹ)n+2-jJ=0\JJJ=0\.JJ(-1)ö+2+("4ஹভ4ஹ4ভiy.+i+(T)2Y"+(M1)33pT+(T)#-2l=2n+2-4x2n+l+6x2"-4x2n~l+2T=16x2n-2-32x2"-1+24x2"-2-8x2"-2+2"~2=2"-210ஹ᝞ü"xr¨mÇA⚗C,ýᏲpÿ=஻+/,/xḄk▤ᑖNf8x904&4m—⚗!A"'"/x=01&'᦮ᦪ஺+,-k.ᵨᦪ01234஺11ஹ:8;&9=^fg+஺kk+}MfkgJ=fk+igk+fkgk=fkiS-fg+fkgki-fkS+,+k+ikM+k=(Ai-fDgk+i+fk(gk+gk)=&\gk+i+ftAgk+.I12ஹX=,=f.g“-fogo-£gk+iᦈk஺k=OA=O+,>&1!@!£fNk+£gk+Nk=E(fM+gk+i⚚)t=°஺k=O,ᦑE஺F.!=E"k(g*+1-gD+gk+id+t—ߟ),=^(gk+lfk+l-fkSk)=fnS-foSonk=Ok=On—\13>OP^y஻Ay஺஺j=o?!+,X"x=Z(4+iᑜ)=X)'.X&஺j=oj=o14ஹYf(x)-a+“|X+…+a“_/"T+%x"ᨵncdef᪷x”/…i0»*_JO,0

10uv)=%n(xj-w)xᵫᖪḄឋ{1|34}:/=1nxkn11/@=£——-----=——,E஺/পf)%(…!/=1ᵫ15ஹn▤ᙳᨵᑡឋ{O1)YF(x)=t/(x),ᑣ“XtpXi…,x“]=c/[XoX],…,@2)YF(x)=f(x)+g(x);ᑣF[x(,,X|,…,x,=/[XoX],-ஹx“]+g[XoXnx,@஺F(x)"cf(x)n»oX|…x,/=--------=-------->=°n(x.-x,.)஺v-)[]1)=CL---------=t/[XoXi…,X,i=0(n(Xj)=°n(x-x,.)>on(x.-x,.)77i=0i=0MjMj16ஹ/(x)=¢+£4+3x+i,¤஻2°,2O…,27],/[2°,2O…,28]=/¦=஺.8!8![§]/[2°,2',-,27]=q=1,/[20,2',-,28]o17ஹ©ª«¬®ᱯ°±²⚗&(x)=/(4'C)(x—´)23-µ|)2/4!,1e(4x*+J,ᵫ·¤¸ᑖ¹«¬®ᱯ°±Ḅº▲஺Q[§]½P30¿P33,º▲&À/0+—/imaxE|஺270᝕“118ஹXXXXXXXXXX.19ஹ¤cᦪdÃÄ4Ḅ⚗P(x),.ÅÆÇP(O)=P'(O)=O,pপ=p")=l,Pফ=1஺

11+§,sP(x)=ax4+ax3+ax2+ax+a,ÊijP'(x)=4ax3+3ax2+2ax+%,432{Q432xᵫn(0)=P'(0)=0,nপ=P«)=1,nফ=14EOfO=P(O)=a°°="°O=P1O)=q°=fl|9z<1=2প=஺4+%+஺2+஺1+஺0§E<,=஺2°1=P'(x)=4%+3a3+2%+&31=n(2)=16ad+Sa.+4%+2a+យÎ=%20ஹs஻x)GC+a,b,,ÑL,ᑖ&nÓᑖÔ᪀⌼c×▤ØḄÙᑖ¹°±Úᦪ᜛“(x),Ü"->00Ý8.(x)ᙠLಘàáᦈãᑮ/(x)஺sup/(x)+inff(x)+§,ç/(x)=3Ü——uè/=1,2,3,…,*21ஹs/*)=1/(1+/)ᙠ—5WxW5àê”=10,ᢥÓì⁚ª¤ᑖ¹îឋ°±Úᦪ(x)ïðᔜ⁚ªòªᜐḄ(x)¿/(X)Ḅ±ôïº஺+§,ᵫ⚪r4}h=l,Üxe+x*,x*+JÝ,++1)2X-xk+lk------r-(X-X,.)+---------5-(X-X,)h(\+k2y+'|Mi+a+i)2,k22ஹ¤/(x)=/ᙠ+aಘàḄᑖ¹îឋ°±Úᦪ4(x),ôïº஺+§,s÷+"ಘᑜᑖ&øù&hḄûvüa=Xo4$4…4x,=8,ᑣÜþ=0,1,2,…,஻1Ý,

12,fIfIv2X_4+iXfxl(X-X)-X1(X-X)+lkk+l/%(x)=/J*+/"*+i=x*+X*+1=X(Xk+l-+Xk+iXk~Xk+\Xk_/.yr—<4+1T4»4+1”Xk&x=X_x«x_Xk+'=X_4x-x«+i2ᦑ|&$|=|%&'஺&)+1|^—°23ஹ-/x
=/ᙠL"/Ḅᑖ2345ᱯ789:;஺<=>?@<"ಘᑜᑖCDhḄEFG஺=xW$4…4x“=/?,ᑣIxwJ,x%+J,&=0,1,2,…஻&1M,/%(X)=fkak+fk+iak+l+fk0k+fk+\Pk*l(O).3X-X,.|,..3X-X/ஹ4P------+-(x-x)+4x---------k--*_%)kk+i(x*-x*"l^-x)+lkr(4)বRᵫk=0.30-0.25=0.05,hj=0.39-0.30=0.09,h=0.45-0.39=0.06,2

13hh,h,=0.53—0.45=0.08,l(8.10)mn=——L—,஻i=——,(/=1,•••,»-1)'5+phM+hJ4_0.099h2_0.062qr4=-,%=--,+/Z|0.05+0.0914/?1+n0.09+0.0650.0844-'&,h+h0.06+0.087230.05_5%0.09_3“2-1%+4-0.05+0.09-14'h}+'2-0.09+0.06-5’h.0.063LL.=——=—-0.06+0.08—7'ᵫ(8.11)mp+(j=1,…”-1)qr,gτ=3(4E஺xJ+஻4K஽D=/[,F)-"')]14Xj-x14x-XjQ23*0.5477-0.5000+2x0.6245-0.54770.30-0.25140.39-0.30.,94775768ஹ192793x(—x-----1-----x-----)=2.7541145001490070002/(X)-/(X,)3/(X)-/(X)g=3(2/[x,x]+///[%,x])=3[-------------2-----------------------1----------------3-----------------2---122122235x-x5x-x2}32c20.6245-0.547730.6708—0.6245ஹ3xz(_x______________τ__x_____________)50.39-0.3050.45-0.393x(2x⍛+x)4x256+3x463=2.4135900560010004/5-/F+3/஺4-/yg3=3(/l3/[x2,x3]+//3/[x3,x4])=3[]7x-x7x-x32430.6708-0.624530.7280-0.6708ஹ=3xx-------------------+-x--------------------)o0.45-0.3970.53-0.454633472ஹ4x463+9x1181457z{…=3xx-----1——x-----)=-------------------=-------=2.0814600780014007005209142.7541--X1.0000142.1112231
}▣m:2m22.413=2.413,=55331.787142.0814--x0.68680277

14m0.907810.8278;S(x)=£[),&+(x)]஺m20.657017=0m32)ᯠᩩgᦑ8=3"]=3/a)7(H)=3x77-஺.5஺*3=2.862i°°1x,-x0.30-0.255000/*“)&/(z-1)0.7280-0.6708572g“=3/[x,ix,=3x-------------=37x--------------3x—=2.145,%fl0.53-0.458002100095X-2.862-“0&20014142.754123}▣m^020m22.413,q=m2,5532.0814m34300277_4_2.1454400027S(x)=¡[ᓃk(x)+⊈(x)]஺j=o25ஹ¤/&)€஺2¦ᔣS(x)¨`a᪵ᩩdᦪ©ª1)1\f\x^dx-[[S\x^dx=f[/*(x)-5w(x)]2dx+2[s\x')[f"(x)-S\x)]dxN2)¤f(x)=S(x)(z=0,1,•••,«),m®¯78⁚±S.a=x

15=S"(b)[f'(b)-S'(b)]-S\a)[f\a)&S'(஺)]&Af"'(x)-S\x)]dx=S஻S)[/3)-S'(b)]-S\a)[f'(a)&S'(஺)]&A[f(x)-S(<=S"(b)[(b)&S'(b)]—S"(a)"'ভ&S'(a)]⊡ᐙ⚪^1ஹÂÃ=0,=1,ᑏÅyx=e-*Ḅ&a78Ç⚗m4x,9:;78É⚗஺<=>ᵫz=yx=e"=1,y=yxj=eTqrir/ஹX-X|.x..-.x-()=,lxx-1+e]xx-0L](X)=y------+M0XofX]—XQ0—1------1—0,=_(x-1)+e~'x=1+(e-1-l)xÉ⚗Hi(x)=’¹(x-x)(x-*)=x(x-V),Je(0,1),0ᦑ|/?|(x)|~~xmax,-]xmax|x(x-l)|=gxlxi="஺2ஹ?/(x)=/,_ᑭᵨÑÒᨽÔ78É⚗XᳮᑏÅ-1,0,1,278⁚±Ḅ`a78Ç⚗m஺[=]ᵫ78É⚗XᳮᨵfভO&(X)=———(X-x)(x-X])(x-x)(Ø-x)023=—(x+l)x(x-l)(x-2)=(x2-2x)(/-1)=x4-2x3-x2+2x4!L(X)=f(x)-&(x)=x4-(x4-2x3-x2+2x)=2x3+x2-2x303ஹ?/xᙠᑁᨵ▤ÜÝÞᦪ-©:max/(x)-[/(«)+"2_J®(X—a)]<|(/?-a)2max|/w(-«)|°<©>ß/ভ+"U/ভd¨a,b78⁚±Ḅ/xḄàឋ78Ç⚗b-amᑭᵨ78Ç⚗mḄÉ⚗Xᳮᑮ^/X-

16max/(x)-[/(஻)+/(")/(஻)(x-a)]<[maxf-max(x-a)[x-b)añ▤ᖪ▤ᖪ`▤ᖪë▤ᖪ1421-3540-26]_1_76124~6011710-6~nTsoᵫᖪ⊤q4aïð78Ç⚗m:

