数值计算方法课后习题答案(李庆扬等)

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(12)1ஹx>0,xḄ3,InxḄ஺/>0xḄᑣᨵ£#(x)=6,(£*(x)=8x,*+᝞-Ḅ/./0។V3450670^,<(lnx)="<=-AoInxInx2ஹxḄ2%,VḄ஺%*xḄ,ᑣᨵ£B(%)=2%,(£*(%)=2%,,*+Ḅ£*(lnx)=|(xn)z|_,£(x*)=|n(x*)zl-,|2%|x*|=2FG.k*J,£B(lnx)=*"n?=2஻Go/3ஹLᑡᔜᦪPQRSTUVᐭXᑮḄᦪᓽ[\Sᨬ^
_Ḅ`aᓫ_cᢣefgQh_ᨵᦔᦪj#x*=1.1021,xB=0.031,k=385.6,xB=56.430,xB=7x1.0஺x#=1.1021ᨵ5_ᨵᦔᦪjBxB=0.0031ᨵ2_ᨵᦔᦪjB6=385.6ᨵ4_ᨵᦔᦪjBX#=56.430ᨵ5_ᨵᦔᦪjBᓃ=7x1.0ᨵ2_ᨵᦔᦪj஺4ஹᑭᵨtu(3.3)LᑡᔜḄ▲ᐸxxB,xB,xB,xBᙳ3⚪ᡠ|Ḅᦪ஺/1\***(I)~+%+Be*(x#+xB+xB)=WLB)=£(XB)+£(XB)+£(XB).=-xl0-4+-xlO-3+-xlO-3=l.05xl0-3222(2)xBxBxBB

1*/*♦*ஹஹஹdf/*ஹ/**ஹ/*ஹ/**ஹ/*ஹ/**ஹ,*ஹe(4)0Z5—£(%)=(஽X3)£()+(x/3)£(Z)+(x/2)£(£)k=\7^^^(0.031x385.6)-xl0-4+(1.1O21X385.6)-X1O-3+(1.1O21XO.O31)-X1O-3B222=0.59768X10-3+212.48488xl0-3+0.01708255x10-3=213.09964255xlO-J=0.213099642553xB/xB஺e*(xB/x#)=££xB=£xB+*#,£xBk=\X4=-J—x-xlO-3+0.0311--------x-xlO56.4302(56.430)22-^^-xlxlO-3=0.88654x1O-5(56.430)225ஹᳫ⌕▲`RᐕḄQ£*1%/?*ᨴ4ᵫ1%=£B—஻A*1=—------£¤3NR£*(g஻(R*)3)=l%xg%(R*)3=4(R*)3£*(/?*)=4/(R*)2X£*(R*),3*+£R=1%X-R,ᦑ£Bᑁ=£=1%X—=-^ߟo3R33006ஹh=28,ᢥ⌴tuᓃ=ᓃ1-®஻=1,2,-
ᑮ¯0°4V783«27.982V_ᨵᦔᦪjc²⚗´ᨵᜧ¶ᓃ⊤¸Ḅe*¹=ᓃ,-G,ᑣe*y0=O»¼ᵫᓃ=ᓃ1
ᯅ*27.982/„=ᓃ—¿*ᔊ£¤Á
ᓃ=-²1
¿x27.982
Â,ᓽe*y„=e*y,i-ᯅX27.982-7783=e*Y_-j^x27.982-Å=…*n2+e*¯0=e*4
27.982-V783=7783-27.982,

2ffi|V783-27.982<|xlO-3,ᡠÈ/(7)=^xlO-310007ஹÉÊ-56x+1=0ḄËa᪷fÍᐹᨵT_ᨵᦔᦪj(V783=27.982)ᵫx=28±7^577^5=27.982(V_ᨵᦔᦪj)£¤/=28+4^=28+27.982=55.982(V_ᨵᦔᦪj)஺+Ð=28-/Ñ=28-27.982=0.018,ÒᨵË_ᨵᦔᦪj[Óᔠ⚪Õ஺ÖQx=28-V783=-----3==------=1.7863x10-22028+V78355.9828ஹ×NᐙᑖᜧÚÛ᪵Ý'
0dx?k1+x2à("J=dx=arctan(N+1)-arctanN,×NᐙᑖᜧÚËaᦪåa=arctan(N+1),=arctanN,ᑣN+l=tana,N=tan஻*+tan(a-0=tana-ta”=W+l)-N=,1+tanatan/?1+N(N+1)N2+N+làæf"
dx-a-B-arctan--
----஺kl+x2W+N+l9ஹçÉèḄéêᜧë100cm,íÛ᪵îïðᐸ☢[\S1cò2?ᵫ£*((/*)2)=|(/*)2ஹ*(/*)=2/"(5)£¤°⌕£*((/*/)=1,ᑣ—0ᓽéêíóô/=ioo±—õ஺20020010ஹs=Bg/ᎷøgQùúḄ+tḄîᨵ±0.1ûḄüý×tþòÚsḄ(þò+ᓾ
஺£*(S)=|()*(஺=gf"(f)=0.1£(5)=⊸==3=!ᡠ$%஺S9(ᔉt5t11ஹ(ᑡ*>”-./⌴1ᐵ3y“=10y“_i-1(஻=1,2,…)=%=⊈=1.41(ABᨵᦔᦪF)GHᑮJ஺KLMᨵNᜧPQRGHSTUVᔩP

3XYZ,[Ḅ]^_£*(`,,)=K-ᓅᑣᵫ஺=efJ”=1஺-Tv=1411___τkl£*(%)=mXi஺-o-%=10("fT)ᓽinq=1஺ᡭ-1-12£*(y“)=10£*(y,i)=10"£*()0),st£*(ᨴ0)=10I°£*(x)=10◘310-2=9108,|GHST}UV஺12ஹGH/=(&-1)6,0=1.4,ᑭᵨᑡGHR%ᑮḄᨬP](3-2]1------L,99-7072o(V2+1)6(3+2V2)3[X]£*(/)=X1()T,ᡠ$£=](V2+1)6e*(/)=||e*(L4)=—S^x,xlOT=6.54X1(]T<ᨵBᨵᦔᦪF'I1I(1.4+1)722£=(3-2/)3,e*(£)=¢e*(L4)=6(3—2x14)2xgxl()T=0.12xl()T

41e*(/i)=(/1)*e*(x)=-------x-xlOt(30-V302-1)2------1------x-xlO-4=0.2994x10-230-29.98332e*(32)=|(/2')e*(x)=-x-xlO-4x+2------1------x1xl()T=0.8336xl()F30+29.98332X+in10r=in1014ஹ¼ᵨ½ᐗ¿XTÀ'2"ᎷVÂᨵABᦪGH±ÃᔲX1+o2=2k☠?1A101A10_7XÇÈXX=T—`2=·^஺ÉÊᵨABᦪËHK%ᑮ10'°-1210,°-1x=l,x=1,k☠஺x215ஹÌlAÍÎ☢Ð=,Ñ^!1஺ᐸÓcÕÖ0

5ã·äå_¿æ40-42ç1ஹ᪷éæ2.2çVêḄìℳîᑡï1X()X஺-cᓃæXoX|J•,x,ix)=ᓃæxçÃn¸N⚗ôḄ1••ò1XX2…xn᪷Ã`2,…X“_|×ᓃæ/õ…=V“_æXoX|,…—ᓃa஺,*,…,x,i,xç=nnæXi-xçnæx-Xjçᵫ'=.j=°k%ª஺஻1=V,TæXoX|,-,x,LiAnæx-Xjçj=o2ஹÉx=l,-1,2K,/æxç=0-3,4,ª஻xçḄ·¸å_N⚗஺(X—X)(X-X2)(o_*0)(÷_/)(X-Xo)(X—X|)L(x)=y20(X஺)(x0-x2)(X|-x0)U(-x2)(x2-x0)(x2-xj(x+l)(x-2)(x—1)(ù—2)+4x(i+i)X=0x+(—3)x(+1)(1—2)(-1-1)(-1-2)(2-1)(2+1)—-—(x2-3x+2)+—(x2-1)=—x2+—x~—236233ஹúÑfM=InxḄᦪ_⊤ᵨûឋå_e·¸å_GHIn0.54Ḅ]^_஺X0.40.50.60.70.8Inx-0.916291-0.693147-0.510826-0.357765-0.223144X=x=0.5X|=0.6,0ᑣ[=/(%)=/(0.5)=-0.693147,J=/(ý)=/(0.6)=—0.510826ᑣ*/ஹx—x.x—x,x—0.6„/see/x_0.5nL.(x)=y------+y.------=-0.693147x----------0.510826x--------10Xo-/-1x,-x0.5-0.60.6-0.5,0=6.93147(x-0.6)-5.10826(x-0.5)=1.8232lx-1.604752stL,(0.54)=1.8232lx0.54-1.604752=0.9845334-1.604752=-0.6202186஺=Xo=O.4,x,=0.5,x=0.6,ᑣ=/(x())=/(0.4)=—0.916291,2=y(x,)=/(0.5)=-0.693147,y=/(x)=/(0.6)=-0.510826,ᑣyi22

6,(ஹ(X-X|)(X-X,)(x-x)(x-x)(X-X())(X-X|)02L,(x)=y()+y,(x-x,)(x-x)(%1-%)(%(-x)■(x-x)(x-xj00202202=-0.91629lx(x-°-5Xx-°-6)(-0,693147)x஺°4)*-0-6)+(0.4-0.5)(0.4-0.6)(0.5-0.4)(0.5-0.6)+(-0,510826)x*04)(x-0-5)(0.6-0.4)(0.6-0.5)=-45.81455x(x2-1.lx+0.3)+69.3147x(x2-x+0.24)-25.5413(r-0.9x+0.2)=-2.04115x2+4.068475x-2.217097st$(ÿ54)=-2.04115x0.542+4.068475x0.54-2.217097=-0.59519934+2.1969765-2.217097=-0.615319844ஹcosx,0°Wx<90°Ḅᦪ⊤!"=1'=(1/60)°,&ᦪᐹᨵ5)ᨵᦔᦪ+Ẇ-ᵨ/ឋ123cosx4526Ḅ789:஺<=>?12⁚AB/=/+/?,EFḄCOSX2Bᐜ,Kᦪ⊤2BL,ᐸᑣᵫ⚪QRST-ᯅKgxlO-5,45/ឋ12Y⚗[B\஺)=]஺^_-+B`aᡠc789BdefIX|eXoR(x)=f(x)-L,(x)=f(x)-L,(x)+L,(x)-L,(x)=C)(x-Xo)(x-X|)+(j'o-y)—~—+(y,-J])—~—0,tu2!x.X]x-x0{0COSJ/ஹ/ஹ/_x-x./_X-X7XxxG=ee-(x-x)(x-x,)+(y-y)------+(KeK)------3(x()xJ0002%es%,-x0|R(X)K1cosJ(X-x)(x-X|)|+Tey|A_A'+'e%|x-x000X-X,1…5x-x஺——(X-Xg)(x_X])+—xlOX-----+-X10x------yeᓛ21h2<----+-X10-5=-x——+-X10-5=-x6.94xl0-5+-X10-5=3.47x1O-5-2422144002225ஹ?ᓰ=%()+|k=1,2,3,3max2(x)|x0-x-x2

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)Q0Q<=>=max(2h)h(-h)=—ymax\(x-x)(x-x-=(x-x-3/i)|000f(x)=(x-xXx-x-h)(x-x-3A)0QQᑣ=x—(3XQ+4/?)x"+(3xj+8//?+3h~)x—(x(+4/zxj+3h~)/'(x)=3%2—2(3/+4")x+(3x+Sxh+3h2),tu᩽2ARBo_2(3x+4//)±74(3x+4/z)2-12(3x^+Sxh+3h2)00o6,·¡B_(3x+4/i)±V7/?_4±V703°34--y/14—yfl1—y8l—5—V71/z-3f(x4-------h)-------hx------hx-------h——(14V7—20)/?,0n3333274+V74+V71+V7V7-51ee7X7z;/(xH-------h)—......hx------hx------h=----(20+14J7)/7,0333327ᯠ1)¡B¢£¤Ḅn▤¦§ᨽ©Y⚗[ᡠc3ᡂ«஺2)?/(>')=(y-x)*ᑣ¢£¤/(>')=(y—x)«Ḅn▤¦§ᨽ©Y⚗[y=x,ᓽ¯3஺7^?/(x)e஺±,“³/(a)=f(b)=0,3´2mµ/"(x)|஺

