Baixe Cap 2 - Peebles e outras Notas de estudo em PDF para Eletrônica, somente na Docsity! CHIAPTER “2 | TT GD dt da desta te trab Hal X cam | | home. (a)For X=24 : Sy=fo, 5, 12). | (b) Fa x= 541: Dto +, 30.25, 1793. (6) Fou X=co(m4): S,=$1,-1,03 (A)For X= 01-24) 3 Se: 11,-0,5,-1/6.5,-1/193. | É) es, dana He aut 4 valia Hot x com kama, (a)Fa x= 20: Sy =ê- E<xXSIOZ. (b) Fm x= gt: 5 Ef-le<xsiass. (C)For X= tes(mro): PIS torenep (d) Fa x=1/(1-34) | Í | | Sy* i-ocxs-T amd CIT) (a) Gomtimusua. ep Mopad. (0) Diseuli. | (4) Disc. EE) Demeim df P à a aba defuimed x 5. 1-0) The demeim 04X 0 5, The manga q P Os P<i. The nomga of X co infinito (X cam home. army alice -cex<0), Vp<x<co sz. 2+ na É1-5) Fa +he. man : Sé mn) ACT, + (HH) un | purehaaed do aqua do Fa prebabit, hett Lodo | to atreve 0.95 (760) mm but vet above 1.05 (760) mm. Thus, from ta.a-re), Í nos tgeo) Ploss(meo)<x 4 iioscro)) = gio- eso 798 -722 | rés aas(160) = — E rT2? = Tés -. oa qJao- éso 270 sis “a aaisã q te preduetrimo rum, QB) (4) How tema io mt vales df X fm cod im m Ss | A) Lo . RI . Fem) 0.75 desp 1] os ess , i 1 , ! 1 1 : L 2 E x 628 7 x ) od X fm toch valua sjs. aim theme o oe Tete) | (C) Nora Lhe poialo 0,1, (b) ag CE (Continud) 30.25 179 “+ 0 to fe pomba 1,-1,9,1 -f “ - o t quê e. 1 R n o o u a + = 3 - « - a. se - R x n & q vo do ca) E gt TEA Ge Sã o “ q K Ss S 29 (2-3) Pix=i3= Pi-alsosr 8.3) = 18:25 Dt-20 39.3 qa-(-2) 7o x 0.561. Í | | Pixz2)= p$is, 3<as2n7)+ ALIIES, E w 0.049, ug- (2) 70 Pix=z3)= Pares < aja 49/2147 273 « 0,390. yu a9-t-21) 7º x e 0%) E6) to 0.561 oe ,S.6iá 0.390 | , | 1 9.049 | | Da or a 3 x 0 1 2 3 I b<x<otra +0.3b3 ao asus to detveas, tha atitidtio me find a<%,<b vo tra ao lena oo a<b, which io tau, Simitanhy, a<x,<b o tau q a<b. Fomally, Thus, ; Pjosa ro ib<x< raro abj= = G2(b-a) d 22, b-a ')Pilarb)/a <x<b3 = -[º a+b “2 30 %<% dq a<b. 0.7e +0.3b 0.90 +0.1 pt -a) 1/2 The nquirvd tuto ou (2.3-6a ambb). Fy reguirad ant a Juma j | [a skuteh, Et) zo q aro, amd b>o à nara + any for vm infinita ana umda $(X). Fo Hess | anual tam: | -(x-m)/b + Jem da = afue | | dy = aab/ e tas | 2ab md | (Tha, ue naguine bro, a=1/2b. | E) Thio & o Esrencultá triste prot uheam Wz 6; | amd pros. ben. j | | | Plow) = (5) com" coief x 0.0467 ' | P(o.sw)= ($) (0)! (o. = 0 | Prrow) = (E) comico a 0.310 PlLSw) =(s)t0r (0.6) x 0.2765 P(20w) = (E tom )'C06)" = o. 1382 Plasw) = (E) (es (o. = 0.036 - aab(-e FI], = 1866 prsow) = (E) om)ó (0.6) = o.oomt. (0) dar x Je a rombam venintta raprrcsndims power “ datinead. From (2.8-5) amd (a.2-6): | EX) = 0.0467 5(X) + 0, 1866 5(X- 0.5) +0.3110 Stx-1.0) +oeves s(x-1.5) +0. 