1757N(X)=4-3(X-1)+(x-l)(x-2)-(x-DO-2)(x—4)4o60+(x—D(x-2)(x-4)(x-6)1o(J78É⚗57=4-3(x-l)+(x-l)(x-2)-^(x-l)(x-2)(x-4)o60+(x-l)(x-2)(x-4)(x-6)RRx)=(x-l)(x-2)(x-4)(x-6)(x-7),JG(1,7)°6ஹ᝞]⊤WXdᦪ^i=0,1,2,3,4,Xj01234/(X,)36111827_;ôÅᑡ⊤dᦪḄᑖ⊤9ᑭᵨïðᔣö78÷mWÅøḄ78Ç⚗m஺<=>᪀⌼ᑖ⊤:/,2ZA4/,x,%A03320016520211723189427N*஺+th)=/஺+©஺+û3{2/°+…ᵫᑖ⊤q78Ç⚗m^_2=3+3/+-1)x2=3+3f+f(f—1)=f2+2f+32

18ü`ýdᦪþÿ
80-821ஹaᑭᵨᣚLbḄ឵ᚆ⚗b!/x=sinxᙠ0,y,-1./3.឵ᚆ⚗12345167Ḅ89:᪍<ᦪ>ᑖ/@ABCD஺FGaHI=஺+K-“M,ᑣOP឵ᚆ⚗B“g9=£f—9P6ᐸRS-n\xk(h-a-y-kxkJbHMT^55ᑣOP឵ᚆ⚗ztᐸRᔾ=xk^-x)1-k7Tjlcᵨ/5x=X/XSx=/0k=0271sinOxx+sin—xx=0x---X\+X=X)22}JjrLBf,x)=Ef(~^)Pk(x)k=0஺,3ஹ*5+2/(0)%r3b|-d+/e—)0+a)27ஹ37tsinOx--X+sin—x3x(--x)2+sin—x3x2(--x)+sin—xx3623223.nஹ23-V327%ஹ33.71~23ஹ3ᚖ)/ᐔ23ஹ3=hX(---X)H-----X(---X)+X=-(X-7CX+X)H-----(—X-X)+X22222422=4x--7T(l-V3)x2--(3V3-5)x38422ஹ-lm(a)nmp5m

19P(%)1LlKfM_1\!==y£-n--xk(i-y-k=Y--------------------»1(஺xx6nkl(n-ky.tf(^-l)!F(n-l)-(^-l)!=x£,…=+(1-ᑘ1=xk=o1!(஻_k)!3ஹᙠ.ᦪ6Ḅ⚗R5-/(x)=sin4xᙠF0,2Ḅᨬ⚗஺FGᵫsin4x,xeF0,2yz5-1

20O+arccos—11?9)'=å/(")+/*2)]+%(x—åsinO+sin(arccos)]+(x-------——-)2227i712J/—4212ஹ2J/—4i2z=-------+—(x——arccos)=x+-----------arccos—2%ã271712ᑍᑍ7C7ஹ-/(x)=e5ᙠF0,1,Ḅᨬ.⚗஺[G]ᵫq=ë^__£1^2=/(%2)=e"=-——¹•=e-lyí2=ln(e-1);OPᨬb-a1-0.⚗y=g"(a)+/(M2)௃+ð—‘2")=+(e—])(x-஺+ò5——)OpIpp—\=-+(e-\)[x——ln(e—l)]=(e—l)x+-------In(e-l)8ஹ᝞õ⌱ör,Äp(x)=/+rᙠF—1÷,µAᨬÐr¥ᔲÏÐFGᵫmaxp(x)=max(x2+r)=1+r,minp(x)=min(x2+r)=ryznµ-1W1-l

211k,-./ಘ12ᙠ0,145ᩗ᜛=89Ḅ;<=⚗?஺@yJX-X212ஹᙠ-1A4ᑭᵨDE᩽Gᓄ/(x)=arctanxḄIJKLᨬNOK=⚗?஺Dk-1PQᵫ⚪SDE⁚UVcosWXY(2=123),8ᓽX1=COSY[2=cos~x3=COSY=cos(\,ᑣ]"%)°13ஹ`/(x)=e*ᙠP-1,14ḄDE᩽GᓄKLᨬNOK=⚗?VL“(x),a||/-4bᨵd-efgh஻21jᙠkᦪ%⊈n]o,ᵨ(x)|<|/(x)-L„(x)|

22sin”+τ(5/5ஹ383273X)=-X+X{|V3!5!41638432-+—x—»7.986xIO7<()005஺7!1201616ஹ/(x)2P-஺,஺Q4Ḅ᜻(Ꮤ)ᦪ-en2᜻ᦪᡈᏔᦪ/(x)ḄᨬNOK=⚗?2᜻(Ꮤ)ᦪ஺PQ/(x)ḄᨬNOK=⚗?2ᵫᑗ=⚗?]ᑮḄᵫᑗ=⚗?Ḅឋ¡4ᓽ]஺17>aஹbn+Pax+b-sinx2dxVᨬGx¢1⚪£6⚪Ḅ¤JOK=⚗?{|¥¦஺nPQᵫ+xdx=—,Fx2dx=—,=+sinxdx=1,J)8X)24Gnn4=Rxsinxdx=(-xcosx)IJ-R-cosxJx=1,]7ta=--(4¤;r)=0.664458b9;]¨ᐔஹaQ7T~24]/,=(%¤3)=0.1148T18ஹf(x),g(x)GC'[a,b],ª«(a)(7,g)=f/'(x)g

23}VÅ—1326஻26a2323a23a1Na>0,ᑣj|x_ax|tZx—j(x_ax~)dx+J(ax--x)dx—(——-6f)_(__G—_)—1Áᳮؤlீa<0Pjx-ax21dx=1,Øa<-1Qt¤*W>1,()ØV1´ᑖq]ᨬG஺21ஹ`/=spa஻{l,x},(p=5pan{xl0°,x101},ᑖ÷ᙠ%,ø4¤ᐗùnᐸV2/eCQlQḄᨬNüýOKx¦ᐸÃÄ஺PQᵫQldx=l=1x2i/x=»<3=,"=7,ᓽᙠ᜜b=\fxl0l.xl0lJx=—ᵫ1201b202b203xm-x2dx^—,|\|°"/=-^,103b104

2411-199x201x202mea=------------------x375.243201202a103103x104=((ᓽᙠ᝞11b1,-98x202x203……’b=---------------------«-375.148202203..104.104x103(375.243,-375.148)o22ஹ/(x)=Nᙠ-1,1(,ᙠq=span*,/,/Ḅᨬ/0123஺[]ᵫ£|xpx=£-xdx+8dx=1,jx?=£-x3dx+b3dx=—22152Cl-----35128a£x5dx+x5dx=,222,210;b=-----357128222105c=-------579128151052105,49:ᨬ/0123;⚗=(p(x)----+-----x--------x12864128sin[(/?+l)arccos%]23>஻“(x)=?@ABᑗDEF;⚗=(GHIᨵ⌴LᐵNM„(x)=2XM„(X)-M„_(x)o+l][GH]O3=85஺(ᑣ3/ஹ/ஹcsin[(/?+l)arccosx]sin(narccosx)(x)=2x---------==----------------==—JlᔆVl-x2R_sin[(/?+1)6^]sin(n^)2cos^sin[(M+1)^]-sin(n0)sin0sin0sin0sin(஻+2)e+sin(஻e)-sin(஻6)sin(n+2)0..=T==W,I(X)sin0sin624ஹS/(x)=singxᙠᢥUVW;⚗=XᑗDEF;⚗=YZ(,[\ᨬ/0123;⚗=]^_`abc(defᙳ1`a஺[]hᢥ᯿ᑗDEF;⚗=YZsin2=1+ZGZ(%)(ᐸk22`aC=—Psin8S”oskl8,k=0,1,2,…hᢥ᯿UVW;⚗=YZ(Ano2sinp=%*s*(x),ᐸk%=t(sin3aodx9:2k=0/

25«o=2Lsin2-Wx=2(_2COS2)-1A0«.=—fsin-=—[(-2xcos-)L.-f-2cos—=—[(-4cos—)+4sin—\\]2X1222■2222=-f(-4cos-)+8sin—]=12sin--6cos—22222ḄAgfτsin]•(3x2-\)dx-07f.x1_஽ஹ/%=-Jsin—•—(5x3-3x)dx7ixdx1A—{[-2x—(5x3-3x)008—]^-J-2cos—K—(15x2-3)dx}=—[-4cos—+fcos—(15x2-3)dx]22o2=-{^lcos-+[2(15x2—3)sin±]—f2sin'30xdx}=Z[-4cos-l48sinl-60psin^Jx]'+222J-12711v-Jy=—{-4cos—+48sin—+60[(2xcosA)12cos—dx\]222212=1f-4cos—+48sin-+60(4cos8sin-)]22222=-(256cos--432sin-)=896cos--1512sin-222229:[\ᨬ/23;⚗=3xsin—=Z4A(X)="i4(x)+%(x)2%=o=(12sin--6cos-)x+(896cos--1512sin-)-(5x3-3x)022222=(2240cos--3780sin-)x3+(2280sin--1340cos-)x222225ஹ/(x)=arccosxᙠYᡂᑗDEFᦪ஺hᢥ᯿ᑗDEF;⚗=YZarccosx=9+£G/(x),ᐸk2k=\C=—1arccos(cos0)coskOd0=—£Oc^kOdO=—[(—sinᦇ6)-1—sinᦇ□lk7Lᐔ)TCk'k2122=—(-yCOS&6)=-^-[cOSkTl-1]=—7—[(-1)A-1]7ikk~7ikb