8<=>¸⊡ᐙ⚪3,ᐸ»¼/½¾=/3¿=0ᓽ¯஺8ஹᙠ-4Wx£4Â/(x)="ḄÃÄ⁚Aᦪ⊤&ᵨÅÆ123e’Ḅ452⌕ÉÊË89ÌÍ1CT6,ÏÉᵨᦪ⊤Ḅ!hF¼YÑÒ[=]ᵫ⚪QRS?XÉᵨ⁚AX஺=Ô-/z,X],Õ2=X|+஻Ö×ÅÆ12ᑣRx)=(x-x)(x-X|)(x-x)0212Ø⚗B/,e/\=—[x-(x-h)](x-x)[x-(x+//)],Jw(X,x)]l]o2ofM=~(^i_h)](x-x)[x-+h)]=x3-3xx2+(3x-h2)x+x-h2)]}19ᑣ/V)=3x2-6X]X+(3x-/z2),tuf(x)Ḅ᩽2ABx=x±—h,ᦑiI/.zJV3,V3V3,2A/3unX3max/(x)=-/?.(14---)h-(1--)/2=--Aue03339|/?(x)|<—max|/(x)|<——/z3=—/z3,⌕ÉᐸÌÍ10“ᑣᨵ26“0ᦻÜ26927<10-6,ᓽ/iW024yx]0-2-.3.4863x10-2=0472x10-2஺27e27.3899ஹ&y“=2",3Ý‷c஺?”=(E-I)4y=ß(-1)ஹàc=Z(T)f]y“+4_jnâ஺\JJ/=o[=]=(_l)o[*y…+(e1)(à+3+(e1)2(à+2+(_1"à+1+(T)]:à°=2,,+4-4x2"+3+6x2"+2-4x2,,+|+2"=16x2"-32x2"+24x2"-8x2"+2"=2"

9ã,=(E—å)4y“æe="(T)(àeç“=E(T)(%+2-jj=0j=0\JJ=(-i)°(K+(-i)o+(-1)0“+(-1)(;àT+(T)H஺=2n+2-4x2n+1+6x2"-4x2"T+2"-2=16x2"-2-32x2n-1+24X2T-8X2T+2"<=2"-210ஹ᝞é/(x)¤mÆY⚗[êV(x)=f(f+&)-/(x),µf(x)Ḅk▤9ᑖAA/½X¿½0W&ீ￤ð—yÆY⚗[ñ³N"M/½x¿=0½1Bô᦮ᦪ¿஺µ
EkÉᵨᦪö÷øùR஺11ஹµ?Fব
=úgAi+f^g-1kkMfkgQ=fk+igk+i-fkgk=fk+\gk+i-fkgk+i+f8ki-fkSkµ
k+=(Ai-f)gi+=(g*+i-g«)=%gk+i++kk+e1.eI12ஹµ=/“g“—•/ogo—Zgk+M஺k=0A=0µ
¡B1yr,e!ZfZk+2^+1⚚=HIᓽ+g%+i⚚)k=01=0k=0ᦑ¯஺eý.e!=£ifk(gk+i-gk)+gk+i(f&+iKfQi=£(gzJk+i-fkgQ=f"g"Kfog஺k=0k=0«-Ii3>µZ'x=4v஻eÿᡭ஺j=Oi.?!
XdX=Z(Ax)=Ay„-Ay஺0J=07=014ஹf(x)=a+fl#%+•••+a,1%"-1+%x"ᨵn*+,-᪷X#,/…,x"0»xMJO,0

10f(x)-aY(x-x,)»<ᵫ=ᖪḄឋA1B38C:jnj/=1£F=£—=H3I=^^,QRS஺K/ব)MNপf)("D!i=lP15ஹn▤ᙳ=ᨵVᑡឋA:1)F(x)=t/(x),ᑣK[x(),X|,…,x“]=c/[Xox”…,x"Y2)F(x)=/(x)+g(x)ᑣF[x(,,X|,…,x,Z=/[xox”…,x,Z+g[XoX|[,x,Z஺4F(x)«cf(xM)\],/…,x,Z=--------=X-------*—K஺^஺ᙠ(1-`)/=0/=0[]1),ᵫVf(Xj),]=CL-------------=cf[xr,x,---,x]()lncdপ-`)i=0(K(Xj)=°n(x-x)\h(1-i)7;/=0i=0ஹfjᑅ016ஹ/(x)=/+/+3x+i,l/[2°,21,27],/[2°,21,---,28]=^—^=-=0o8!8!mn#஻2஺,2p…,27
=£^q=l,/2஺,2:…,2ு஺17ஹrstuvwxᱯz{|⚗~&*)=/ভC)(x—Xk)2(x—x*+i)2/4!,(4,4+1),ᵫlᑖtuvwxᱯz{Ḅ=▲஺Qmn#P30P33,=▲஺জ)+—hmax஺27118ஹXXXXXXXXXX.19ஹl*uᦪ+4uḄ⚗P(x),P(O)=P'(O)=O,F(l)=P'Q)=1,Pফ=1»

11[ft?]9K(x)=Q/4+Ḅ/++ᓽ1JP'(x)=4ax3+3a3/+2ax+%,42<ᵫK(0)=K'(0)=0,Kপ=pপ=1,K(2)=18Sp0=P(0)=a°-Q0=Pz(0)=a0%9z<1=2প=%+%+%+஺1+஻()nS<]=஺2°QR1=P'(x)=4%+3a3+2%+431=P(2)=16%+8%+4஺2+2%+¢=%20ஹ9஻x)eCma,b#,¦§,“ᑖn©ᑖª᪀⌼*▤®Ḅ¯uᑖz{°ᦪ8“(x)±"->8³°.(x)ᙠ§ಘFµᦈ·ᑮ/(x)஺supf(x)+inff(x)mn#»ᜐ(x)=3±——K½i=l,2,3,…,*21ஹ9/*)=1/(1+/)ᙠ—5Wx<5FÁ”=10,ᢥ©Ä⁚slᑖÆឋz{°ᦪ(x)ÇÈᔜ⁚sÊsᜐḄ(x)/(X)Ḅ{ËÇ=஺mn#ᵫ⚪78Ch=\,QR±xwmx*,x*+J³1%—T7T1+(/+1)2X-xk+lk------r-(X-X,...)+----------5-(X-X)h(\+k2y1Mi+u+1)2]k22ஹl஻x)=/ᙠ§Ï#FḄᑖÆឋz{°ᦪ4(x),ËÇ=஺mn#9ÐᑜᑖÒÓhḄÕ3Öa=x0WX|W…Wx“=8,ᑣ±xe[x£4+J,%=0,1,2,…,஻1³,

124(x)=fJk+fk+h+1=xlXXk+Q2X-XkXk+\ÙÚÛÜX*ÙX—X*+#Ü+<1X“1-x&_X(XY+1-Þ)+4+1XY~Xk+\Xk_/.Yrr84+#ᓝád4+i43-4QR=`(X)=')(X-XJ(X—X*M)=(X-X)(X-X),kMÏ2ᦑâÙã|ä|ÙxåÜ஺%+ÜKç஺23ஹl/ÙxÜ=/ᙠma,"FḄᑖvwxᱯz{ËÇ=஺mn#9ÐᑜᑖÒÓhḄÕ3Öa=xÙ,Mx௃W…Wxa=b,ᑣ±xeé,z+J%=0,1,2,…஻1³,/%(x)=fkak+fk+\ak+\+fkPk+fk+\Bk+l(Ú)8Ud(f)+4ëb&k-GQR=&(x)=(x-x.)2(x-x)2=(x-x)2(x-x)2,Ak+}kk+iᦑ|&Ùᑮ=îïÜ2Ù%%|Ü2,ð஺24ஹñòᦪó⊤᝞VpXj0.250.300.390.450.53yj0.50000.54770.62450.67080.7280ªltu᪵ᩩ°ᦪSÙxÜ,ᩩù:1)5/(0.25)=1.0000,5z(0.53)=0.6868Y2)S஻(0.25)=S"(0.53)=0஺mn#ᵫ%=0.30-0.25=0.05,4=0.39—0.30=0.09,h=0.45-0.39=0.06,2

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஻22/io+T0.05+0.09144+0.09+0.065Ï20.063=h+/z0.06+0.08723ᵫÙ8.11üj=1,…”18C,9/'(xj-/(x°)τ5/(4)-/(ý)g,=3(A1/[X0,XI]+//1/[X1,X2])=3[]14%1-%014x2-Xjc/90.5477-0.500050.6245-0.5477=3x(—x---------------------+x-)--------------------140.30-0.25140.39-0.30c/94775768ஹ19279=3x(—x------1—x-----)==2.7541145001490070002/(X)-/(X,)3/(X)-/(X)g=3(A/[x,x]+x//[%,x])=3[-------------2--------------------1---------------3----------------2---122122235x—x.5x-x232c20.6245-0.547730.6708—0.6245ஹ=3x(z—x______________τx______________)50.39-0.3050.45-0.3927683463ஹ4x256+3x463-o3x(—x-----1—x-----)=——135900560010004/5)-/þ)τ3/(X4)—/&)g3=3(A,/[X2,X3]+//3/[X3,X4])=3[]7x-x7x-x3243c40.6708-0.624530.7280-0.6708ஹ=3x(-x---------------------+-x----------------------)oQR70.45-0.3970.53-0.4544633472ஹ4x463+9x1181457ÿ…=3x(-x-----1—x-----)—---------------------=-------=2.08147600780014007005209142.7541--x1.0000142.1112231▣:2m22.4132.41355m31.7871432.0814--X0.68680277

140.9078m20.8278S(x)=Z[y(x)+.(x)]஺i=o3.0.65702)ᯠᩩᦑV-x/iᘵ=362^0.7280-0.6708572S=3/[X“TX,=3X3x=3x—=2.145,nX“_X"_10.53-0.458002100092500X-2.862-“0&14142.7541mx23▣%020m=2.413,'(2,2554332.0814m3002_m_2.145jn7744400027S(x)='^[ya(x)+ni/j(x)]஺JJj=025ஹ*/&)€஺2ᔣSQ)/01᪵ᩩ3ᦪ561)[\f\x^dx-[[Sr(x)]2dx=£[f\x)-S\x)]2dx+2[s\x)[fXx)-S\x)]dx2)*f(xj=S(x.)(z=0,1,•••,«)789:⁚<=a=/"

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%)"'ভ&S'(஺)]&A[f(x)-S(<=S\b)[f\b)-S'(6)]-S"(a)"'3)&S'(a)]⊡ᐙ⚪%1ஹ^/=0,`=1,ᑏby(x)=e-*Ḅ&19:g⚗4(x),jkl9:m⚗஺noᵫp=Xxo)=e"°=1%=y(xJ=eT'G,t/ஹx-xx-x1x—1_ix—0Li(x)=y-----}L+M----0-=1x----+ex-----0x-x-x0-1l-o,0l0=-(x-1)+e~]x=1+(e~}-l)xm⚗z={(…஺)(…)=.&),8(஺,1),ᦑ|/?|(x)|-~xmax|e-^|xmax|x(x—l)|=gx]x="஺2ஹ/(x)=/,ᑭᵨᨽ9:m⚗ᳮᑏb(-1,0,1,29:⁚<Ḅ019:g⚗஺[]ᵫ9:m⚗ᳮᨵfভC)&(X)=---(X-X஺)(x-X|)(x-x)(&x)239=—(x+l)x(x-l)(x-2)=(x2-2x)(/-1)=x4-2x3-x~+2x4!L(X)=/(x)-&(x)=x4-(x4-2x3-x2+2x)=2x3+x2-lx303ஹᙠ[a,"ᑁᨵ▤ᦪ5%max/(x)—"(a)+
3)(x-a)o(z,-fl)2|rw|a"b-a-iS0n5o/ভ+/ম3(i)/(a,b9:⁚<Ḅ/(x)Ḅឋ9:g⚗b-aᑭᵨ9:g⚗Ḅm⚗ᳮᑮ%/(X)-n/(«)+"?&(X—஺)o=:C)(x-a)(x-b),b—a2