26/819:arccosx=giLx
=-26ஹᵨᨬA,c᝞y=a+b/Ḅ=(Iᑡᦪᔠ,],ᙳ1`a஺1925313844%19.032.349.073.397.8[]ᵫ4=3ᓣ
,/£
=Z%=19.0+32.3+49.0+73.3+97.8=271.4஺/=154=%¢,/a,=Zy>x1=1=19.0x192+32.3x25z+49.0x312+73.3x382+97.8x442஺=6859+20187.5+47089+105845.2+189340.8=369321.55£9i¤
(9i□=Z1=5,/=15¥¦,᜜X஺=ZX=19?+25?+3/+382+4421=1'=361+625+961+1444+1936=53275᜜¤,᜜¤=2%=194+254+314+384+444/=1=130321+390625+923521+2085136+3748096=727769955327Ta271.41ª[a=4.578ᦑ1©(<53277277699b369321.5J[h=0.047ᙳ1`a£sx..
-/«¬=+᝞2-/X,.
2=6.477025+2.732409+0.555025+0.729316+4.9729=15.46667527ஹ¯°ᱥ²Ḅ³´µ¶(_·ᦪ¸¹tº00.91.93.03.95.0»¼s½010305080110¾³´µ¶A\;⚗=/x
=a+foc+cx2,ᑣᵫ

2764=%¤,/À=2ஹ=0+10+30+50+80+110=280oi=I.6d=᜛2Ä(/¤=2/a2/=1=0x0+10x0.9+30x1.9+50x3+80x3.9+110x5,=9+57+150+312+550=10786“3=஺3«"X,='//=1=0x02+10x0.92+30xl.92+50x32+80x3.92+110x52஺=8.1+108.3+450+1216.8+2750=4533.26ÉɤÊX,.=£1=6,Z=16Ì3,᜜¤-Í(5¤=Zd=°+°9+1§+3+3.9+5=14.7,i=l0a,/£=03᳝,8P\X,.=02¦(0256=^2=o2+0.92+1.92+32+3.92+52=0.81+3.61+9+15.21+25=53.63x1=1692x,(93x,=e3x,(GXi=Zx=஺3+09,+1.9,+33+3.9,+53i=l=0.729+6.859+27+59.319+125=218.907693x,,°3x,=Zx=4+0.94+1.94+34+3.94+54<=I=0.6561+13.0321+81+231.3441+625=951.0323614.753.63a-280a=—0.5837ᦑ1©14.753.63218.907h=1078;•&=11.0814o53.63218.907951.0323c4533.2c=2.2488ᦑ³´µ¶/x=-0.5837+11.0814x+2.2488-஺

28ÕᵨᨬAÖᳮØÙᵯÛRḄᜧ஺ᵯÞஹᵯÛᵯßà¹áâ᝞ᐵNU=IR.ãᵨᨬAÖᳮ(,Rl/?)=£(/,R-6)2åᑮᨬ஺ç_R),èᑮd(R)=2f஺i=l/=1ê/O(p'(R)=0,ᑮᵯÛRR=----o%/=12ஹçëìíî°ïðn\(ᑮn3ñò,2,…,ó(ôõö0ᙳòë=^(X|+2+…+X”)øᡠ,íî(úûHᳮᵫ஺nO᜛(x)=S(x-xj2,,X9(x)åᑮᨬ஺ç9(x),èᑮ/=1(p\x)=2^(x-x,),Od(x)=O,ᑮx¤(ýûHö0ᙳò/=!஻/=1X=—(%1+X,+…+x”)ᙠᨬAþÿ
ᑮᨬ஺n3ஹᨵᦪ᝞⊤⌕ᵨy=a+3ᔠᡠᦪ!"ᔠ#Ḅa%boX,-3-2-10123-1.760.421.201.341.432.254.384567%(x)=l(Pi(x)=x3,ᑣ66(9o(x)8o(x))=Zl=7,(9O(X)9I(X))=3(X),°O(X))=ZXC=஺/=0/=06(9I(X)9I(X))=ZXC=1588,D/=066(eo(x),y(x))=Z%=9.26,(᜛|(x),y(x))==180.65஺ᦑIJKi=0i=070"9.264=1.32295P01588KᡭJ80.658=0.11376

294ஹᙠRSTUVJ#ᦪyWXYUZ[࠷]Ḅ^_ᦪK4567%`]=஺%`6]=>,ᑣ44`b`஺],%`஺]]=c3=30,`bযᵨe]=`0e%`8]]=c3f100,;=11=14h`]ᵨ`0]=ZT=354,D/=144`᜛o`e],y`e]]==17.2,`°|`e],y`e]]==55oᦑIJKi=lZ=1k3010013`17.2ஹ-fa=0.9497=,5P1o100354mn`559M=-0.11295ஹᓫqrsᦪḄtK]=aeuᢥ᯿ᨬfxy"zᦪa%b,{|ᦪ᝞}X0124y2.0101.2100.7400.450456~=஺"7~ᦪPlny=lna-bx,Y=lny,A=lna,ᑣᔠᦪKY=A-bx,ᡠᦪᓄKX0124y0.69810.1906-0.3011-0.798578o(x)=l,᜛](x)=x,ᑣ443O(X)9()(X))=E1=4,(0o(x)9](x))=⊈(x)9o(x))=Zx}=7i=\i=l4(᜛I(x)(x))=Zx}=21,Di=l44(0o(x),y(x))=Z%=-O.21O9,⊈(x),y(x))==-3.6056஺ᦑIJKi=li=l

3047lfa9f~0-21099=5P=05946721m``3.6056]DᔠᦪKb=-0.3699/=0.5946-0.3699X,qᔠᦪKy=eO^-஺,=18123e369"

31ᦪᑖᦪᑖ(107)1ஹ!"ᑡ#Ḅ"zᦪᐸᦪ¡Z¢£¤¥ᢣ§ᡠ᪀⌼ªḄᡠᐹᨵḄᦪ¡Z஺ff(x)dx«+4/(0)+Af(h)C1)tJ-h456ᑖ¬7/(X)=1,,ᐭP¯1m}A-+4+4=[jdx=2h=-h6A_1+AQ+A1—2/zA,,(-஻)+A()•0+A/==0;ᓽA7fA15P»=¼3A1,A,(-A)2+A,-02+A/?2=fx2Jx=-/z3A.4-A4,=-ht134=-/236½K¾=/¿A_(-h)3+A-O3+Ah3=--h4+-h30=xydxC1o1661112九5+力5A5W力5¾஻X)=x4¿,A_1(—%)+&.()+A஻4-6-6=-3-5ÁDÂᨬ¤ᐹᨵ3Ãᦪ¡Z஺2)rfWdx«A_,/(-/z)+4/(0)+AJ(஻)CJ-2/J456ᑖ¬7/(x)=1,,ᐭP¯1m}%+4+A=f}ldx=4hA-i,+UA)+AI=4/z(

32456ᑖ¬7஻x)=x,ᐭPᑮ:(-1+2x+3X)/3=^xdx=0l22x.+=1ᓽ1[(-I)2+2xC+3Ò]/3=[x2dx=|2x}+3%2=12-3V22+3V2M=X]=775PVÔ1+2V21-2V2X2~M=77+31+2Õ]\7J8-36V2+108-54V2J+6×+24+16ؽK¾/(x)=d¿=[-l+2x----------------------+3-----------6-C--------343343=[j3dxKR+2Ù8+36Ú+108+54Ø1-6Û+24-16ᦈ[-l+2x----------------------+3-----------6---------343343-36+11472c0=^x3dx343ÁDÂᨬ¤ᐹᨵ2Ãᦪ¡Z஺4)«M/(0)+/(/?)6/2+Ý"'(0)-f'Wh0456ᑖ¬7/(x)=/ᐭPᑮ}/7(0+/)/2+Ý(_2/?)=13,ᡠÞ஺=½K¾/(x)=d¿/1(0+ᝯ)/2+à”Ë2(32)=C4,////¾/(x)=/¿/(0+/I4)/2+—a/i2(-4/i3)=-/z5^-h5,ᡠÞÂᨬ¤21265ᐹᨵ3Ãᦪ¡Z஺2ஹᑖ¬ᵨât%ãäåæçᑡᑖ:(1)f—^CJ,4+%2

33k`7117T=-[f(a)+^f(x)+f(b)]=-[-+^-8sk,k=\1஺4è=]4+0164é256+51mê84242401256ஹ1ஹஹ…=K[F2(-----4-------1--------1------1--------1------F----)4—]=0.111401642576526517281733055i77Sg=Í/ভ+”X,)+2c)+/(&)]64=0A=12᝕+1k7í16+2Z-8m2k=l4A+716(2᝕+1)8k+2Z-----------—«0.111571024+(2^+1)24=1256+5¡!Kf—^)2dx,n=10C(ᶍ)X(4xdx,஻=4C3)456`ᶍ]¡!Kð5=2]|}=2`27-1
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£/6^/-sin28pd8p,஻=6C`ᶍ]஺3ஹñò_óôᱯö`2.4
ᐹᨵ5Ãᦪ¡Z஺4ó§6÷ᯠ⁚úKÊûüû,”ýÍᑖ¬7/`]=1,k/,/,/,/,/424ᐭP¯U}^^7+32+12+32+7=6—a=jldx,b-a-2,3a+bஹ-a+bஹ+3/7x——[7Q+32(——)+12(——)+32(——)+7b]90424b—cih—aa=------[7a+32(஺+Z7)+6(஺+8)+lb]=——-——=[xclx

34"[7/+32þ+ÿ+12("+')2+32(")2+7Ḅ90424b—Z7=90[7஻2+2(9/+6"+/?2)+3(Q2+2"+஻2)+2(஻2+6+9/)+7஺2]b—a2cjcm2\b;—ap,=(30஺~+30஻஺+30/?~)==x^dx9030——7«3+32(——3+12——)3+32(——3+7/90424=+-(27a3+21a2b+9ab2+Z?3)+-(a3+3a2Z?+3ab2+b3)9022+^(a3+9a2b+27ab?+27/)+7/]b-a.45345,45,45,.b-a....,,,.22322=------(——aH------crbT-----abH------b')=-------(a+b)(a~-ab+b'+ab)90222244J/ᓃ;7a4+32(^-^)4+12(^-^)4+32(^^)4+7b4]90424^^-[7a4+-(81a4+l08a3b+54a2b2+12ah3+b4)9083i+-(a4+4a3b+6a2b2+4ah}+b4)+-(a4+12a3b+54a2b2+108ab3+81h4)+7h4j;ah-n=-^-(18«4+18a3&+18a2/>2+18a&3+18/>4)=-j-(a4+a3fe+a2/>2+ah3+b4)ᓃ37as+32(/+12(+32($+7য90424^Z£[7«5+_L(243Q5+405஺48+270a382+90஻2ᓃ3+]5a//+ᓃ5)=90323+-(a5+5a4b+l0aib2+10a2/>3+5tzfe4+b5)8+—(a5+15a4/7+90a,2+270a2b3+405ab4+243b5)+7b5]32=^^(15a5+I5a4b+\5a3b2+15a2/?3+15ab4+15/75)90b—a4a,2,4,ᓃ'ߟa"A,=-------(a+/?)(஻+2a~/72+//)=------------xS'dx661

35b~a[la6+32'+")6++஺)6(fl+3fc)6+7&6]+3290424^b~a[7a6+1(72946+1458a%+1215a%2+54஺//+135//+180+1)901283+(a6+6a5b+\5a4b2+20a3b3+15a2b4+6ab5+b6)+1(a6+18a5/7+135a4/?2+540a3/?3+1215a2/?4+1458a65+729h6)+1b6]128h-a^2564051710_219531710405,825,6ஹ(a+a5kb+a41h+ab+a2';b4+ab5+b)906432128161283264b1-o,=£x6dx656789:;ᨬ=ᐹᨵ5@AᦪCD஺4ஹᵨFGH:;89ᑖk-,:KLMNO஺S=+4/f-]+/(b)]="(0)+4/(Q]+/(1)][R]6I2J6I2J1-11=U(/°+4e2+

36]J/,(x)\jdx=)l[/,(;—a+—b)ஹ+/m“(—a+—t>)ஹ/(x__a+b.)2f_”A(^o.,(__a+—b,y2]1d,x+xppH6="r/(/—஻^+b)ஹx+1/r;(,ak+)b(ஹ/x—U஺+—)22+Z/"7(஻2-)/(^UU஺+—ᓃஹ)33]M«஺2222o2=")S-a)+p=஻)3-a)+(1)36ஹg:;(2.9)FGH:;(2.11)஻-8ᦈᑮ9ᑖj'/(x)dx஺(ஹ23/"(஻)=-//"[n)12஻/-s„W/<4)()=--f—>l74)()=_S-")/(4)()87180<2j180I2nj2880n47ஹᵨᓄg:;89ᑖ1/(x)dx,⌕9ᑖ¡¢£a,¤ᑖᡂ¦§yᑖ¨©ªNO«¬£(®«M¯ᐭNO)i£R±ᵫ/—7“=-q■s”)=T/77)=—%/஻(஻)´µ1212Un28ஹᵨº»¼½¾M¿9ᑖ2fe~xdx,⌕8NO«¬IO'஺[R]ᵫT®=1--^—T_(h)ÁR,„(//)=஺("ᒹ)஺(ÃÄ95mmy4-1kZ74—1⚓)9ஹÆÇÈ⍝ÊUËÌᙊ,ÌᙊᕜÏḄM¿:;ÊSÐÑaÊÌᙊḄÒÏÓcÊᙢᳫpÈ⍝p(Ìᙊp)ḄÖ×ØhÚÛᙢÜÖ×,HÚÝᙢÜÖ×,H=6371:ÑÚᙢᳫÒÞ,ᑣa=(2R+4+/z)/2,c=(஻-à)/2஺ᡃâãU⚩à⌼ÆÇÛᙢÜÖ×h=439:Ñ,ÝᙢÜÖ×Ú2384:Ñæ8ÆÇÈ⍝ḄᕜÏ஺2R+H+h2x6371+2384+439£R±ᵫ஺==7782.5,22H-h_2384-439=972.522

373,6,12çḄqᵨ᜜`¿¾8éḄÛêq஺£±ëÚ"(3)=3sin-=2.598,T(6)=6sin-=3,036TCj)=3.1058,ᵫT(12)=12sin—=120h1TmWTm-iS
274™-14141T(6)=-7j(3)--7j(6)=-x2.598--x3=2.464,4141Tj(12)=-2j(6)--7^(12)=-x3--x3.1058=2.9647,r(12)=—Tje)--T(12)=—X2.464--x2.9647=2.43062஺2l1515151511ஹᵨbᑡ½¾M¿9ᑖ,Kîïðñ஺1纻¼½¾jò2çdÜÁóÜ=ô:;j3ç9ᑖ¡¢ᑖÚõyᑖᵨᓄöÜ=ô:;஺£R±/ᒹ=In)lh=ln3=1.0986஺12ஹᵨdÜ:;÷óÜ:;8=ᙠx=1.0,1.1÷1.2ᜐḄaᦪqKò1+XçLMNO/òXçḄqᵫb⊤ûü:X1.01.11.21.31.4f(x)0.25000.22680.20660.18900.17361h2£R±ᵫdÜ:;x°ç=é£ÿ+"-5+,1h2/'6=-஺+&2-@

381h2=2""஺"+3+31,f'(x)=ெ3x0.25+4x0.2268-0.2066]=-0.247,0O.l2-240I2&'(|M+x0|---x-------<—x24=0.0843(i+a3f\x,)=—^ߟ[-0.25+0.2066]=-0.217,&'(2x0.1O.l2-240I2|“(9)|=-6-X(l+^)5<--x24=0.04,6f\x)=*[0.25-4x0.2268+3x0.2066]=0.18720.12-240I2&'(<+=2|---x-------<—x24=0.08o3(1+P3ᵫABCDf'(x)=ߟ1—[-25X0.25+48X0.2268-36x0.2066+16x0.189-3x0.1736]012x0.1=-[-6.25+10.8864-7.4376+3.024-0.5208]=-0.2483/'3)=------[-3x0.25-10x0.2268+18x0.2066-6x0.189+0.1736]12x0.1=f^[-0-75—2.268+3.7188-1.134+0.1736]=-0.2163f\x)=---[0.25-8x0.2268+8x0.189-0.1736]212x0.1o=y^[0.25-1.8144+1.512-0.1736]=-0.18831ஹIJ[-1,1]ḄLᑖ/=£/(x)dxḄPBQLCD£/(x)dxag/(Xo)+(yJ(X1)஺[T]QLCDḄUᦪWXYZ2஻+1=3,\QLCD],ᓰ_QL`ᦪg,ab(4cde`ᦪfghiLjᦪ/+x(UᐭQLCDlᑮnop:

39g=iজ஺+g=2g%o+(vxl12,vTlw=_y22z{QLCD(00r0+(VX1lgx4+st;/=|£/(X)dr«/(--y-)+/(})஺2ஹ~CD(y(x)dx^—f(a)+f(b)CD2^f()dx«(h-a)f(~^\ᐹᨵgUᦪWX{CDx;7h—/7a+br/(«)4/+/S)ᐹᨵgUᦪWX஺+2[<]পfg\/(x)=l,x,UᐭCDljb~~ab—ci;)--[/(«)+/0)]=——(l+D=^-«=J"x422&b-ab—ab2—a~p,—^"(a)+/3)]=-^(a+஻)=---=xdx4222*b—ab—a,2ஹb;—ab-+crb—a;b;-a;(*>2>-y-[/(«)+f(b)]=-^-(«-2+b')=-----------------------=ߟ--=jx-dx,z{CDᐹᨵgUᦪWX஺(2)fg\/(x)=l,x,᮱UᐭCD,lᑮ:(b-a)f\"+'\=(b-a')xl=b-a=I*Xdx4,,.Ja+hyS-a)f\J=(b-a)x=jxdx4,,.a+b\(a+h\(b2-a2)(«+&)b3-a3->(஺)/1=஺)><)=-------------=jᔆCz{CDᐹᨵgUᦪWX஺(3)fg\/஺)=1,/,|,UᐭCDlᑮ

40=""ভ+"6“x6=஺-a=jldx4^-T^-lf(a)++/(/?)]=+4x+b\6I2J62,b—ab——a-F=——x3(Q+0)=——-——=jxaxb-a.ஹ.(a-\-b\...h-aA¢,2i%-[r/rভ+4r/¡+/(஺)]=-^-[r/24x+/r]+»=-~~-x2(a2+ab+b2)=-———=fx2dx631b-aa+b\.....b-a.(a+b^.ff331^—[/(«)+4/--+/(&)]^^^[«3+4x--+h3]6\276\2J.=~—x—(tz3+a2b+ab2+/)=————=fx3dx6241b-a.ஹ.,/a+by\...b-a.(a+b\.^^[/r(r«)+4/——+/(&)]=~—r[a44+4x——+b441]6k276k2Jb—ci54332427354b;—a'«4=----x(—஺+ab+—a~b~+ab+—b)w-------=xdx642441z{CDᐹᨵgUᦪWX஺3ஹQ®¯QLCD(f(x)dx«|[2/(1)-/(I)+2/(1)]ḄUᦪWX஺[T]fg\/(x)=l,x,/,x3,UᐭQLCDlᑮ-/(1)+2/(1)]=1(2-1+2)=1=pJx4|[2/4)-/(1)+2/(1)]=1(2xl-lxl2x1)=l=Pdx4+JIIJII|[2/(1)-/(1)+2/(1)l=|f2x(l)2-lx(1)2+2x(1)2]=l=^2Jx4—/(g)+2/(1)]=1[2x(4±-1x§)32xg)3]=4=(/³.+?2´-/(1)+2ᔩ]=ᩗx$1x(᜛+2x}±]=ℿA4=»"¼½ᡠ¿QLCDᐹᨵgUᦪWX஺4ஹQcÀḄ⁚Br2_ÂᦪC,ÄQLCDJ(x)dx=C[/(x)+/(M)+f(x)]ᐹᨵÅÆÇḄUᦪWX஺02Tfg\஻x)=Lx,/,/,UᐭQLCDlᑮ:

41_2C(1+1+1)=3C=2=cc=2-3JC(x,+x+x)=0=[xdx323%]B|J.%]+r2+=°,Tl■—-r,r4+X4+X4—1x=02x+x4+x4=0_V2C(x+Ì+Í)=0=3dxr32½ÏQLCD(ff(x)djc=-[/(--)+/(O)+/(—)],ᐹᨵ3gUᦪWX஺ÐÑ322/*)=ÒUᐭQLCDl2V2Ó2ÔDDÕ421112d4—f/(---)+/(O)+f(—)1=—[(----)+0+(—)]=—[+—]=-==fxdx32232234435Lᡠv½QLCDḄUᦪWXÌᨵ3g஺5ஹᵨc⁚B(஻=2)ḄGaussQLCDIJLᑖ/=f—Jdx(=2ᐔ)஺[T]c⁚BḄGaussQLCD(r«4/548,54I=I---7dx=-------——~d—x4H-----------%+/9({¢9%(ᔍ¢I5)I5J025322519Ü=—+—+—=—«6.33331891836ஹÝÞeÂᦪA,B,C_a,ÄlᦪßLᑖCDfJ(x)dx=A/(-a)+B/(O)+Cf(a)(GaussàCD஺[T]⌕ÄᦪßLᑖCD=Af(-a)+B/(O)+Cf(a)(GaussàCDᑣᐸᐹᨵ2N+1=5gUᦪWX஺fg\f(x)=1,x,x2,x\x4,x5UᐭäåWÞᡂç