16max/(x)-[/(஻)+/(")/(஻)(x-a)]<௃maxf-max(x-a)(x-b)a

1757N,(ᐗ)=4-3(x-l)+(x-l)(x-2)—(x-l)(x-2)(x-4)o60+%(x-l)(x-2)(x-4)(x-6)1o(J9:m⚗57=4-3(x-l)+(x-l)(x-2)-(x-l)(x-2)(À-4)o60+(x-l)(x-2)(x-4)(x-6)R(X)=(x-l)(x-2)(x-4)(x-6)(x-7),Je(1,7)஺A6ஹ᝞Â⊤µ3ᦪ%i=0,1,2,3,4,Xj01234/(X,)36111827lÃbᑡ⊤3ᦪḄ¦ᑖ⊤jᑭᵨ¸¹ᔣÆ9:ǵbÈḄ9:g⚗஺no᪀⌼¦ᑖ⊤%xiᵗA2/,A3Z[i03320016520211723189427N4(X0+Ì)=/o+?A/oD-"o+"ᵫ¦ᑖ⊤'9:g⚗%_2=3+3t+^^-x2=3+3t+t(t-l)=t2+2t+3

18Î0Ï3ᦪÐÑÒlÃ(80-82)1ஹ(a)ᑭᵨÓÔÕᣚ×bÓÔna,"ḄØ឵Úᚆg⚗(b)Ü/(x)=sinxᙠ0,^Þ11¨31Ø឵Úᚆg⚗jßbàjÒáâḄãäå᪍çᦪèᑖ¨é¦êbëì஺no(a)^À=a+(b-a)f,ᑣØ឵Úᚆg⚗3).—)")ᐸ7")=᜜ï&ð஺(b)^À=5ᑣñn0,1o,Ø឵Úᚆg⚗B.(ò᜜=£/(ôõ(x)ᐸ7P,(x)=^Vø&X)".஺&=0I"Jᓽ…Xú)")="஺)ᓽ(>>B3(fx)=Ef(7)Pk(x)k=0°=/ᖳ*3+ᵨý"+ᔩÿ
+ᔩ)/
".71,71ஹ2.ᐔஹ2/\.7T3+sin—x3x(---xY+sin—x3x(---x)+sin—xxH623223Kஹ23-V32,4ஹ33.TT23ஹ3`>/ᐔ23ஹ=--X(----X)H-------X(-------X)+X=-(----X—7DC+X)H------(-X-X)+X322222422=-x--^(2-V3)x2--(3A/3-5)X38422ஹ!"#(a)%ᵨ

19ᓻP(x)<;mPk(x)£?(ᑍ)=£xk(1-x)n~k=.x+(1-x)0H=1,C>D"஺k=O(b)%f(x)=x),3kk(n\=)4஺)=Z஻—),/(I—x)zk=O஻1=0df(0)^0JILMn(_1\fn=V-X--X“1—X)T=V--------------------X?T(1—X)-஺஺£nkl(n-ky.h(k-\y.8(n-l)-(k-1)Ql=X>———~———x"(l—X)"""=x.x+(l-X)ST=x3ஹᙠUᦪWXY6Ḅ[⚗]^*!/(x)=sin4xᙠ.0,2)0Ḅᨬa
bcd[⚗]஺.e0ᵫsin4x,xe.0,24089*-lᨬghij1,k┯mj—7T,~7T,-7T,—7T,—7T,—7T,nᓽjP(X)€஻6Ḅᑗstuk┯mv*C>88888888P(x)wxyzmj{|⁚mḄ~ᨽ[⚗]*8D(x)=0o4ஹᎷ/(x)ᙠx*!/(x)ḄUᨬa
bcd[⚗]஺.e0m=inf/(x),M=sup/(x),ᑣ/(x)="±'ᙠ.aಘᐹᨵᨬghi2aixihx,C>jUᨬacd…U[⚗]஺25ஹ⌱ᦪa,Dmax*
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Ucd[⚗]j

20..220+arccos—y=[f(a)+f(x)]+a(x-a'X2)=[sin0+sin(arccos)]+(x-------———)2tn2227T7T2J%2—4212ஹ2dᐔ2
412z=-------+—(x——arccos—)=—xd------------arccos—24Ã2ᐔᐔ2஻ᐔ7ஹ!/(᜜=/ᙠ[0,1]Ḅᨬa
Ucd[⚗]஺[e]ᵫ஻1
-f\x)=eX1--——±=e-l8D·=ln(e-l),C>ᨬ2b-a1-0a
Ucd[⚗]jy=g"(a)+/(Æ2)]+Ç(X-È;஽]+(e-l)(x-*
஺)OpIpp—\=-+(e—l)[x——ln(e-l)]=(e-l)x+-------In(e-l)8ஹ᝞Ì⌱Ír,p(x)=/+rᙠ.fl0Îhiᨬg¥rwᔲ¤
¥.e0ᵫmaxp(x)=max*?+r)=1+r,minp(x)=min(x2+r)=r89%Îhiᨬg)*l+r=r,C>*=-L2Ðe#ᵫᳮ789*ᙠ.-1,10ÎhiᨬgḄU[⚗]j—T{X}=—(2x2—l)=x"——,C>r=—029ஹ/5)=/+3/-1,ᙠ.0,10!ÑUᨬacd[⚗]஺.e0ᡠ!ÑU[⚗]jA(x),ᑣᵫᳮ78914-2+从f(x)-P(x)=—T(X)=—(8x4-8x2+1)XX-348IIIJ421)=(X4+3X3-1)-(X4-X29P(x)=f(x)-(x-X+38ioஹ4r„(x)=r„(2x-i),x€[o,i],!/(x)ஹT+(X)ஹT*(X)>4প஺[e]ᵫT.(x)=T.(2x—1),X€[0,1]89*x=l+5,re[—1,1],ᑣT(Ô+1)=*Õ/w[-14]*C>TM(x)=

21iiஹÖ"ᓄ#(ᑴÙwᙠwÚÛᩗ᜛=JḄÞk[⚗]஺?yjx—X212ஹᙠ.-1,10ᑭᵨ{|᩽gᓄ!/(x)=arctanxḄÑUdàᨬacd[⚗]஺Dk-1.e0ᵫ⚪â89*{|⁚mjcos-----ᐔ,(k=123),8ᓽã=cos+%,ä2=cos~*x3=cos-^/r,x=cos0),å18!Dæ஺)஺413ஹ/(x)=e*ᙠḄ{|᩽gᓄdàᨬacd[⚗]jL“(x),çᨵè*"/éêÌ஻¥1*ëᙠᦪ&*í*D%(x)|<|/(x)-L„(x)|<îg(x)|(-lÍmin|/

22Y2/1+1.e0¦jsinx=x-----1----1---1----------1■…
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ᑮ3!5!(2஻+1)!51rL(X)=X-—+—,inx-A(x),=0.0002,#$5X5^-T+-X3--X,ᡠ&3'()*⚗+S16416

23sin=/(5/5ஹ383273X)=~X+X,453!5!41638432-+-x—«7.986xl0-4<0.005o7!1201616ஹ/(x);<-a,a>?ḄAB᜻(Ꮤ)Eᦪ
GHIJn;᜻ᦪᡈᏔᦪ
/(x)ḄᨬM()*⚗+N;᜻(Ꮤ)Eᦪ஺

/(x)ḄᨬM()*⚗+;ᵫᑗSTU*⚗+ᑮḄ
VᵫᑗSTU*⚗+ḄឋX4ᓽ஺17>[aஹb]p2dxᨬa
bc1⚪e6⚪Ḅf'()*⚗+gSh஺nᑍhn_3ᐔ

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Qn~ab-U-3)=0.1148T247T18ஹf(x),g(x)eC'[a,b],uv(a)(7,g)=f/'(x)g'(x)dx/(b)(zg)=f/'(x)g'(x)dx+/(a)g(a)஺{|};ᔲ᪀ᡂᑁ

(a)$/(x)=0=>(/,/)=j"'(x)>2dx=0=>/'(x)=0,Iᡂ,ᡠ&I᪀ᡂᑁ஺(b)᪀ᡂᑁ஺19ஹᵨᐻI+(4.5)f?Ḅ?
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14¥=/,p·,P"=f7,ᓽᙠÉ?b=lᵫ1i00mfx,°°.xl01Jx=-1-fxl0l-xl0lJx=—x-xdx=—201J>202b203yoo•x2dx=-^ߟ,(?Ë/=
p·,103

25111”99x201x2*375243201202a103103X104,ᓽᙠᑖ?
P11b1,-98x202x203b=-------------஺-375.148202203104104x103(375.243-375.148)o22ஹ"x)=Wᙠ[-1,1]?
[ᙠ᜜=span^.x21,xÏ?ḄᨬMÇÈ()஺[P]ᵫ]=£-xdx+jxdx=1,£X2|X|JX=[[fx3dx+(x3dx=—22152CI----35128a12JO£x4|xpx=x5dx+5dx=gp·,222-得---b212835711O51222-C-一--328579¦¨ᨬMÇÈ()*⚗+Û+Ü/105X,48ÑxÏ=12864128sin[(஻+l)arccosx]23ஹM„(X)=;ÔÕᑗSTU*⚗+
GH|ᨵ⌴ØᐵÚÉÝ(x)=2xu(x)-u_(x)onn][GH]Þx=cos6,ᑣ_/ஹ/ஹcsin[(n+l)arccosx]sin(narccosx)2%,(x)-u_(x)=2x------==------------==—n}\\-X~yji-X1__sin[(/?+1)^]sin(஻e)2cos^sin[(w4-1)^]-sin(z?=2cos0--------------------=---------------------------osin0sin0sin0sin(஻+2)e+sin(஻6)-sin(஻e)sin(஻+2)6,ஹ-==w.,(X)+1sin6---sin024ஹá/(x)=singxᙠ?ᢥãäå*⚗+eᑗSTU*⚗+æç
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ᐔm2sin±=(x),ᐸ4=÷ø
sinø÷(x)dx/¦¨2i=o212

26ᓽ=/jin/•1ù=/(f2cosᢘ=஺/3dv3v*H-v-3iv-4fsin-=—[(-2xcos—)L-[-2cos—=—[(-4cos—)+4sin—iL.]21222û2222=W[(-4cos-)+8sin—]=12sin--6cos—22222=g]sin(3x2-l)dx=0/a2=g(sin]g(5x3-3x)dxa371xAX1C=—{[-2x—(5x3—3x)008—]!.1—£-2cos——(15x2-3)dx}=—[^4.cos—+fcos—(15x2-3)dx]22Ý27]Y"V=—{Teos—+[2(15/f3)sin—ᓃf2sin—30xdx}^[-4cos-L48sin-L-60psin^Jx]+2222711v-Jy=—{-4cos—+48sin—+60[(2xcos—)!_1-£2cos—Jx]}222212=—[-4cos—+48sin—+60(4cos--8sin-)]22222711=-(256cos--432sin-)896cos--1512sin-22¦¨è'ᨬM()*⚗+3xsin—=aP(x)=aP(x)+a3A(x)kk}}2A=o=(12sin—6cos-)x+(896cos—1512sin-)—(5x3—3x)஺22222=(2240cos--3780sin-)x3+(2280sin--1340cos-)x222225ஹý/(x)=arccosxᙠ?æᡂᑗSTUþᦪ஺

°ᢥ᯿ᑗSTU*⚗+æçarccosx=⎃+£G(x),ᐸ2A=1G=—farccos(cose)cosZft/e=—/ecosAft/e=—[(—sinZe)j-sinkᵨ7t7T)7Ck)k2]22=(C0SA6)=y^—[COSl]=Yy-[(-iy-1]7T7tkkKk71M