42A+B+C=4=jldxA(-a)+5xO+Ca-(C-A)a=0=^xdxA+8+C=4A(-a)2+BxO2+Ca2=(A+C)a2=é=^x2dxCAᦑᨵ4,ᓽ¡Ca-=8TlA(-a)3+BxQ3+Ca3=(C-A)(z3=0=£x3Jx3,_3244444jxCa4A(-a)+5x0+Ca=(A+C)a=?=f/-TAja)'+BxO5+Ca5=(C-A)a5=0=^xbdx—,C3,a;{஺99957ஹÝÞeÂᦪA,B,C_%,ÄlᦪßQLCDf(x)dx«A/(0)+”ë)+ìপᐹᨵÅÆÇḄUᦪWX஺½ÏḄUᦪWXíîïðñíᔲíGaussàCDðTfg\/(X)=1,X,X2,/UᐭQLCDlᑮ:1A+B+C=l=A+B+C=lAx0+Bx+Cx1=Bx+C=—=/xdxBx,+C=—x{12B=-2.ᓽ.321TlfAxO2+5x,2+Cxl2=8X4+C=5=02dxBx+C=-'3c=-16AxO3++CxI3=Bx+C=N=»3dx+C=-4A=-6z{QLCD(f/(x)Jx»|/(O)+|/(-)+^/(-l),Ð/(x)=/UᐭlᑮD)6326jx஺4+2x(t¢+txr=2*_!=f/óz{QLCDÌᐹᨵgUᦪWX,363\26245J)íGaussàCD஺

43ôAõÂöᑖnoᦪßT÷(141-142)1ஹøùßú⚪y'=«x+஺y(0)=0ᑖüýþÿ
ᦋḄ
ḄḄ⊤y=ga/+bx஺ᵫy“+i=+h(ax+b),ᓽy,-y„=hax+b),!ni+lnyi_yo=X"("%+')=Z*%)+Ḅ)+b]n+*=°*=0,ᓽ஻n(n4-11=+kah2)+hh]=ah{n+l)xH----------ah2+(஻+l)hh0k=02y“=/+஻bh,012y()=0,x=0,ᡠ*0)’"=஺5/+nbho6ᵫx“=nh,782y(/xnஹax1N2+b,x-[rߟn(«--—1)ah,-2+nb,,h,

44=-an1h1+bnh-ߟ—ߟah2-nbh=—222_hᵫᦋḄy“+i=y„+-[(ax„+b)+(ax+Z?)],n+lah...,=y“+—^+x)+bhnn+lᓽy“+i<*==(xn+X"+l)+bh;!%+1<%=£[g(x*+x*M)+"]=£{g[Xo+(2k+l)h]+bh}k=02k=l2ah(n+1)(1+2«+1)(/7+1)ah2..,=1%+---------'-y+(«+x1X;ᓽnnah{n+1)(//+1)2,,.B=—<-x+-

45y
x“-y“=axn+bx,.'0

46y=1.105x3.01236352327260443898828125+0.05x1+0.055x0.9I0=3.32866169321644890508205078125+0.05+0.0495஺=3.428161693216448905082050781253ஹᵨᦋḄ
k’='+“<)‘QRS"=0.1UVy(0.5),[y(0)=0y=-e~x+x2-x+1஺[]ᵫᦋḄ%+1=ᓅ++X"-%),)'"+1=+]*q+x”0=0,A=0.1,\y,+]=0.905y,+0.045(xt+X“)+0.05(XtM+x“+1),!H=0.905x0+0.045x(02+0)+0.05x(0.12+0.1)=0.0055t2=0.905x0.0055+0.045x(O.l2+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=0.0501443875>4=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=0.144992256972187554ஹᵨ
KLM⚪=°,ᐸ2j]',F[y(O)=l-U+//J஻-0ᦈKLM⚪Ḅy=6<஺[]ᵫy,=y+|(-y„-J„I)»!(l+g)y“+i=(1-,ᓽ1+1n+%+1=)',!X=(s]s0ᵫ2=1=(

472nh᝞OT2—஻4/?limy„=limlim1-=lim1-202+/1h^0\2+h"TOi+12h75ஹᑭᵨ
UVᑖ[e,2dtᙠx=0.5,1,1.5,2ḄL஺(x2[]"{e'2dt,ᑣ‘<,!/?=0.5,ᑭᵨ
\ᑮ:20)=0yi=y„+hf(x,y„)=y"+0.5/,0ᵫ¢=0,\ᑮqn+n%=+0.5xe°=0+0.5x1=0.5t2=_+0.5xe°-5,=O.5+O.5xe025=1.1420127t%=2+05ஹJ=1.1420127+0.5e=2.5011536ty=%+0.5xeH=2.50]1536+0.5e225=7.2450215஺46ஹQ"=0.2,ᵨ¤▤¦ᐺḄ¨©-ªᛞ
J¬ᑡKLM⚪qIஹ(y'=x+y,0cx<1I)<;b(O)=l[]ᵫ¤▤¦ᐺḄ¨©-ªᛞ
K|=/(x“S)=x“+y”“/hh"ஹhhh..h...K2=f(x„+5,³“+5K|)=x“+´+y“+5K]=-+(1+5)(x“+y“)thhhh&=+ὡ¶+=·)=x+-+y+5K2nnhhhhhh~hh2=-+x+y„+-[-+(l+-)U„+y„)]=-+—+(1+-+—)(x„+y“)n[[p[pIpI¸=f(x+h,y+hK)=x+h+y+hKnn3nn3,,hh2..hh2..ஹ]=஻+%“+y“+Alr2T++2T)(Xn+K)]0h2h3h~hy=(஻+3+])+(1+"+=+¹)஺“+ᡭ)

48hy-y+(K,+2K+2KKjn+ln2i+ohBhஹ,ஹr—h/?<ஹBh//ஹ/5f=¼+½{([++)+2[+(1+)(%+y஻)]+2[(+)+(1++)(%+%)]OZZ24Z4஻"2h\,,h2/z+('+2+4)+(l+q+2+4)*+%)}hh2h2=y”+JÀ+஺")+7+(2+/0"“+஺“)+Á+)+(2+/!+)(x„+y„)oZZ*h3h2/+(஻+2+4)+(1+஻+2+4)(x.+y,)]=y“+/(3"+6+)+(6+3஻+/+)(x“+y“)]o44■nÅ,y„.|=y„+—[0.642+6.642(x„+y„)]0ᵫ"=0.2r]+i”30=y+0.0214+0.2214(%+y“)=0.2214%+1.2214y“+0.0214n!ᵫx0=0,%=1\q=0.2214x0+1.2214x1+0.0214=1.2428t2=0.2214x0.2+1.2214xl.2428+0.0214=0.04428+1.51795592=1.58363592t2=0.2214xO.4+1.2214x1.58363592+0.0214=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=3.43650Æ2y=2/-x-l஺BjV=3y/(l+x),0

49[]12Kஹ=f,Ô=/„+thDf„+|D2“+…,nfᔩ=/.+(1-)/Ö“+”×Ø஺%+…ᡠ*h%+i=*+-(^2+^3)=y„+y{/„+thDf+^-D2f+-•-+/„+(l-t)hDf+«t)ÚD?}“+-••}nnnhs/1cr(2Û—2f+V)h~2r[=%+-[2/„+W„+-------------------D-f+-••]n<"2(2Üߟ2t+l)/=y„+hfn+—Df+--------4D-f+-nn.,h2„hy„y.+i=y++GÝ+~ry»+…n!26Þᦪᡠߨ©-ªᛞ=y+¥„+—Df„+—(^2/+fஹDf)“+-••n26Ͻ▤ÆàḄ஺8ஹ¬ᑡá⨩-ªᛞ
Ïã▤Ḅqhhy“+i=y,+3K3)y஻+i½½%+A(2K|+3K2+4K3)KmK\=(1)■“hh஻ஹt(2),/hhஹt=/(X"+§,y“+§K])K?=fg+/,y“+=&),22336K2)K3=f(xn+-h,ytt+-hK2)%+i=*+//(4(+4·+4/)&=-f^n,y„)äᙠã▤¨©-ªᛞ(X.+ph;y“+phKJ&=:f(x+qh,y+qh(rK]+sK))nn2½:2=0,2=312পQ4:23<,p=<,q=,r=0,s=l஺ᓽ2ᡠß
,433

50r+5=14+4+4=1cC1çèéA2p+A3q=-1!ᐹᨵã▤Æà஺Ap~+^q~=—24Pqs=%21413(2)Q4=—,A,=—,4=—,p=—,q=—,r=0,s=l஺ᓽ2ᡠß
,9•3924r+s=14+%+ñ3=1çèéòA2p+-1!ᐹᨵã▤Æà஺24஺2+4/-3.1%pqs=-9ஹᑖóᵨ½▤ôõFö÷
½▤◚õFö÷
¬ᑡM⚪qy'=i-y,y(0)=0,Q"=0.2,-=0ù=0.181UVy(L0),y=1-1஺ᵫ4=0.2Fúᵨ½▤ôõFö÷
,hm=ᓅ+5(3/„-)=y+0.1[3(l-y)-(l-y„_,)]஺!,nn=+0.1(2-3y„+y,,.,)=0.7y„+0.1y„_,+0.22=0.7y,+O.ly+0.2=0.7x0.181+0.1x0+0.2=0.3267,oy=O.7y+O.ly,+0.2=0.7x0.3267+0.1x0.181+0.232=0.22869+0.0181+0.2=0.44679y=0.7ü+0.12+0.2=0.7x0.44679+0.1x0.3267+0.24=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