27L24iarccosx=y[(-l)*-l]T(x)=—~3)஺kk=\ᡂᐔk=iQk-1)26ஹᵨᨬ᝞y=a+b/Ḅ!"#$%ᑡᦪ()*ᔠ,-ᙳ/01஺Xi1925313844%19.032.349.073.397.85[3]ᵫ4=(Ḅ6),/(8))=29=19.0+32.3+49.0+73.3+97.8=271.4஺i=l5d?=(82(X,)J(X,))=Zi=\=19.0x192+32.3x25?+49.0x312+73.3x38?+97.8x4420=6859+20187.5+47089+105845.2+189340.8=369321.55:(%(ᜩ),(p\(X,))=Z1=5,/=15(8),=(x,))=Z*=19?+252+3/+382+442i=l'=361+625+961+1444+1936=53275(8,(x,),>(x,))=Zx?=194+254+314+384+444=i'(=130321+390625+923521+2085136+3748096=727769955327a271.4a=4.578ᦑ/AB3CD53277277699b369321.5b=0.047ᙳ/01BE[S(x,)-/(Xj)=Zb+bxo-/(G)]:=6.477025+2.732409+0.555025+0.729316+4.9729=15.46667527ஹIJᱥLḄMNOP!CQR%ᦪ(STtUVW00.91.93.03.95.0XYsUZW010305080110[3\]MNOPB^_⚗/x=a+bx+cx2ᑣᵫ64=(b(□),/(᳝))=2%=0+10+30+50+80+110=280஺i=l

2864=U82Ux,WJUx,WW=Zy!x!i=\=0x0+10x0.9+30x1.9+50x3+80x3.9+110x5,=9+57+150+312+550=107864=U/&W,fUu,WW=Zyx-t/=1=0x02+10x0.92+30X1.92+50x32+80x3.92+110x52஺=8.1+108.3+450+1216.8+2750=4533.26:U᜛\UXW,᜛\UX,.WW=Z1=6'/=16U9iU⚗W,gU8WW=U=UXW,aU8WW=Zx,=0+0.9+1.9+3+3.9+5=14.7,/=13UX,.W,%Ux,WW=U%Ux,WᵨUx,WW=U%UX,W!“2U8WW6=^2=o2+0.92+1.92+32+3.92+52=0.81+3.61+9+15.21+25=53.63xU/=16⊈UX,W,>Ux,WW=U>UGW!3Ux,WW=Zx?=஺3+0.93+1.93+33+3.93+53/=1=0.729+6.859+27+59.319+125=218.9076U>U8W,>UWW=2=஺4+0.94+1.94+34+3.94+54»=1'=0.6561+13.0321+81+231.3441+625=951.0323614.753.63a-280a=-0.5837ᦑ/AB14.753.63218.907b—1078,3C!Z?=11.0814o53.63218.907951.0323_c_4533.2_c=2.2488ᦑMNOPB/(x)=-0.5837+11.0814%+2.2488X2O28-31ᶍ஺⊡ᐙ⚪1ஹJCᵯRḄᵯIᐸḄᵯU᝞%⊤:IAA....U544....U.ᵨᨬᳮᵯRḄᜧ஺[3\ᵯஹᵯ$ᵯET᝞%ᐵ¢U=IR0£ᵨᨬᳮ!R"CMR)=E(/,R-U,)2¦ᑮᨬ஺¨᜛©ªCᑮ0(R)=2«(//-U,)/,஺i=li=l

29d(R)=O,CᑮᵯRBR=°±2j=l2ஹ¨²³´Jµ¶n^!Cᑮn¸¹º»,,…,x“!½¾¿ᙳºX=-(x+4+…+x“)ÀBᡠ³´!ÂÃÄᳮᵫ஺(n[3\3(x)=£(Å-8)2,x"C᜛(x)¦ᑮᨬ஺¨᜛(x)ªCᑮ/=1"*)=2£஺-8)!"(x)=0,CᑮxÈÉᵨ!ÊÃľ¿ᙳºi=Inf=IX=-(^1+%2+…+X”)ᙠᨬÍÎ%01¦ᑮᨬ஺n3ஹᨵÐᦪ᝞%⊤!⌕ᵨy=a+b/*ᔠᡠÓᦪ(!*ᔠḄaÔboXi-3-2-10123y1-1.760.421.201.341.432.254.38[3\¾90(X)=1,(p(x)=X3,ᑣx66(8O(X)!8O(X))=Z1=7,(/(X)M(X))=(8I(X)4O(X))=ZX?=°1=0j=0.6(8I(X)M(X))=XX?=1588,,=066(8o(x),y(x))=Zx=9.26,(@(x),y(x))=%=180.65஺ᦑ/AB1=0/=070\Öஹ×9.26ஹpz=1.3229=|3C×01588È(ᑘ1,180.65Jᔊ=0.113764ஹᙠÜÝA!ÐᦪyÞ߲ݴ6CC)Ḅáᦪ(Ba1234%0.81.51.82.0

30âãḄBy^ae+bO2,äᵨᨬQaÔb஺[3\¾å6=6,§s=ᱏ,ᑣ44U%©,%3W=2æ=30!Uç©èU஺WW=⊈U஺W,᜜3=23=100!i=li=\4®UeWMUeW=Z64=354,1=144Uçয,yUeW=£e,y,=17.2,3UeW,yUeW=Zex=55஺ᦑ/ABi=l:=1ë3010017.21fa=0.9497=!3C4o100354ÈìU55,=-0.11295ஹᓫîïÐᦪḄBW^=Êð!ᢥ᯿ᨬóôᦪaÔb,âãᦪ(᝞%X0124y2.0101.2100.7100.450[3\¨y=ae”õ¾¨ᦪClny=lna-Z?x,Y=lny,A=

31a,ᑣ*ᔠÐᦪöB÷=A-ø!ᡠÓᦪ(ùᓄBX0124y0.69810.1906-0.3011-0.7985¾%(x)=1,Qi(x)=x,ᑣ44(%(x)!eo(x))=Zl=4!(8o(x)M(x))=(%(x)!eo(x))=Zxi=7,i=li=l4(8i(x)M(x))=Zx=21!i=l44(᜛()(x),y(x))=Z%=-0.2109,3(¶),¶(û))=ü8%=-3.6056oᦑ/ABi=li=l47'-0.2109ஹA=59463Coý*ᔠÐᦪB721ஹ3.6056,h=—0.3699÷=0.5946—0.3699x,*ᔠÐᦪBy=eg’e-oþ%=18123ef699x஺

32ÿ
ᦪᑖᦪᑖ(107)1ஹᑡḄᦪᐸᦪ!"ᢣ$ᡠ᪀⌼(ḄᡠᐹᨵḄᦪ஺1)f/(x)dxN4"(-5)+&/(())+AJS);J-h<=>ᑖ?@/(X)=1,X,YᐭFGIJIA_)+4+4=JUx=2hA.=-h-l6%+A஺+A[=2hA_](-A)+A().0+A/=[R=0ᓽA-=A=F■A)=-h°3WXẆ+4Z+452=f/2dx=2533+A4ஹ"33[A'.=—6h]^_`/(x)=/aAS-hy+A-o3+Ah}=-h4+-h3=0=(x3dxoot664`"X)=x4aA(b%)4+A.()4+A%4=J_555H255=d/dx;°6635஻ghiᨬ!ᐹᨵ3kᦪ஺2)ffMdx=A_J(-஻)+A°/(O)+AJ(஻);J-2/J[=]ᑖ?@/(x)=Lx,bᐭFᑮIA_1+A஺+A1==4hA[++A=4஻-1UI

33<=>ᑖ{“@/(x)=x,/ᐭFGIJI(-1+2x+3X)/3=^xdx=0l22x.+=1ᓽ7[(-1)~+2x1+3%2]/3—1ᔆ=§2x;+3xl=12-3W2+3ᓰ=X]=77=F1+2⊈1-2V2%2=I”b7+31+)]/3]^_`/")=/a#2x8-36+*53*3;r,c8+36+108+541-6+24-16=[-l+2x--------------------+3------------------1343343=-36+114W=Z"J-ighiᨬ!ᐹᨵ2kᦪ஺4)8f{x}dxM/(0)+/(/?)>/2+"'(0)--(o<=>ᑖ?@ᐭFᑮI/7(0+/)/2+(-2/?)=33,ᡠ஺=\,]^_`/(x)=/a/2(0+/)/2+*”2(-3%2)=;64,`/(x)=/a/z(0+/i4)/2+—a/i2(-4/i3)=l/z5^-h5,ᡠiᨬ!1265ᐹᨵ3kᦪ஺2ஹᑖ?ᵨ¡ᑡᑖI(1)

34kh71177;=-If(a)+2£f(x)+f(b)]=-[-2^-8k+,k=\1஺4¢=]4+01178A[=]£¤+2¥+)256+k211¦§84242401256ஹ1ஹஹ…=—[-+2(——+——+——+—+-—+——+——)+-]=0.111401642576526517281733055s=-[/(«)+4^/U,)+2^/(xJ+/(&)]g°k=02&=12᝕+1k7v+ᵯx16+2Z-8*m2k=\A4+716(2k+l)8k©Zª+2Z------------—«0.111571024+(2^+1)2256+5k=\_f—^ᶍ®,_¯:=2°5|I=227-1=8஺3334£6.7-sin2pdp,஻=6;ᶍ®஺3ஹ±²³´µᱯ·2.4ᐹᨵ5kᦪ஺<´$>¸ᯠ⁚»_¼X,Z,”G5ᑖ?@/½®=1,k/,/,/,/,/424ᐭFGUI^^7+32+12+32+7
=/?—a=jldx,b-a-“,3a+bஹKa+bஹ“a+3bஹ——Da+32(——)+12(——)+32(——)+7b]90424b—a/?—-ci~/=——[7஺+323++6(஻+஺)+7¾=---=Jxdx

35b~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—ci2cÃjcm2\b?—ap,Æ(30஺~+30஻஺+30/?~)==x^dx90301—b-—a7a3+32(——3+12——)3+32(——3+r7,&33r90424^^-[la3+-(27a3+21a2b+9ab2++3a2b+3ab2+b3)9022+^(a3+9a2b+27ab?+27/)+7/]b-a.45345,45,45,.b-a....,,,.22322=----(——aH--a~b-\-----ab~H---b')=-----(a+b)(a~-ab+b~+ab)90222244h^-[7a4+32(᝞`4+12(È+32(È`4+7h4]90424=7a•4+(81஺4+i()8a%+541+12/+//)9083i+^(a4+4a3/>+6a2fe2+4a/+/)+ÌÍ412a3b+54a2b2+108஺/+81/)+7/]+=^^(18஺4+184%+18஺Î2+18ẓ3+18/)=/^(஺4+஺3ᓃ+஺2஻+m3+஺4)b-Cly5cc/3஻+bஹS1Ã/஺+ᓃஹ5CC/«+3/?ஹ5r,5r——7a5+32(——)5+12(——)5+32(---)5+7&5]90424=^^-[7a5+—(243a5+405«4Z?+270a3/?2+90a2Zj3+\5ab4+b5)90323+-(a5+54%+10/62+]0a2b3+5+/)8+Z஺5+15஺7+90/62+270a2b'+405+243/)+7/]="஽15஺5+15஺Î+15஺3/+15஺2/+15+15Ô)90b—a4c2>4\I஺_a”Õ'5¦=----(a+/?)(஻4+2a~b~+b)=-------=x'dx661

36"ߟ"[7.6+32R+°)6+12("+஺)6+32("+%)6+7%90424=b~a[7a6+1(729a6+1458a5Z>+1215a4/72+540a3b3+135a2b4+18ab5+b6)901283+(ab+6a5b+\5a4b2+20a3b3+I5a2b4+6ab5+b6)16+1(a6+18o5Z>+135a4/?2+540a3/?3+1215a2/74+1458afe5+729b6)+Jb6]128b-aS2564°5+17K),0*195Ø.Ù*/*405.825(a+906432128161283264b1—a1_1x6dx6b1ghiᨬ!ᐹᨵ5kᦪ஺4ஹᵨᑖk-,"ÛÜÝ஺S=N"(a)+4/(Þ]+/Q)]=à"(°)+4/(á]+/প][=]6I2)6I2)1-11=—(£b°+4e2+)=b(1+2.42612+0.36788)=0.6323366R/<4»()-1^2±^-7,ghææ-L-L=3.472x10s7=518012J18016151180165ஹçèᑡéêëI|7(x)dx=/(a)(6-a)+A^S-a)2;4,2(f(x)dx=f(b)(b-d)--a)2;[f(x)dx=/(--—)(/?-«)4-~~[=]ᵫᑖᳮᨵI/(x)=/(a)+/'(஻)C—a)gh/f(x)dx="ভ+/'(஻)(>-a)]dx=+=f(a)(b—a)+V^(b—a)2ðᵫᑖᳮᨵIf(x)=F(b)+f'(")(x-b),ghffMdx=f[/(&)+f'U)(x-b}ydx="(b)x+ñ(x-bYt-/(b)(b-a)—'(b-«)2ᵫᑖᳮᨵI/(ò=/("2)+/'(óX)0-”2)+ôõ(½_5)2,g22222

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b^஺222262=W?®ᔢ஺®+ᓟᔁý=Xþ—®+ÿ3-஺
36ஹ2.92.11஻->8ᦈᑮᑖj/xdx஺ᵫ/—T“=—Ḇ/஻ব=#$J/஻஻
=12121஻J12஻l-S„=--^\/<47
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+,-180<2j18012஻J2880/7ஹᵨ/ᓄ-ᑖj/xdx,1⌕3ᑖ45a,“ᑖᡂ789ᑖ:;<=>?@AB£D@EFᐭ>?
HIᵫ/—T“=_ᒘ~/8=-^f—Y/77=-JKLM+NO1212I஻
ফP=QR஻ম:ᑣUV஻8ஹᵨWXYZ[E\ᑖ2fe~xdx,⌕->?@ABIO-ஹ஺IᵫT®=-f-T,JT,„_,য^RW=஺_"`
+,஺ab95mm4—1yZy4—1⚓
9ஹdef⍝h#ijᙊ,jᙊᕜnḄE\hSpKahjᙊḄqnr:chᙢᳫu_f⍝u_jᙊu_
Ḅvw:xhyzᙢ{vw:Hy|ᙢ{vw:R=6371Kyᙢᳫq}:ᑣa=2R+4+/0/2,c=H-~/2஺ᡃ#⚩⌼dezᙢ{vwh=439K,|ᙢ{vwy2384K:-def⍝Ḅᕜn஺r^-,,2R+H+h2x6371+2384+439Iᵫ"---------=------------------7782.522H-h2384-439c---------=972.5+,22

3810ஹ9஻sin&=+---஻sinᓛ(஻=3,6,12)Ḅ:ᵨn3!/5!/n᜜\[-஻Ḅz஺yT()(3)=3sin—=2.598,T(6)=6sin—=3,o06=3.1058,ᵫA,n_¡P¢+,'I”ಘ=~^r~i4—14141Tয=/ব-/য=§x2.598-ªx3=2.464,Q4141r(12)=-7^(6)--7®(12)=-x3--x3.1058=2.9647,ir(12)=—7®(6)--7®(12)=—x2.464--x2.9647=2.43062஺21515151511ஹᵨ¯ᑡZ[E\ᑖ/i:±²³´µ஺1)WXYZ[®(2)¶{^·{¸¹®3)3ᑖ45ᑖyº9ᑖ:ᵨ/ᓄ»{¸¹஺I(ᒹ=lnylª=ln3=1.0986஺12ஹᵨ¶{¿·{-=ᙠx=L0,1.1¿1.2ᜐḄÃᦪ:±(1+x)-ÅE>?:/(x)Ḅᵫ¯⊤ÇÈ:X1.01.11.21.31.4/(x)0.25000.22680.20660.18900.17361Ë2Iᵫ¶{Ì/)Í—")7&)+ËÎ),1h2/'6)=Ï-Ð஺)+Ð2)-@Ñ©,

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+31+N:f'(x஺)=—[-3x0.25+4x0.2268-0.2066]=-0.247,2>?y|M(x°)|=^x஺^0I<^-x24=0.08®3f\x,)=^-^-[-0.25+0.2066]=-0.217,>?y0.12-240I2-----x---------<--x24=0.04,6-6//(X)=_L[O.25-4X0.2268+3x0.2066]=0.1872>?yº4ÔÕÖ^or<—x24=0.08o3ᵫ·{+N/'(/)=~i~[-25x0.25+48x0.2268-36x0.2066+16x0.189-3x0.1736]12x0.1=*[-6.25+10.8864-7.4376+3.024-0.5208]=-0.2483f'(xj=--------[-3x0.25-lOx0.2268+18x0.2066-6x0.189+0.1736]12x0.1=A[-°,75-2268+3.7188-1.134+0.1736]=-0.2163f\x)=[0.25-8x0.2268+8x0.189-0.1736]2o=j^[0.25-1.8144+1.512-0.1736]=-0.18831ஹE\[-1,1]ØḄᑖ/=[j(x)dxḄ»{-=//(/)+)஺[I]-ḄÚᦪÛÜ@AB2஻+1=3,3-P,ᓰ¿-Þᦪ᜜,ßày4iáâÞᦪ:ãäåæᦪ/xyÚᐭ-:,ᑮZçè:

40%=1y+q=2(O\=1+஺[X]=0x.=_BUV-y,222,+íI,î+ïᑘ=33V3a)Xo+0]Xª=0o=ë^f(x)dx~/(-g)+/(-y-)஺2ஹñòó=—[/(«)+/(0)]uõØ2f/(x)dx=(b-ù0ᐹᨵ#ãÚᦪÛÜ:Vüff(x)dx=p"(a)+4/(ÿ)+f(b)]ᐹᨵᦪ஺[](1)/(x)=l,x,/ᐭ!U#b—cib—ci)$"(a)+/S)]=k(l+D=8—a=11,-22”b-ab—ab~-a~—^[fM+f(b)]=——(a+b)=---=xdx-222*b—a...b—cii.2b3—ab~+a~b—b3,-a3p>2-y-"(a)+/3)]=-^-(஺-+b-)=-----------------ߟ--=jx~dx,9:ᐹᨵ;ᦪ஺(2)஻x)=l,x,x2ᐭ=ᑮ:(b-a)ஹfr\-஺-+--A=(/?)-6Zஹ)xl1=b7-a=[1"$-a+b=(b-a)'X----=-------=xdx-22A,(a+h)(a+b\^(b2-a2)(a+h)b3-a3,z2(j)/[HIj)x[HJ=-------------^—^-=[x-dx,9:=ᐹᨵ;ᦪ஺K3L“N=1,O/,P,;ᐭQRSᑮ:

41b-a.a+b^\..b-a..,6[/(«)+4/12J+/S)]=$x6=W-a=]ldx-b-a

42C$C(1+1+1)=3C=2=c=23C(x,+x+x)=0=yxdx3A/223ᓽ.ᓛ+x2+x3=0,j.C(—-)=#="x-+%-+x-=1x=02;ox-+x#+x-=0C(x#+)=0=jFFrehf/(x)Jx=-[/(--)+/(0)+/(—)],ᐹᨵ3ᦪ஺322/*)=ᐭeh!ூ#-[/(--)+/(0)+/(—)]=)4+04+(ߟ)4]=-[1+=f32J232234435ᓃᡠrehḄᦪᨵ3஺5ஹᵨu⁚y(஻=2)ḄGaussehhᑖ/=f;2])஺J-1l+x2[j]u⁚yḄGausseh£/(A#)dZx«|/(-^p-)+|/(o)+|/(^p-),ᡠrW4,548,54I=I----7dx=-------------H—X4H------------%+/9J:¢99(£¢I5)I5J025322519¤=----1------1----=—q0.33331891836ஹ¥¦§|ᦪA,B,C{a,~ᦪ©hᑖfJ(x)dx=Af(-a)+B/(0)+Cf(a)Gaussª஺[j]⌕~ᦪ©hᑖf,/(x)dx=4/(-a)+6'(0)+ty(a)Gaussªᑣᐸᐹᨵ2஻+1=5ᦪ஺f(x)^l,x,x2,x\x4,x5ᐭ¯°¦ᡂ²,

43A+B+C=4=jldxA(-a)+BxO+Ca=(C-A)a=0=^xdxA+8+C=4A(-a)2+6x()2ca2=(A+C)a2=g=^x2dxC=A+ᦑᨵ4ᓽ4Ca'=8-jA(-a)3+BxQ3+Ca3=(C-A)a3=0=[x3dx332Ca4=—A(—a),+BxO4+Ca4=(A+C)a4=y=5A(-a)+BxO5+Ca5=(C-A)a5=0=^xbdxA=W,B=3,C=W"=2A஺99957ஹ¥¦§|ᦪA,B,C{´~ᦪ©ehf/(x)dx=Af(0)+Bf()+Cf(l)XlᐹᨵḄᦪ஺rḄᦪµ¶·¸¹µᔲµGaussª¸j/(x)=l,x,/,x3ᐭehᑮ:1A+B+C=l=jldx4+B+C=lX,~2Ax0+Bx+Cx1=Bx+C=—=fxdxBx.+C=—{[122.ᓽ.321jfAxO^Bx^+Cxl2=Bxf+C=-=^x2dxBxM+C=-'3c=-6AxO3+Bx^+Cxi3=+C=($»3dxBxM+C=—4A=-69:ehf/(x)dx=/(0)+1'/d)+/(T)/(x)=x4ᐭᑮ:)6326-x04+-xl|+1x14=¼஺½=1vdX,9:ehᐹᨵ3ᦪ,63ব6245)vµGaussª஺

44¿ÀÁ|ÂᑖÃÄᦪ©jÅ(141-142)1ஹÆÇ©È⚪y'=«x+஺y(0)=0ᑖÊËÌÍÎÃÅ{ᦋÐḄÍÎÃÅḄfgjḄ⊤ÒÓÔÕ¦jy=ga/+bxÖ×Ø஺[j]ᵫÍÎÚy,+i=y„+h(ax+b),ᓽy-y„=h(ax+b),9:nn+1ny"+i;)'o=Z%+஻)=Z64*0+kh)+b]k=0k=0,ᓽ=y^[ahx+kah2)+bh]=ah(n+l)x+"(஻+°a+2+(”+Y)hh(}0*=o2y“=+ahnx+ah2+nhh,Ûq>0=0,x=0,ᡠ00y=n^n-^-ah2+nbh஺Üᵫx“=nh,ÚÝÞny(/x“)\;%=31%2,+bAx„-[ߟ--ah2+nbh]=-an2h2+bnh-ߟ—ߟah2-nbh=222y=y„+Kax+b)n+in_hᵫᦋÐḄÍÎÚy„i=y+-[(ax+b)+(ax+/?)],+nltn+lahஹ¸=y஻+—z+x)+bhn+lஹ|ᓽy,,+i;%,=g(%+x,,+i)+ß9:%+i;=£[g(x*+x)+bh]=Y[^-[x+(2k+l)h]+bh}k+ij0k=0k=l2ah(n+1)(1+2/1+1)(H+1)ah2....,=----------2------------—+(n+l)bh,ᓽah(n+1)(H+1)2,=---------x+——-——ah+(”+i)bh0>'n+i=>o+~~xo+~Yal1'+nhh,Ûq>0=0,x=0,ᡠ02^-ah~+nbhoÜᵫà=஻஻ÚÝÞ%+i

45yx஻L;y஻=;ax-஻;ah2-k-nbh]=^an2h2+hnh-ah2-nhh=0o2ஹᵨᦋÐḄÍÎÃÅejÇ©È⚪)'=x+'0

46y=1.105x3.01236352327260443898828125+0.05x1+0.055x0.910=3.32866169321644890508205078125+0.05+0.0495஺=3.428161693216448905082050781253ஹᵨᦋÐḄÍÎÃÅj»’=ᔆ+";)‘áâãA=0.1y(0.5),ÓÔÕ¦jb(o)=oy=-e~x+x2-x+lÖ×Ø஺jᵫᦋÐḄÍÎÚ4+1=ð+ẑ4+%;Ã)')'"+1=)'“+g{*+X”;)'“+x“+i-8,+஻(ᱏ+x“-y“)},Ûᵫ%=°,,,h~.ஹ%/2ஹ=(1;஻+—)y„+--—(x„2+)+-(x,“|+x)n+ló=0,h=QA,y“+=0.905y,+0.045(x-+x“)+0.05(x-+i+x“+J,9:ë=0.905x0+0.045x(02+0)+0.05x(0.12+0.1)=0.0055-y=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(0.32+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=0.144992256972187554ஹᵨÃÅjÇ©È⚪F'+>=°,ᐸfgjôõ¢Óày(O)=l12+3஻70¹ᦈ÷øùÇ©È⚪ḄÕ¦jy=e-*஺jᵫÚy„=y„+|(-y„-x,i)9:(l+g)y“+i=Q-1)Ãᓽ+l+y“+i=9:ᡭÛᵫ)'o=iÚ'y„=f|-r'l°2+/i+\2+hJ