51Fúᵨ½▤◚õFö÷
%+1=*+g(3,<¼|)=*+s1W<%)+(1<ÝÚ)=ᓅ+0T(2-y-y);nn+iᓽ92l""+i=09y.+0.2,!yᵨ=ýþ+ý஺ᦑ9+2-9s/niQi_L2-3629-'n72QOJO/O7.
>2:R11~1111929249691y3-11%+x0.3299+—=-UJIJ1/JU,11~1111119_2_22=6.065624=055]42+x0.451736+—H11119292_6,96278_+x0.55142+—=-U.UJ47஺o11~1111111-e-i=0.6321஺1h10ஹy'=/(x,y)Ḅᑡᑖ=3+y.T)+%4)-y+3yi)▤Ḅ
!"Ḅ✌⚗஺%203&'(y,=+Ḅ+
y+!>"••
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y+i=/,+஻”+/0+•••,nnnh2y-i=y-3:+*++…
ᡠ08y+y,-i4+54y+i-y'+3y_i4nn=:5>“+y-hy'„+஺y"-jy"+•••4n226hh2h29:1:+/4y+hyn+;y+…
:y+3y-/iy+—+-,,
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J!"✌⚗4+-KL7=-M+஺624811ஹNᐹᨵᑡOḄP▤DQy”+i=&>“+%D-1+஺2yᔙ2+%5%*+UKT+/H-24஺

52MA3[](y„=y„+hy'+—y"+—)C+—+…
+1n2O24y,1-ic,,(2஻)2஻(2஻)3(2/z)4ভy“-2=%-2᜜+—%-ߟy+*])+26244%3o7?4=y“-2hyN+2/J”--^-y^'+—^-y^+,•,஻2"3y'-\=yN-hy+—+—]"+…’ny'n-2=y'n-2hy"+K-y"-ᑏ-]4>+…=y-2hy+2h2y-*y',4>+•••,2o3dᐜ+%y“T+஺2h:2+஻(i*+33+-yL)%2h3//=ᓽi,+aJy”:+/y:zஹ+k'W"+…]ZOZ4Aly37/47+W[%-2hy+2h2y"--y-y+-y-m>+…]஻2n3ᡠ+h{hy'+b[y'-hyN+—Xf+—+…]Qntn2o4/?3+஺2[y'„-2o:+2h2y"--y-☜0+…]},.h2=(஻o+%+஺2”஻+(:஻[-2/+஺()+4+b)hy+(஺[+4%-2஽-4/?)—y2n2n403h+(—%—8%+3/7]+12%)-^-y0+(%+I6a+44—32/?)——y^4)+•22624஺0+Q]+஺2=1<=vᐹᨵP▤I
ᑣxyᨵz:2+/+&+k=1%+4-2஺1-4%=1—%—8%+3b]+12b2=112ஹ}ᑡD~ᓄ:▤D~1)-3y'+2y=0,y(0)=1,<(0)=10\y'=ny(0)=1[]y'=p
ᑣ//:3஻+2y=0,p(0)=1,<=ᨵᓃP=3
-2y஻(0)=1

53y=,ᑣo⚪஻=Y,5஺4=504஺&yx4=e
2)y"—0.1(l-y2)y
+y=0,y(0)=l»(0)=0஺y'=P&'y'=p,ᑣp'-0.1(1-y2)p+y=0,p(0)=0,<=ᨵp'=0A(l-y2)p-yy(0)=1P(0)=03)x"=——k,ᔆ=7x2+y2,x(0)=0.4,x\0)=0,y(0)=0,y\0)=2஺rrx=py'=q&'£(/)=p,yr(x)=q,ljp'=ஹ
q=--ஹ
<=ᨵ<"=:_orrz/°;_yq=4-rIrx(0)=0.4z஺)=0op(o)=oq(0)=2y"+y=013ஹn=0.25,ᵨᑖQ⚪y(0)=0,yপ=1.68&'ᯠ஻=4,y+)2?+y“T(”=1,2,3),i=0,=1.68,ᐭy-2y(=-h2yy+☢-2)ᨴ=02}2BiI«%—2%+%=:%2%ᓽ«+(:2)%+)1=0'1.6S-2y+y=-h2y(/i2-2)y+y=-1.6832332'6-210%ஹ'0ஹ1h2-21%0ᵫ/?=0.25,ஹ01ஹ—1.68,

54ஹ311016‘ᨴஹroஹy=0.494383111=0,B•y-0.95786஺2161—1.68)73=1.3614831ஹ,0116014ஹ©D~y"=/(x,y)«¬ᑖ+i=2y“-y“_1+//2/(k
¯,)
°ᵨ±:3=1r2-Yo⚪);´µ¶ឤ¸¹ºy(x)=---y(0)=y(l)=02'-2஻11-2h1¼=1&'ᵫᑖ¾«¬D~-2hj\y_J,,115ஹ/?=0.2,ᵨᑖDQ⚪Q+fÀ3)'=6X-3ly(0)-y(0)=l,yপ=2&'ᯠ஻=5,ᑘ=2
9=:+i-*=%-1(஻=I,2,3,4);h2hᐭBᑮ(1+/)>Ã:20+>1_y"+L_3y“=6Ä-3,ᓽh2h(2+2Å-᝞-(4+4/+6%2)Ç+(2+᝞+2x0)y,i=6%2(2X,-1),Èᵫ>0~—=1B(%+1)>0-x=/?,<=ᵫ/?=0.2BD~:h/ஹ12-1000%<0,2ஹᡭ=1.014872.12-4.42.0400%-0.144%=1.0178502.4-4.882.240%-0.048,B=1.07010002.84-5.682.6y30.048%=1.21930003.44-6.87ஹhஹ—6.096))4=1.51329

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ᦪஹᢣᦪᦪஹᦪᦪᦪ᝞sinx,e,lnx,᪵Ḅ஺ᨵ!"Ḅ#$%&'()*+,-./0ᔲᨵ᪷ஹᨵ34᪷5678ᑨ:஺;஻22?@ᦪ!•BCDEFGឋIJ/(x)=0,ᐸQ/3)0!4ᓫTUḄVᦪWX80Y⚗$ᦪஹᦪ[$ᡈὅW^Ḅ_ᔠ[$஺ᡠb᪷c0de!4X*,hif(x*)=0ᡂl᪵Ḅ//(x)=0Ḅ᪷()5ᦪ/(x)Ḅmn஺'oᙠq᦮ᦪm,hi/(x)=(x-x")"'g(x),&0<|g(x*)|<+8,ᑣDx*E/(x)=0Ḅm}᪷஺~ᵨ=1x*DEᓫ᪷x*஻%*)=0,/(—0஺!"ḄFGឋ/(x)=0,ᵨiᑮWḄ07Ḅ᝞e-'-x=0஺FGឋḄc0Ẇ஻x)=0ᙠVḄᩩ,᝞ᑭᵨiᑮx*Ḅ¡X,hi¢£Ḅ¤£>0,,*-ὡ<£,¨DXᐵ£0Ḅ஺ᐹ«Ḅ¬⚪✌ᐜ⌕ᦪ/(X)±8V²ḄẆᑨ:³Ḅ᪷Ḅ4ᦪ´ᜧᭆ·¸¹º»¼ᙢ⌱¿ᨵ᪷ÀÁ஺᝞Â⌱Ãi¼ÄX8ÅḄ᪷⌲4ᑖÈe³ÉÊḄᨵ᪷ÀÁ஺ËᑖḄᱯn0~/(x)=0ᨵᓫ᪷ᐹᨵᦈÎÏḄᱯn஺ᯠ%ᨵ}᪷ᡈÑ᪷ḄÒÓËᑖ#$ᨵᜫᦔ஺1ஹᵨËᑖ--X-1=0Ḅq᪷⌕Ö×<0.05஺ÚÛÜ/(x)=x2—x—l,ᑣ/(())=—1,/(2)=1,ᡠ8ᨵ᪷ÀÁE(0,2)Ý

56ÞE/প=7,ᡠ8ᨵ᪷ÀÁEá1,2âÝ/(1.5)=1.52-1.5-1=-0.25,ᡠ8ᨵ᪷ÀÁ(1.5,2)Ý/(1.75)=1.752-1.75-1=—>0,ᡠ8ᨵ᪷ÀÁE(1.5,1.75)Ý16/(1.625)=1.6252-1.625-1=—>0,ᡠ8ᨵ᪷ÀÁE(1.5,1.625)Ý64/(1—)(1_1)2_i_2__i_2L<0,ᡠ8ᨵ᪷ÀÁE1.6251==161616256Ãx*=çá12+1*â=1è=1.59375,2168321a1W;ḄêÈ<஽1.625-1—â=—<0.05஺216322ஹᵨì᪷/áxâ=l-xsinx=0ᙠÀÁ[0îḄ!4᪷ᑮ¡᪷ï¤|/Àâ|<0-஺஺5ðñ஺?3ஹE/!/_]=஺ᙠ/=15▬Ḅ!4᪷õöᦋᑏᡂᑡú[$ûülÉÊḄý@#$þ1âx=l+l/x2,ý@#$4+]=1+l/xÝÝ2â/=]+ÿ2,x*+]=+x3x?=—!x*+]=1/.Jx-14x2=x3-1,x*+1=Jxoykᑖ᪆Ḅᦈ!ឋ#⌱%&'ᐹᨵ*+ᨵᦔᦪ.Ḅ/01஺[4]15°7x=1+89U"7X=2—I>?“(1.5)]ᡠFX2GHIJᦈ!஺25Kᐝ=¥1+,ᑣ"7O=P]71+O23,>?|^(1.5)|=jxl.5(1+1.52)^=◤<1,ᡠFGHIJᦈ!஺I1-11f—3)5᜛(x)=[----,ᑣd(x)=-(x-1)2,>?|᜛'(1.5)|=——x(0.5)2=<2>1,VX-122ᡠFGH]ᦣ஺____□_2_4)5e(x)="/_],ᑣd(x)=1)5,>?