472nhH+l-(^+l)2-h4/zlimy„=lim=lim1-=lim%T0/IO{2+h2+h20+12h5ஹᑭᵨÍÎÃÅhᑖe,2dtᙠyx=0.5,1,1.5,2Ḅfg©஺_X2j
>=e'2dt,ᑣ>'9:6=0.5,ᑭᵨÍÎÃÅᑮ:A»(0)=0y=y„+hf(xð)=%+0.5/,Ûᵫý=°ᑮ#n+in)>i=+0.5xe0'=0+0.5xl=0.5-=ë+0.5xe஺'=o.5+O.5xe025=1.1420127-%=+05xJ=1.1420127+0.5e=2.5011536-y=y+0.5xek52=2.5011536+0.5e225=7.2450215஺436ஹáA=0.2,ᵨþ▤ᐺḄ-ᛞᑡ⚪(V=x+y,0+K)=-+—+(i+-+—)U„+y“)||||I|I=/(x“+஻,+hK)=x+h+y+hK3nn3,,hh2..hh2..ஹ
t=஻+%+y“++1+(1+3+7)(z+K)°h'/?'h2h3=(/?+y+y)+(l+/7+y+y)(X„+y„)

48hy=y+(K,+2K+2K+KJn+in23oh,ஹhhஹ,ஹஹ—h/?♦ஹhhஹஹz~y»+,{(x«+y„)+2[+(1+)(x„+y„)]+2[(+)+(1++)(x“++)]OZ22424஻h\”,h2/+'+2+4)+(1+#++4)(X"+&)}2hh2h2=%+*[*“+y“)+/7+(2+/?)(x“+>“)+(஻+)+(2+/?+)(x“+y”)oZZ*h3h2/+(஻+2+4)+(1+஻+2+4)(x“+y,)]=y„+A(3h+h2+)+(6+3A+/Z2+)(x„+y„)]o44.ᵫ஻=0.2,>n+l=>'"+30[°,642*6-642(X"+),„)]=y„+0.0214+0.2214(%+%)=0.2214%+1.2214y“+0.021456ᵫ7=0,%=18y,=0.2214x0+1.2214x1+0.0214=1.2428%9=0.2214X0.2+1.2214x1.2428+0.0214=0.04428+1.51795592=1.58363592%%=0.2214x0.4+1.2214x1.58363592+0.0214=0.08856+1.934252912688+0.0214=2.044212912688'y=0.2214x0.6+1.2214x2.044212912688+0.02144=0.13284+2.4968016515571232+0.0214=2.6510416515571232'%=0.2214x0.8+1.2214x2.6510416515571232+0.0214=0.17712+3.23798227321187027648+0.0214=3.4365°:;9y=2e'-x-l஺hJy'=3y/(l+x),0?@ABᦪt,ᑡ-ᛞEFG&▤Ḅ஺h.y„+i=y,,+-(^2+H)I<&=/(x“,y")%oK]=f[x+th,y+thK);nn}K=f(x+(l-t)h,y+(l-t)hK)3nny

49[=>]K9K|=/“K=f+thDf+᱆Dᡭ“+…,2nnK3=/■+(1-"72“++…ᡠThy஻+i=ᓅ+§(Y2+K3)h7C/(th)-2rrx>r^r[(1-t)h]~7r1fr=y„+-{/„+thDfn+—^Df+-••+/„+(1-OW„+-----------D-f+-••}nnh□/,~(2/--2t+V)h~2r[=%+-[2/„+hDf+-------------------D-f+-••]nn..#2c,(2[-2t+l)h3c,=y„+/\"+]஺“+-----4+-,h2„h3”y,i=y),+^+7~y“+…1+626_`aᦪᡠb-ᛞE=%+c+—Df„+—(D2f+fDf)+-••yn26FG&▤:dḄ஺8ஹ=>ᑡef-ᛞGg▤Ḅ:hhK+i=ᓅ+i(+3K3)j=%+6k2+3l+4lmK\=/km&=/*“,7,)(1)■hhI2,hho1+pq+rsmH=஻t+[+i2233K3=f(x+-h,y+-hK)K^f(x-h,y-hK)nn2n+n+2JD)‘e=ᓅ+/?(4(+4w+4஺)&=/(x,,y“)u=>rᙠg▤-ᛞEFKi=f(x„+ph,y+phK)niK3=f(x"+{ᐜ+}/~+SK))21317(1)4=—4=0,4=—,p=—,q=—,r=0,5=1oᓽ9ᡠb,4433

50r+s=14+4+4=i/,14P+4᜛=]K6ᐹᨵg▤:d஺Zp-+4q~=~4Pqs=%21413(2)4=—4=-,4=—,p=—,q=—,r=0,5=1oᓽ9ᡠb,93924r+5=14+4+4=142P+4q=IK6ᐹᨵg▤:d஺4P*+4/=19ஹᑖᵨ&▤F&▤◚Fᑡ⚪:y=l-y,y(0)=0,஻=0.2,=0,%=0.181y(1.0),;y=l-eT£_`஺urᵫ*=0.2¤ᵨ&▤F¥h%+1=ᓅ+5(3/„-fn-\)=y„+o.lu3(l-y„)-(l-)r஺56=+0.1(2-3y„+ᓃ¨)=0.7y„+0.1+0?9=0.7©+0.ly+0.2=0.7x0.181+0.1x0+0.2=0.3267,0%=0.7y+0.1^+0.2=0.7x0.3267+0.1x0.181+0.22=0.22869+0.0181+0.2=0.44679y=0.7y+0.1y+0.2=0.7x0.44679+0.1X0.3267+0.2432=0.312753+0.03267+0.2=0.545423%=0.7y+0.1y+0.2=0.7x0.545423+0.1x0.44679+0.243=0.3817961+0.044679+0.2=0.6264751

51¤ᵨ&▤◚F¥%+1=T+g(3/¨qT)=T+0-1[(1—ᓅ)+(1—+1)]=ᓅ+0-1(2-y„-y„),+lᓽ921”"+1=S9y“+o.2,567+]=7ᓅ+7஺ᦑ92923,6290.3299I)'=-X+--x0.181+■—¯=°ir1111111119294.9691K3=¨#+x0.3299+—=¨"=0.451736I11-1111111192“26.065624--x--0.451736+—=-=0.55142>4=¨±3+-11311111111929_26.96278)’55=H>'■>+X0.55142+—===0.63298o1111111111:;9l-e-i=0.6321஺1h10ஹ=>/=/(x,y)Ḅᑡ²ᑖEFy=-(y„+y_,)+-(4/-/+)n+1nI+1G&▤Ḅ³´µ¶²Ḅ✌⚗஺#203[=>]K9%+1=y“+¹+<+!<+…2஺y-\=y,,~hy+?ᐜ¨g+…)\+i=ᐜ+Ḅ“+±+…nnZoZh2y"=¼¨Ḅ+]½+…ᡠTIh,-(y+y-\)+~(4),“+i-y+3y“_i)nnn=ீ(y“+x,-hyf+gy-jy+…)n226zh2h2¨—2+/4(y+hy*+—+■■■)-y,,,+3(y^,-hy*+-ym-\—)]56_`aᦪn1h2஻3,7A2=5(2y“-hyr+—y^,-—y1^+••')+~(6y+hy^+-—y^+---)nnZ2o4Z,%2¿3=%+À+yK~24~y"8²ᑖEFᐹᨵ&▤:d´µ¶²✌⚗94Á)=--<-624811ஹ³ᐹᨵᑡÃFḄg▤y“+i=஺஺>“+஺2y.2+%(%”+Ä+%¼_2)஺

52MA3[]K9y“+i=y„+hyo+—y*+—)?7+~y«4)+…ZO24(2/7)2”(2■3”(2/?)4XT=%¨2᝞,+——y„¨——y“+——yo+26244#3OA4=y“_2¹+2/Jy_Î-Ï+-^-½Ð+…y»-2=y_2hyM+(2?yM
(??y*4)+•••=y-2hyM+2h2½)+…,n2o3Ò”+%y“T+஺2Ó-2+%(%¼+-y-i+Ôq¨2)h2h3ᡭ4=«()y„+/Ö-hy+-y[--y"+—y^+…]nZOZ44/,37/47+%[%-2/iy+2/1×-Ø-y+-y-yÐ+-••]஻2h3ᡠT+/?{%+b[y,-hy^,+—y"+—+…]xn2o+%H-2hyM+2h2y"-Ú-y*4)+-Û•]),62஻=(Ü+%+%)y+(¨Ý-2%+bo+4+%)hy+(/+4%ߟ2bl-4/7)—y“tln2஻3h4+(-%-8a+3b+12%)-^-y+(4+16g+44-32/?)--y^4)+…2l2o24஺0+஺2=1-%—2a2+%+å+4=156àEFᐹᨵg▤:dᑣâãᨵ:%+4஺2—2Z?|—4b2=1-%—8%+3b]+12b2=112ஹèᑡéᓄ9¨▤éë1)y/-3y'+2y=0,y(0)=1,y\0)=1I(y=ny(0)=i[]ìy'=p,ᑣp'-3p+2y=0,p(0)=1,56ᨵp=3p-2yp(o)=i'

53îìy=,ᑣ⚪9=8Y,ï(஺)=()஺u:;9y(x)=er22)/-0.1(l-y2)/+y=0,y(0)=1,y'(0)=0஺y=nurìy'=pðU"'—0.1(l-y2)p+y=0,p(0)=0,56ᨵïp=0.1(1-y)p-yy(0)=1p(0)=03)x"«)=-,yr(t)=-y,r=+),2,x(0)=0.4,x'(0)=0,y(0)=0,y'(0)=2஺rr(/X=py'=qurì£(f)=p,y\x)-q,ðUp'=,q'=-,56ᨵ

54ஹ311016roஹy=0.4943831119=0,8•y=0.95786஺216ஹ—1.68,%=136148310116I14ஹ?éy"=/(x,y)þ¼²ᑖEFy,,+]=2y“-y“_]+/?2/(x”,y”)ÿᵨ
-if_12⚪4V=ឤy(x)=y(0)=)!প=021-2஻1%%)(1][]ᵫ*ᑖ,-./0121—2஻14=1஺<1-277v>15ஹ=6>3ly(O)-/(O)=l,yপ=2JKLᯠ஻=5,N=2!O"=P+|ߟ2T+,-1U4="+1%t(஻=I,2,3,4),h2hWᐭYᑮ[(1+X])ᐗ+1—2?+y,,Tᐜ+CIZH_3%=6x,_3,ᓽh2h(2+2b-—(4+44+6h2)y+(2+hx+2c3=6d2%-1)nneᵫf——=1-Y(஻+l)y-y=h,ghᵫ஻=0.2Y012i:01h\12-1000'l<0,2ஹᡭ=1.014872.12-4.42.0400-0.144%=1.0178502.4-4.882.240p=-0.048,-qYi=1.07010஺002.84-5.682.6>30.048%=1.21930003.44-6.87஺4,ஹ—6.096))4=1.51329

55stu01᪷(163T64)▅yᩞᧇ[|Ḅn⚗01%x"+O,TX"T+…+஺+ᓽ=0inWᦪ01஺3ஹ4Ḅ01!ᯠ-qᙠᦪᑮ!ᩖ஺5qḄ01ᨵᡂḄ஺Wᦪ01-qᨬᓫḄឋ01!¢iᯠ£¤¥¦ᙢ¨©Ḅ᪷!ª-q«⍝!n01|ᐹᨵn®᪷஺|ᵫ¯▭⚪±²YᑮḄ01³´´µᨵ¶·¸ᦪஹᢣᦪ¸ᦪஹᦪ¸ᦪº»¸ᦪ!᝞sinx,e!,lnx,
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᪵Ḅ/ÁÂ01/(x)=0Ḅ᪷()!Á¸ᦪ/(x)Ḅëì஺Åíᙠî᦮ᦪm,éY/(x)=(x-x")"'g(x),Ä0<|g(x*)|<+8,ᑣx*i/(x)=0Ḅmó᪷஺ôᵨ=1õ!x*eiᓫ᪷,
õx*ö÷஻%*)=0,ø(x*)H00|Ḅឋ01/(x)=0,ᵨúû0@Yᑮ©Ḅü¥ýÑḄ!þ᝞e-!-x=0஺ឋ01ḄẆ
஻x)=0ᙠḄᩩ,᝞ᑭᵨᑮ
x*Ḅ!X,#$%&Ḅ'(£>0,+,,*-x|<£,012xᐵ4£5'6Ḅ஺$4ᐹ9Ḅ:⚪<✌ᐜ⌕$@ᦪ/(x)DEFḄẆ<ᑨIJ
Ḅ᪷ḄLᦪMᜧᭆPQ