573IQ__8Q(1.5)|=x1.5(9)2c1,ᡠFGH]ᦣ஺2oV384ஹfg&e+10x-2=0Ḅ᪷ᑮj+kᦪᡠ◤Ḅlmno1ᙠqrs0,1tᑁᵨ8ᑖH2ᵨH&ᵨ=72-//10,%x1x0=0஺s4t1)yᵨ8ᑖHz/3)="+10{-2,ᑣ/(0)=-1,/প=e+8,ᨵ᪷qr}s0,1t/(0.5)=e05+3>0,ᨵ᪷qr}s0,0.5t“0.25)=e°25+0.5>0,ᨵ᪷qr}s0,0.25t/(0.125)=e°125-0.75>0,ᨵ᪷qr}s0,0.125t111311/(—)=e16=-0.5605<0,ᨵ᪷qr}16816'8oA171Q/(±)=e32_--0.03578>0,ᨵ᪷qr}—321616325-395?/(—)=e64--<0,ᨵ᪷qr}6432/(±11-)=/8—73<0,113ᨵ᪷qr}12864128?3223—141233/(—)=e256--<0,ᨵ᪷qr}25612825653247277-inR/r-ta2347/(—)=e512----->0,ᨵ᪷qr}——,——51225625651293—5592393/(•^)=8஺24—>0,ᨵ᪷qr}XV/IJX256'1024'>?x*=L(8+-2L)=_L^_=0.090332,ᐳ8ᑖ10஺22561024204822—2°2-e2)yᵨHA*="—ᑣᓰ=3^=0.1,=0.0894829,

5820,089482920.0906391=0.0906391,x~------=0.0905126,41010ᓽx*==0.0905126,ᐳ4஺5ஹᦪ/(x),5ᑗx,/'(X)ᙠ0ீீr(x)ீM,0<2<2/MᑁḄ¡¢ᦪ£¤¥=4-4(஽)ᙳᦈ!/(x)Ḅ᪷ᐗ*஺stᵫX*M=4-4(4)ª«z᜛(X)=x-4(x),ᑣd(x)=1-¬(X),®}0᜛'(x)>-1,ᓽ°>?±ᦈ!஺6ஹ²«x=°(x)ᙠqrᑁ³ᨵ᪷?´a?᜛(x)|"(ᑘt=——<—<1,ᦑÍ=0Tq)ᦈ!஺(P(%)kz0(x)=tanx,ᑣ(p\x}=sec2x,>?Ï'(4.5)|=sec24.5=22.5,½ᦋÑ}4+1=arctanx*,Ò¶(p\x)=—8>?Ó'(4.5)|=——---=0.047,1+x1+4.5±ᦈ!஺%X஺=4.5,Xt=arctan,q=4.49372x-x-arctanx-4.493424஺2}7ஹᵨÕᑡGH&/(x)=/—3x-1=0ᙠx0=2▬/Ḅ᪷஺᪷Ḅ×Ø1x*=1.87938524…⌕&lmÛÜ×Øᑮ*+ᨵᦔᦪ.஺1)ᵨÝÞH;2)ᵨàáH%/=2,a=1.93)ᵨâᱥäH%/=1,å=3,9=2s4t1)Xk-3x*-1_2x*+1Y-o/U)3x^-3-3x^-3,°-2?3t2x23+l_17æ_9_10555_çèḄéXt-z——1.oooooV,~~——1.o/V4O,11ë11-°13x22-3928/17ஹ25616“73'

59")—(Ê)x*+i=xf(x)-f(x_ykk2)9XQ=2xl3x*-1z_ஹXL.+X"|)+1r4-1/—22cXk+XkXk-\+4-1131.9x2x(1.9+2)+l=1^Z=I.881O94X1=1.9,x21.92+1.9x2+22-38.418411582,C1582,cஹ,----x1.9x(z----+1.9)+1841841__________~,1582.,1582._I,ஹ,()■+xl.9+1.9-3,ïð஺8418419558143.42+84121026542442…î…-------------------------------7=----------=1.87941115822+1582xl.9x841+0.61x8412546204321f(x)ki3)4+1x------/ஹ.;ᐹñkco=f[x,x_]+f[x,x_,x_](x-,Xo=1,X|=3,஽=2,ᦑkk}kk]k2t17-(-3)/(x)=-3,/(%,)=17,/(x)=l023-1x-x2-32x,rif[x,X]~f[x,X]16-10஻14,஽c1ஹf[x,%],xJ=----{---2-------Q---{=-------=6,জ=16+6(2-3)=1l0n,02x-x2-12Q“2------/=2------==1.9465745,Õᶍ஺10+V102-4x1x610+V768ஹᑖöᵨ8ᑖH÷ÝÞH&x-tanx=0Ḅᨬkù᪷஺[4]úûü6⚪J=4.493424஺9ஹẆÿ
Ḅx*+]='4+x>0,ᑗA=1,2,…02x.x>^~aᑡX],%,…$⌴&Ḅ஺k[])ᯠX,>0,+,-4ᵨ_6=14+⁐_2=3_.0,ᡠ6242s[-2*`,ᦇ=1,2,…+=஽஽+;—x*==->0,ᡠ6ᑡ$⌴2?2%,

60&Ḅ஺10>@“X)=0Ḅ஽+]=x*-/(஽)/E(x&),%=(x«—XQ/KT-4.2)2ᦈIᑮ/"3)/(2/**))MNO*-/(x)=஺Ḅ᪷஺Q11ஹSTUᑡVᦪXYZḄᦈIឋ\ᦈI]^஺ஹ_Vx,x>0ஹ_V?,x>0I)/(x)=';2)/(x)=—o_-J-x,x<0_ߟV?,x<0_hi1)ᵫ0(x)=x-,))=x---k=-lmn/'(᜜=-1,ᦑZqᦈI஺2yx<->ஹ1+,/ஹ/(x)V?2)ᵫ(p(x)=x-----=x------mn=ᦑZ▤ᦈI஺f'M24—x3312ஹsᵨZ@tuO3—4=0,vwxt᪷yḄz{|XYᐸᦈIឋ஺/(%.)X-a2x+a2a_hi~/(x)=1-a,ᑣx*+1=x*`H------r°/U)333x13"3xl13ஹsᵨZ@tu/(x)=l-==0,vw&Ḅz{|VTEḄx஺.ᓝ஺_hi~g(x)=/a,ᑣxk+l(P(x)2x2x22xkkkk8O14ஹsᵨZ@tu/(x)=x"-a=0\஻x)=l-£=0,ᑖvwḄz{|13-%)/(᪗'-8)2஺f(x)_Xa_-1)K+஻_஻-1a_hiZ+1=lkfr(x)`nx^nx^xnknx^~'k

61hm*4lim>00!ᔳᯅf)2(A/^—XkY_28a-xk)஻x[i--n(n-l)x^1(஻1)lim-------=--------------=lim-----=-----------2஻[஻xt-(஻+1)ᵞ]10°2[nr\fa-(஻+1)%](H-1)_I"-"2[n\[a-(A?+l)y[a]2'y[a,,r_("+l)a-_].ni[a-(஻+l)ax+x^+1nakCy/a-x)228na^y/a-x)2kk5+1)஺+(஻+1)ᨴ(஻+1)(§஺)(஻+l)஻xi=lim----------------=lim-------------=lim----------is-2na^a-x)k^-2na(Va-x)…2nakkM-I_(஻+1)Q஻_஻+12a215ஹz{
=+")$ª«¬Ḅ▤tZ஺Ꮇ¯°x°ᐙᑖ☠3K+Q³x*,-x)/(yfa-x)2ok+lk஻>00yZ(x+3஻)1.4a-x,..3X+Q_4a(3x+a)-x.(x+3a)k+hm—=——=lim---------µlim——-----——-----[h]28(¶_4)318(7a-xj3kT8(º-x*)3(3x+4)o»(V^-Xj3111(4a-x)\3xl+a)5°3x+a3(7«)2+a4ak⊡ᐙ⚪1ஹᑨ¿UᑡtuᨵÁÂÃ᪷|ᢣwᐸᨵ᪷ÅÆÇ1)/_6x—5=02)x=2—[h]1)È/(X)=X3-6X—5,Éijr(X)=3X2—6,Ë|x|ீÎÏ/(x)<0,/(x)-&VᦪËÐ>ÑÏ/(x)ு0,/(x)-ÓVᦪ஺+,-/(-V2)=4V2-5>0,/(V2)=-4V2-5<0,/(-2)=-1,/(3)=4,ᡠ6mn/(x)=0ᨵÂ᪷ᨵ

62᪷ÅÆᑖ-(ߟ2,—V2j(ߟV2,O|,A/2,3)o2)ÔÕtuᦋᑏ-2-x=er,ÙVᦪÚ(x)=2-xÛ/2(x)=e7ḄÜÝᵫÜÝmnÞÂVᦪᨵÞÂßàᐸáᙶ᪗ã@ÅÆ(-2,-1)Û(1,2),,äᡠåtuᨵÞÂ᪷஺2ஹz{æXi=Å+°~,&=01,2,…èéḄᑡ@x021ᙳᦈI@ë஺2XkX111_iÈ9(X)=7+—ᑣ°'(x)=7——T°2x2xËíî1Ï(p{x}=—+—>2l—•—=V2>1,|='--y<—<1,ᵫzy2x\2x2x2{æèéḄᑡᦈI@tuX=2+ðḄñò᪷X*=V2஺2x3ஹᑭᵨ〉ËḄz{ælimj2+õµ•+ᡃ=2okT»--------ஹ,-------'kXn=0,-_iὃ⇋z{æ,-----;ᑣᵨ=y,Z+i=J2+Ûk=0,1,2,…%2=»2+;••••,Xj.=d2+2+.,,+o\V________/k~(p(x)=~+x,ᑣ(p\x)=—,oËxe_0,2iÏ;2j2+x8(x)e[᜛(0),᜛(2)]=[a,2]u[0,2],|;>"(x)“þ,äz{æèéḄᑡᦈI@tuX=VTT7ᙠ0,2ᑁḄ᪷X*=2஺4ஹa᦮ᦪḄ!"#⌕ᙠ!"#&'(ᨵ◀+,-.ὃ⇋"#Ḅᦈ2ឋ஺4ὃ⇋56/(x)=,-஺=(),ᑣ,=>56Ḅ᪷஺/“)=—eᵨxax1----ci!"#x=x_/(&)=4D=X(2-ax),k=0,1,2,…஺!Fᦪk+lkkkf(X.}1