56/প=1,ᡠEᨵ᪷Z[(1,2)/(L5)=1.52-1.5-1=-0.25,ᡠEᨵ᪷Z[(1.5,2)/(1.75)=1.752-1.75-1=—>0,ᡠEᨵ᪷Z[(1.5,1.75)16/(1.625)=1.6252-1.625-1=—>0,ᡠEᨵ᪷Z[(1.5,1.625)64/(1E)=(iE)2_iE_i=_?<(),ᡠEᨵ᪷Z[2,1.625161616256I16=-(1—+1-)=1—=1.59375,2168321a11'6Ḅ¡c<¢(1.625-1=)=—<0.05o216322ஹᵨ¤¥}᪷h}/(x)=l-xsinx=0ᙠZ[0,1ḄL᪷<©ᑮ!᪷+,'(|/Z.)|<0.005ª«஺?3ஹ}
//_1=஺ᙠ/=1.5▬ḄL᪷<®
ᦋᑏᡂᑡ³´µx<¶·¸efḄ¹ºwx»1)X=\+\lX~,¹ºwxX=1+1/x2)X<=1+X*,¹ºwxX=y1+Xk+ik+l3)x2=—!—,¹ºwxx*+=1/Jx*-14)x2=x3-1,¹ºwx&'+|=QxM-1oÁᑖ᪆ÃĹºwxḄᦈnឋ<¶⌱]Äwx}JᐹᨵÆPᨵᦔᦪÇḄ!஺1)e(X)=l+3<É"(X)=-W<Ìq|᜛Î1.5)|=---=—<1,ᡠExx1.527¹º
hÏÐᦈn஺2)8(%)=Ò1+<<ᑣ᜛'(Ó)=,Ô(1+12)3,Ìq|^(1.5)|=jxl.5(l+1.52)-i=(×<1,ᡠE¹º
hÏÐᦈn஺I1-I1f—3)g)(x)=/,ᑣ(p\x)——(x-1)2,ÌqØ1.5)|=——x(0.5)2=V2>1,Vx-122ᡠE¹º
hÚᦣ஺_____□__4)e(X)=J/_l,ᑣ᜛<(%)=Q/,0”,Ìq

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hÚᦣ஺ZoV384ஹ¤T}/+10x-2=0Ḅ᪷ᑮâPãᦪᡠ◤Ḅå»1)ᙠZ[0,1ᑁᵨgᑖh2)ᵨ¹ºh=(2—e*)/10,]x()=0o1)#ᵨgᑖh0,ᨵ᪷Z[0,0.5/(0.25)=e°25+0.5>0,ᨵ᪷Z[0,0.25/(0.125)=e0125-0.75>0,ᨵ᪷Z[0,0.125/(-L)=eU=_o.56O5<0,ᨵ᪷Z[—1681683—1713/(—)=e32=0.03578>0,ᨵ᪷Z[—3216116325—39F53'ê)…
<0,ᨵ᪷Z[11—73113/(—)=i2s_22,e<0ᨵ᪷Z[1286412853223—141233/(—)=e256--<0,ᨵ᪷Z[256128256532/(—47)=e—512_±277>0,ᨵ᪷Z[2347512256256?512/(•9^3)=/—24-5ï59ு0,ᨵ᪷Z[2393XV/IJX256'1024’“q*1/2393ஹÌqx=—(----1-----)----=0.090332,ᐳgᑖ10ô஺2256102420482—2—22)#ᵨ¹ºh/+i=——<ᑣÓ1=ᐗg0.1,x=—=0.0894829,2

5820,0894829_0.090639)2x,==0.0906391,ö=¢g-----=0.0905126,1010ᓽX*=ö=0.0905126,ᐳ¹º4ô஺5ஹ@ᦪ/*ø,$ᑗx,1úxøûᙠü0ú,ýþ$40<2<21MᑁḄᦪx*+=x*-/஽ᙳᦈ/xḄ᪷x*஺!"#ᵫx*+!=4-"4'()0x=x-*x,ᑣ᜛'x=l-4'X,12740dx>-1,ᓽ?@ABCᦈ஺6ஹF(x=3xᙠIJ!a,bᑁMᨵO᪷APaZ:>1,XY᝞[\x=Qxᓄ4〉ḄBC`ᓄ4〉ḄBCabx=4.5ef▬hḄ᪷஺!i\x=8xklmnoᦪpᑮx=aix,A@T$X%&'=/(@A9x,8“(x)][=—yOW{<1,ᦑ}Cx=(p~'(4)ᦈ஺k+l(f)(%)kx)=tanx,ᑣ(p\x)=sec2x,@A?'(4.5)|=sec24.5=22.5,\}Cᦋ4A+=arctanx-R஺'0)=—@A?'(4.5)|=——---=0.047,1+x1+4.5BCᦈ஺m%=4.5,x=arctanx=4.49372,x*=x=arctanx=4.493424஺}02}7ஹᵨᑡb/(x)=/—3x_i=஺ᙠ/=2▬hḄ᪷஺᪷Ḅx*=1.87938524…⌕bᑮᨵᦔᦪ஺1ᵨ;2ᵨm¡=2,x=1.9{3ᵨ¢ᱥ¤,m¡=1,¥=3,x=22/(4)__Xk_3/_1_2x<+1[i]1)4+1=xxkf\x)-rߟ—3x{-3—3%{-3k2(—)3+lU*W988889&ª=1.87945,«¬஺3(¨35616

59%=4O…l)f(x)-f(x_ykk2)9XQ=2,xlO3x*-1z_X+x*1)+lr1.9x2x(1.9+2)+l=1^Z=I.881O94%)=1.9,x21.912+1.9X2+22-38.418411582,±J582,cஹ,----xl.9x(----+1.9)+1=841841__________OJ582ஹ1582—in-o()■+xl.9+1.9--3,«¬஺8418419558143.42+84J1026542442…±…----{--------------------------7=----------=1.87941115822+1582xl.9x841+0.61x84/5462043213)4+1=4ᐸ¶জ~জ2(0=f[x,]+f[x,,x_](x-x_),Xo=1,X|=3,஽=2,ᦑkkk2tk}/(x,)-/(x)17-(-3)0==10>—3,")=17,/(x)=l,f[x,]20XiM(%o3-1…]=43=·=16,x-x2-32{/[x,x,x]="*ᑗO=1,-0=6,0=16+6(2-3)=10,012x-x2-12Qx=2------/=2------==1.9465745,ᶍ஺310+V102-4x1x610+V768ஹᑖ¼ᵨᑖ½bx-tanx=0Ḅᨬ¿À᪷஺[i]ÁÂÃ6⚪J=4.493424஺9ஹẆÆb¿Ḅ}Cx*+]='4+Çx>0,"#ÈOᑗ4=1,2,…02Xkx>yfaÉ®ᑡX],Ê2,…¯⌴ËḄ஺k["#]Ìᯠ%,>0,124Xi—6=4+⁐O±OÏ>20,ᡠ:242xk1a—2x>y[a,k=,Xx-x=—x+—-x=-~—<0,ᡠ:®ᑡ¯⌴kk+lkkk2Xk2xk

60ËḄ஺10ஹÈ/x=OḄ}CÑ+i=x*-/஽//'%&,"#R=4-Ò/%7"22ᦈᑮOÓx*/2ÓÔÕ*4/X=0Ḅk᪷஺`11ஹXÖᑡoᦪ×ØḄᦈឋ½ᦈÚf஺ஹ!Vx,x>01)/W='!—J—x,x<02*0°!i1)ᵫ0»=%-{^=3-1^=-%'(1'0)=-1,ᦑÜᦈ஺2\8xcஹ1+,/ஹ/(x)V?-gx'(dx=-gwo,ᦑO▤ᦈ஺2)ᵫ“প=.(/0ߟ-*ߟffW24—x3312ஹáᵨ/=0,âãbä᪷åḄ}Ca×Øᐸᦈឋ஺/(%.)x1—a2x{+a2a!i)/(x)=1-a,ᑣx=xXkk+ik3xl~3xl~3+æ°f'E)13ஹáᵨ/x=l-W=0,âãb&Ḅ}CabVTEḄX஺!i)gx=x-,ᑣÒ=_*=/_f=ê=—+ë஺ìpí&2x2x22xkkkÂî8o14ஹáᵨ/x=x"-஺=0½/x=l-=0,ᑖ¼âãbCḄ}Cabðñ-ò*+I/ñ-஽ô஺fgx—o.(஻Ol)xr+an-1a!ixt+l=xk{----Xk---77ÓInxo'nx^~nnx"k

61,r(஻T)AI—7a-------x------k..'\la-xnnx=hm———k—+l=hm---------------=hm——-j("Na_Xk)2ia-Xk)2i_2&a_Xk)nxo-n(n-l)Xj-1(M-1)=lim------------------=hrm----=---------k-8-2஻[஻VaxT-(஻+l)x{]—[„»/a-(஻+l)x,]2_(H-1)_1-n2[n*l\[a-(஻+l)\[a]2å„r_5+1)ab—X”_].na'yja-(«+l)ax+d”nakC1)X3-6X-5=02)x=2-e-XoBC1)D/(X)=X3—6X—5,FIJ/"(X)=3X2—6,J|x|ீLM7N(x)<0,f(x)PQRᦪJT>VM7f\x)>0,/(x)PWRᦪ஺YZP/(-)=40-5>0,/(⊈)=!4V!5<0,/(-2)=-1,/(3)=4,ᡠ]^_/(x)=0ᨵ`4᪷7ᨵ

62᪷<=ᑖiPjߟ2,-⊈lj-V2,0l,jV2,3lO2lmn01ᦋᑏP2-x=er,sRᦪtjxl=2-xu/2jxl=e-'Ḅxy7ᵫxy^_{4Rᦪᨵ{4|}7ᐸ~ᙶ᪗<=j-2,-1luj1,2l,Zᡠ01ᨵ{4᪷஺2ஹu+1=<+7=01,2,…Ḅᑡ%ᙳᦈ஺2AV111BCD᜛jXl=—+—7ᑣ/jXl=-----7O2x2xJx21M7p{x=—+—>2J——=V2>1,8jl|'—<,<17ᵫ2xV2x2x2Ḅᑡᦈ01X=2+Ḅ!᪷X*=஺2x3ஹᑭᵨ〉JḄlimj2+¢•+=2okT8ஹ--------------'vkXn=0LBCὃ⇋,-----ᑣ/=V2,§142+u7k=0,1,2,…%2=J2+,....9Xj,=2+J2+…+0©ejxl=j2+x,FIIp\x--JoJ£[0,2]M,2y12+X9jxle[9j0l,᜛ফ]=|V2,2]c[0,2],8;Wp\x

63(p{x)=x(2-ax)º»¼ᨵ◀¾¿À஺ᵫ1!È+i=1-ax(2-ax)=(l-ax)2,k=0,1,2,…⌴ÊËᑮkkk1-ax=(1-6zx)2+7,k=0,1,2,-••,Ëx=—[1-(1-tzx)2],k=0,1,2,…7k+{ok0alimx^=Qlim(l-ox஺)a=0<=>-1<1-ezx<10

64ÐÑÒÓឋ01ÔḄÕÖ0¾(198-201,Øᑖ)a\\a\2ஹ(a)DAÙÚ▣ÜÝÞßàáâ¾!ã7AäᓄP0A2A2ÙÚæ▣஺0.6428é+0.3475ë2-0.8466x=0.41273(b)ᵨßàáâ¾Ú01Ô:■0.3475ᓰ+1.8423í2+0.4759x=1.73213-0.8466X,+0.4759X+1.2147X=-0.862123BC(a)îºḄᐗðñòt=஺!ó1,(i,j=2,3,-,n),YZPAÙÚQUa,ci..▣7ñò%=%,.7i,j=,ᡠ]d=&'~--a1---=ᓽA,ÙÚæ▣஺(b)ᶍ஺4ஹDAPn▤ø᜻úæ▣ᨵᑖA=LU,ᐸºLÙᓫ.`ü▣7UPÃ`ü▣7AḄᡠᨵýþÿᙳ஺(I()A(Ji1QஹLUᑖᙽL=M,U=ᦈ”3),ᐸk▤ᓫ▣Ugk▤!▣ᑣAḄk▤%&'(…*+ᯠ-᜻/஺7ஹ1A234567▣89:;<=>?@AABᓄᓽao,ᐸ0A_2A=(%)“&=(4")"TNO(1)AḄ3ᐗRS>00=1,2,-,//)N(2)%234567▣N(3)«<2)0o