63(p{x}=x(2-ax)&'(ᨵ◀+,-஺ᵫ1-H+i=1-ax(2-ax)=(l-ax)2,k=0,1,2,…⌴JKᑮkkk1-5+i=(1-ax஺)M,k=0,1,2,-••,4K/=ᓃ1(1஺x0)2],%=0,1,2,…alimx^=—<^>lim(l-6zx)2'=0<=>-1<1-tzx<1«>0

64RST4Uឋ56VḄWX5+(198-201,[ᑖ)2ஹ(a)A^_`▣bcdefghi+jkAlᓄ111;0A_2no&^_`q▣஺0.6428X+0.3475஽-0.8466x=0.41273(b)ᵨfghi+4_`56Vz{0.3475|+1.842312+04759/=1.7321஺-0.8466X,+0.4759x+1.2147x=-0.862123no(a)A,&Ḅᐗ~=஺”0,/=2,%••,஻)A^_`QUU,CI..▣%=%,.i,j-1,2,•••,/!,ᡠa=%—-~---a„---!--a'..,ᓽA,^_`q▣஺(b)ᶍ஺4ஹAn▤᜻q▣bᨵᑖ4#A=LU,ᐸ&L^ᓫ▣U>▣nAḄᡠᨵ#ᙳ'஺(1()A(11TJஹnoLUᑖᙽL=Mkx(n-k),U=M,ᐸ&4¢k▤ᓫ▣U-kk▤>▣ᑣAḄk▤#|4*¥ᯠ᜻஺7ஹA^_`§q▣defghi+jkAlᓄᓽ°N,ᐸ&0A_2A=(%)n,&=(aij2>)"Tªnoz(1)AḄ_ᐗ~«>0a=1,2,-,«)ª(2)4^_`§q▣ª(3)a<2)ª(5)maxLr!2)0஺

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660164231642310-25~250100-25—05555251312_19_1312_19010-00100525525525525—>18_7118711000001-05_25525525525or3_1431450010001—-5~2!52f85178517_418_23_]6'100085858517336214130100851742517—>195380010-851785-1731450001-851785174182316'~858585173362141385-17425174T=O19538851785173145-85-1785172-1000-12-10013ஹᵨÖ×+4_56V=ᐸ&4=0-12-1000-12-1000-12

67411125ᡠ=4=£᜛3='᜛2='4032J~214ஹᵨᦋÚḄÛ5᪷+456V-11510723[4ÜX]=§»2=§,P~915ஹᑡq▣ßᔲᑖ4LUãᐸ&Lᓫ▣U>▣äMÅßᑖ4áâᑖ4^ᔲ஺4AḄஹåஹ▤#ᑖæ1,0,-10,ᡠ=A'ßWXᑖ4▣Ḅçèéᣚëkì=஺BḄஹåஹ▤#ᑖæ1,0,0,ᡠ=B'ßᑖ4▣Ḅ

68çè஺CḄஹåஹ▤#ᑖæ1,5,1,ᡠ=Cßíᑖ4▣Ḅçè.bᑖ4^Ḅ஺16ஹî¸[ᑖ⌱ᐗ~ᑖ4+᪾ñ.bᵨò+456V4X=(,X2=-1^30.60.518ஹA;ó-AḄëᦪᑡᦪ2-ᦪõF-ᦪ஺0.10.34Ml=max{0.6+0.5,0.1+0.3}=1.1,|A|,=max{0.6+0.1,0.5+0.3}=0.8,0.60.10.60.50.370.33AZ=0.50.3_0.10.30.330.342-0.37-0.33=(2-037)(2-0.34)-0.332=22-0.712+0.0169,-0.332-0.34,0.71±V0.712-0.13271±271218z=--------------------------=----------------,2200·ö÷2="max(A7)=J"N=8839஺ML=A/O.62+0.52+0.12+0.32=Vdjl=0.8426஺19ஹnz(a)K.(b)3MhM(ீMF஺(a)IkL=ø»

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A-J

72co஻d(A)8=A~]A=max<111+2>-max{2/1+4,1+1}+1,-00822=(|i|+2)-max{3|42}713t4WK7,max{3g,2}=2,OP2224'72max{3,2}=32OPcond(A)^=(-+2)-max42}=(-+2)-3S|=3+6|2|>7஺|A|27oᡠ2co஻d(A)8=77ᨬ$27g=§,ᓽ4=±§஺31ஹWAj*▣2XᐸᑖA==2ᐸW=஺⋭஻2Z(a)cond(A)=[cond(W)]2N(b)cond(A)=cond(W)cond(WT)<>22222[]ᵫA==W'WDE2A(A)=22(IV),A(WT)=A(W),l((WT)T)=஻(WT)T)=l(WT),OP஻AT)=/l2(WT),ᦑU,¡2=|W¢,//1AhM2IW1L=|%2||(¥%=||¦§2(a)cஹo஻d(A)2=||A-2|||A||=|ᓺᓅ|ᖹ=,"|%2]2=[co஻d(W)2b«22য2஺e)2=}|21AhMᓱ|ᖹ஺=(b_1||M2)(||(Wr)_2||kT|l)=cond(W)cond(WT)°2222232>W4=,_°AḄᩩ³ᦪco஻d(A)ஹ,(v=2,oo)஺999o10099--9899[]ᵫA=DE,,OP999899-100-9899-989919405-19602”3)=99-100j|_99-100-1960219801

7312-1940519602ᵫ(AT)T(AT)!=·-392062+1=0,196022-19801AZ40°9º°஺991980119602[99981999819602194052-19801-19602ᵫ!/_4“|==»2-392062+1=0,-196022-19405DU||A||,=[A]L=Jl9603+¼4277608,OPco஻d(A)2==19603+7384277608®39206஺|AT,=199,(A[=199,OPco஻d(A)8=s]1||¿,=199x199=39601஺33ஹ᝞ÁAÂÃ▣2ᑣco஻d(A)2=l஺ÄAÂÃ▣2ᑣAT=",OP"A=/,(A-')TA-'AA-'I,ᦑIÅTHjco஻d(A)2Ç3ᓽ=1஺34ஹWABeQX"XMR"ஹ"*▣Ḅ°Ëᦪ2cond(AB)ஹ-3,/ஹ/ஹ’12-334X.1'15ஹn23ஹá1’14ஹ-183-1-1x2-15(3)012=8«(4)1111X.6<24IJ3Jஹ31-11/kX4>3,q2(5)22=3ஹT-32(1)ãᦪ*▣Ḅäx*▣å.æç.èᣚ,

74ê1-13)<1᳝=12-130-0-35-6ᦑ<=2஺C-21-5)10-10X3=°(2)ãᦪ*▣Ḅäx*▣å.æç.èᣚ,(/32-33-12-33-12-3-1，11144242故!22-0-3->0-3<.-I2133333—.1-3.-5_7_]110-1003~3)1477(3)ãᦪ*▣Ḅäx*▣å.æç.èᣚ,12314ஹ’12314ஹ=10128->0128,ᦑ2X2=2o24113/ஹ00-5-15?í=3(4)ãᦪ*▣Ḅäx*▣å.æç.èᣚ,'12-33415ஹ12-33415ஹ037515222-183-1-1-1553219111160————443431-112,777Xj—10———0—ஹ444)x2=2,ᦑ஺12-33415(12-33415x3=3஺îï5”஺îï5”X4=஺222222->1129,-»cð1129,00——1100——113636lð735ccc91c00-—7000—01361331(5)ãᦪ*▣Ḅäx*▣å.æç.èᣚ,‘1210ஹ'1210ஹ121022330-213-»0-213ஹ-1-302,NT12)0022>2ஹᵨᑡóᐗGaussÒÓÔZõᑡÕÖ×:

75=Z~\\/-X1Ḅ-1531X-ZX-/jj-II1ö~~1/-32ஹ/51|ஹ-2஺1ஹZ*\ஹ஺3OOO|ooo1II8/——343|42-1112O--12oc001333757—2327_________/5—_/OO2|33||2|36|7L31133ü3ஹ0üßýIi|i1<,<;________/9H¢÷|L6|78173|71II3X2X—KI.I.6|7-—τ-4001___-Zஹ56ᔵIIî8K9|⊤ᵨ86|5L6|500|3|ùl-i1J1rஹ_____/—C—/1—_/ஹ஺ஹ6_________7_________4_/9τ6÷5O23H9|"-L2i1L1155ஹ__________________________________________________/\_____________jjjZ3-G¦Lஹᔆ-'X~1OOO|ooo100.8>000011313,JOO2|3316172133I3|1-O02Oᓺ"7L317kû67L4LO14"86|5L31KCO|6|5X2|5211561t'1265581஺9|3-]1___________/2
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79(1n1i--1’422ஹ(4ஹ2211(2)2101—-1910o1_=6?J221212,1ஹ11\_a-010112qk)127%=314o251M64=I?Jk110x29_1lX3>M1^3>21£៣=5I726ஹᵨxy9:2X|+£=32%]—ᐝ2=02N+x2=1(1){x.1+2x,2—3%->3—3(2)—X]+2%2~g0(3)%1+3X2+£=23%2—7c3+4%=—10~c2+2c3-=0x2+x3+x4=22X+5X=2~+2%=52X+x=03434xy9ᐸ▣iᣚ;100(110033912-30-30--302203-74-1003-74-10X4=0ஹ00252(00252Jx=13(1)OJᑮ>21003ஹ>21003ஹX,=—13B93X[=20-30--0-30--->22->2200-14-100-14-1ஹ00252,ஹ000130j

80(2-1000ஹ’2-1000ஹ—12-1000--100-»20-12-100—12—10ஹ00-125,1°0-125q%4g4x=3(2)"2-1000ஹ,2-1000ஹ,OJᑮ■3x=232~3~~0--1000--10025i=1p—>-»4-4~00--1000--10335ஹ00-125J000-5[47>21001’2100n53131020-10-—>220111201112ஹ00123ᓃg2ஹ00120'21001ஹᐗ3=-1ব(21001ஹ>OJᑮ■x=132530-10010—22ᓛ=022->■373700-100i—5555oj14ஹ0012000-7ஹx=(3,-1,5,8)"ន>>[«]||4=|3|+|-1|+|5|+|8|=17o|=max{|3|}=8஺,g+(—1)2+52+82==3vH஺8ஹ£¤1)41M“⊈q2)|§,¨4MH8஺0[£¤]1)=max|x,.|

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