65x2yA,ḄᐗRz{&/=2,3/-,”y|uA234567▣z{}i,j=i,2,-,n,ᡠv=%-`=5=ᓽA22347▣஺x3yuᓽ~0,ᡠv☜y=%—3=%—/w%஺awa\\x4yvᶍ஺-21-3-1310712ஹᵨ:;-B>AḄ⌮▣O-124-210-15r-21-3-1100஺-1——3—]—1000ஹ222231070100K31070100—124-20010—124-2001010-150001?10-150001-13111-????-000N131122220002~2~2219130---8---10001-9-173-2002222—>T11102-2--2---01002-2--2--01022222222o-111-10---5---0015001L2222-1L2222-j038-1100■■1038-1100"01-9-173-20001-9-173-200—>—002540-75100o1—052552500-4-31-10100-4-31-101

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170i-3-1450085178517.418_23_16-858585173362141385-1742517ᦑA-=o19851785173-85-1785172-1000-12-100013ஹᵨ>3=ᐸA=0-12-10h=00-12-1000-12

67ᑄ-»2-100020100333T1000445100-12044000-1202-10001201--00u333]_7001-04441_000155620055ᡠv=!=!᜛3=!22=<05OJZJ-214ஹᵨᦋḄ᪷>-11510723LWJX=~^2=5*3=§஺15ஹᑡ7▣¤ᔲᑖLUxᐸLᓫ▣U!▣y©ª¤ᑖ¦§ᑖ2ᔲ¨?஺'123'-111-'I26-A241,B«221C=251546733161546uAḄ?ஹ«ஹ▤%&'(ᑖ¬1,0,-10,ᡠvA¤®ᑖ▣Ḅ¯°±ᣚ³A´v஺uBḄ?ஹ«ஹ▤%&'(ᑖ¬1,0,0,ᡠvB¤ᑖ▣Ḅ

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69XxX+XX1+xp=Þ(X+X2)=P\+P2-PX1+&2=\2piÈIk,2R"2p!ᔣÖḄ?Úᦪ஺21ஹ1Ae/?"ஹ"34566×|x|=(Ax,x)"¸|x|2R"!ᔣÖḄ?Úᦪ஺τ____[]uA3456ᡠvkI=(AX,X)5=yjxTAx>0,2||cx||=(Acx,cxy=Vc2xTAx=|dJx7x=|c|||x||,(4IN+X2IO=(4Ï+á2),Ï+x))=(x,+x)rA(x+x)22]2=Ax+xfAX+x[Ax+xT^x2iÈØA2R"!ᔣÖḄt2xឋ@ᐵ஺

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86limA-A,̾?ᯠᡂÎ஺kk—g7ஹ*Ax=8,ᐸÐAMÑÒÓVÔ¡¢ijkḄ£_ᔲ#Óᦈ;Öὃ×⚪5(a)ijk஺=¡>¯#ÓV?ᯠ5(a)ÐḄ¦ᦪ§▣_MÑÒÓ§▣VÙ¯ᦈ;஺111111X2-7X3-Ú4=-4428ஹ*ijk.9111-iii=ÛÛ+“7(a)u¡¢ijkḄ£Ḅ§▣ÜḄÝÞß'(b)u¡¢ijkḄ-Ḅ§▣ḄÝÞß'(c)ὃ¡¢ijkḄ£¤-Ḅᦈ;ឋ஺=¡>ᵫ¦ᦪ§▣A=44©,\11110000444411111000014444(a)Bo=D''(L+U)=VᵫI11II00004444\11100004714474420A44="(%—L)(4+à)=0©,P(B0)=3஺22A0~441]_0A44

87-1/'1000ஹ1_r000100442G=
D_L-'U=1000-4~444000001-41<0000,ábâ,ᵫ/’1000ஹ0010000--100440088110000--0111144Jஹ°000--0088401_14~40A1_14~4£á4_lâ=o©áGâ=-o|A/-G|=p440000(c)DEA_åæMçᓰé§▣VêëÂᦈ;஺9ஹᵨSORi¡ijk(ᑖïÉðñDò0=1.03,0=1,஺=1.1)4$-x=12<-%]+4X-X=4'23—=—3=஺⌕uö{*…ôõ¡X*<5xl()YøùúVûüMý#\oKõÓÈᦪ஺(ᶍ)஺5%1+2/+£=—1210ஹᵨSORi¡ijkáÉ0=0.9â,#᳝+4]2+2/=20⌕2x-3X+10x=3123"<1()T஺

88421ஹᵫ!ᦪ#▣A=-142'0=0.9,L=(D-COL)-'((1-a))D+a)U),(0ஹ2-310,f=,஺-ᡈᔆ012,-1’500ஹ'0.5-1.8-0.9ஹ,=-0.94000.4-1.8J.8-2.710,ஹ001,(\ஹ'_L__2___2_ஹ0010-25-505).5-1.8-0.9ஹ21o919981c0.4-1.8=200440010002000J01?-53174795879-531271I20000400ioj(40000100()0020()000J<_108ஹ-C0-w‘500-•125J12ஹ940h1f=0.9-0.94)20=0.9-020=,FG2004100()J.8-2.71<3)ஹ3)-5312711771741200()0400ioj)00J<100(ᵫ-=LQ)+/1H஺IJKx=-4,X=3,X=22311ஹLᨵNOPAx=b,ᐸSAKTUVW▣஺XYx(k+l)=x(k)+a)(b-Ax(k))(A=0,1,2,…)[\]^0_஺_`abcᦈe(ᐸS0_஺_஻4)ீ/?)°iK#▣K8=/-34,G/l(8)=l-0஻A),ᵫ0_aW/l(A)m᜛12[0_஺_o[-1_2(B)_1,ᓽr8)|_1,FGcᦈe஺12ஹᵨuv-wxyNOAx=b,ᵨV+Dz/M)Ḅ}i~ᑖ[=4-£%/1-£0)஺7=1j=l.+1)(a)]^X*M)=T)+±—%

89M+l)(b)᝞£Ḅ=)-X*,ᐸSX*NOPḄIJ[]¥"=¦)/_,aiiᐸSw=W4ᳫ+J=Ij=i(c)LATUḄ[஺(£0)(A£য,£(),]^Q—+D)-0)=——஺>1aji(d)ᵫ[᝞AᐹᨵVT¡ᐗ£Ḅ¤᜻¦#▣[uv-§xyNcT¨©ª«ᔣx(°>ᦈeḄ[ᑣAVW▣஺[](a)ᵫ-=(O-L)TUx±+(஺-K-/1H(D-L)x(t+1)=Uxw+b,FGDX(M}=Dx(k)+[b+Lx(k+l)-Dxw+஻(*)]=Dx(k)+r(t+1),ᐸSr(i+,)=b+3´-Dxw+Uxw,ᓽH]஺(b)ᵫX(*+D=(D-L)TUxµ+(஺-1H(D-L)x(k+l)=Ux(k)+b=Uxয+[D-L-U)x,FG(஺-L)[x(*´-x*]=U[x(«)-x*],ᓽ(஺-L)£«M)=U£")[FGD£(*+D=£>£(*)_[—1஻+0£(*)_஻£(*)]=£>£(*)_஻·[ᓽH],ᐸSi+D=-L£3)+0£(k)-U£(3(C)?o(d)¹uv-§xyNcT¨©ª«ᔣx(°)ºᦈeḄ[»¼ᵫ(c)2ATUḄ[½ᵫAᐹᨵVT¡ᐗ£Ḅ¤᜻¦#▣[ᡠ¿AVW▣஺13ஹLAÀBKn▤#▣,A¤᜻¦[ὃ⇋NOP&1+8᳘=Ç[▬+Az=b,22ᐸSz,z,d,deR"ol2l2(a)ÊËbNcᦈeḄᐙ⌕ᩩÎAz*=4-Bz*,Azᵨ)=Ç-&[)(m>0)(b)ÊËbNcᦈeḄᐙ⌕ᩩÎ=Ç-Ñ[,4Ò)=%_&Ò>

90(m>0)ÓÔÕÖ~NcḄᦈe×Ø஺(a)Lza)=,/?=Ù1ᑣÞ:FG-1AOY7OB'A0ஹ%0ஹ஺à+'4T0ஹZ("
+D=1^+b--f°b0A7\B0<04(0oj;0[0A~'B\^[A''°V+^A-'B0)[oA-1J0A-'B>iᦈeḄᐙ⌕ᩩÎKp=[p(A-1B)]2<1,BPp(A-'B)<1oA-'B0,(b\7Bஹ(b)L*=[0=,[ᑣᨵæYz(")MJFG1:ᓅãF*b,iᦈeḄᐙ⌕ᩩÎKfO-A-'B](A-10)z+(0A''BA''B)(-ᑁé-c(b)Ḅᦈe×Øc(a)Ḅᦈe×ØḄ2ê஺1aTë-a஺VWḄ[GìíÔîT14ஹ]^#▣A=a1aa-9”ïᦈeḄ஺1aa1]^ᵫA=1,A,=I=1-Q2,|A|=a1Q=(2஻+1)(1-஺)212[aaa1

911-a2>0<2a+1>0,ᓽ-[

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93ஹ12s/2”)=1,x(4)=12A{oUl-G\=2=42+±4=0H\,p(G)=(,-6½¾-¿ÀÁ@ᦈ%஺10A+-33"2{1JT4ஹ¸iÖឋ'(111x1,ᵨºH»@¼½¾-¿ÀÁ@21{2Ù%3?1Âᔲᦈ%Ø2YY01-PB஺=£)T(L+U)=1-10-1-2)[-1-10,+),(1)ºH»É▣.flᵫ2(01-10-1=-10-11[{1-12)

942-11225h=1,஻-Ü=1A1=2(Ý+/=0H\p(5)-6ºH»0211222@Ðᦣ஺(2)½¾-¿ÀÁÉ▣.ஹ002(200(Q1-nro1-OG^(D-Ly'U11000--1000-1211~2J000),21000JJ22)ᵫ11022110221304411A22,11=+*%+g)=0H\,5+"\M-G\=0A4——P(G)=<1,-6½22810A+-44¾-¿ÀÁ@ᦈ%஺1£122115ஹ¸iÖឋ'(Ax=0,ᐸ_A1,ᵨºH»@¼½¾-¿À22]_152Á@Âᔲᦈ%Ø+),(1)ºH»É▣.[ஹ/002222(\\_]_Bn=D-\L+U)=10-20,ᵫ222V112I2

95-8஺=jAj=(4+1)(/1-;)2=0H\(Ì)=1,-6ºH»@Ðᦣ஺11222(2)½¾-¿ÀÁÉ▣./\/11\/(ஹII)Í0————0——1002210022111-1ooo1G=(D-L)-U=--一一--1000--222211ooo1-1-1110002-2--2—I727IJ,ᵫ]_]_222\M-G\=02--=஻7{±/1+2)=0H\,X?(G)=<1,-6½¾-444160A--42¿ÀÁ@ᦈ%஺+à)áᯠA.KgÉ▣¤PaḄᔜ▤åæçèᜧ&t56A.KghiÉ▣H\½¾-¿ÀÁ@ᦈ%஺,'a13ஹ6ஹEÖឋ'(Ax=AḄÇᦪÉ▣.A=1a2,QéêºH»@ஹ{32a,ᦈ%ḄaḄ¥ì஺+),í஺=0îÇᦪÉ▣A.᜻bÉ▣GéêᵨºH»@஺íî,(13ஹ0--——(aY'fO-1{31aaI0ºH»É▣.8஺=£>T(L+U)=a-10-2={{0{{---aaa)(3-20J2---0.aaJ

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