1382 5(X-2.0)+0.0369 g(x-2.5) l +0.00%41 8(x-3.0) 33 É3 (Continud) o RX) =0. 0467 UM) wolgce u(x-0.5) +0. 3110 UlX-1.0) + O.276SUlK-S) +o.1ag2 U(x-2,0) + 0.0369 u(x-2.5) + 0.0041 U(x-3,0) - F (x) 0.9959 500 io * PH | 9.9590 q ls o. 8208 OB | 06 03 . tags O. E443 | 02io ss | 0.1282 I 0.2333 í o 0.00%H oz 6 cg ) | loover , L A Aim o (o ' a 37.0 ' 2 3 x 0.0467 | | (b) PlOvenlead ) = Pl2. sw) + Pla. OW) = 0.041 or tida 4633) de va Frita 23- 2 Heis co a Boxm su lti frialo | prt, Fa He em uid» By ua aj Cr7-5) Plow)= (5 5) to. +) (tom) = 0.00218 P(a5w)= (FP) ce. “) tro 4) x 0.057W1, | Sumitoaly, our prai df drmaiwsy various | poser Juvelo ara PlLow)x 006385, etosua ! “Orm8a, Pla.ow)= o. 21284, Pla.sw) = 0.22703, PlBow)x 0.57658, PlSsw)z 0.10090, Plpow) x 3+ WEI) (Cmtiniad.) | Corro, Plrsw)z doam, Plsow)a o.00249,| | P(s.Sw)= 0,00030, Pleow)= 0.00002. “Thus, P(omelead )= PlWSW) + P(SOW) + P(SSW) + Pl 6.0) ) Mo.ois27 a 153%. Fo tha tuo imdapamden 2 unia doféma. sd 9,="ginot 2w tunit orrenovudo omd 0,=" second : 2W um ommenlrado” Ouulsad Ha amgatem | ocemmo mlum Ha find anão va bata umito Plovenlrad) = P(0,U9,)= Pl) +P(0,)- PlGno,) | = Pla, )+P(o, »= Plo srta). Howesen Pl(o,)= O. em pre frotas 2-8, axd Arara Ple,) = Flo ) hara | breamas Pe Furo uma, Ploventoad) = tdos)“ (ooey? = 00803 «1 8.03% Thuo, uae df Me em unit “w babar Ham furo 2w upato. É) By depimitia Elm = Pfxsa). df xe | He uomt fXS- o) ha vir amando ae Eee, Simitanty, é Eee) = a] fu prata, mui be uma o tha às, Fte) =1. Fimalta, pro amy | -0<x<co the meat ixsajes amd Lo (2.2-20) nenults. 35 x63-1) Two como. Court: 70. Let de ax+b, diz a du. Gta b)=(CA(tb)sm dE = 2 A(=2),ar0. =. Coe 2: €0. Lt 4c-tarn+b, dás -taldo. G(a,b) = “bos da tg(+ o. (asd) h (E 7) é Lar E = lia)» a< Thua, Gla,b)= A). -v<a<0, amy b. CI) Tent 1º too=ali-ÉJro 4 b>o and x>0 q a>o amh ocKte<bfa c/b<i) Taat 2: Qua = [alt ET dy =a[c «SIS. Thio comuna por c=btbfi-ca/ab). Onty He novt urizh mesatire covuspendo fo efb et 4o ferrar cometi amei aro, ceb, amp Sb = - / t-(a/eb) - é Dm É3-13) (a) Cs f/Li res] = 25/26. (bleos(W3/6)=0. (e tEt) =e"=t. (a) Ito ti=2. (b) a risadas suteida vstag pablo Bim) (De act Ye +47 — ee Dorrsco? +€2)*7 = Ee gos E From was 4 (C-39) amd ce -ut): , EO dy = efa x*) eso (7 %/2) dx =s[£-S(E- =x mat, no kK = 73/32 = 0.7689. 38 BM) qm) Pélxi>z)= Pigexo + PExe ca Pix <ejepixee). Fram (e.+-3) thro agudo Pílxi>ej =1-F(2)+ F(- 2) = 1-F(2) +1-F(2) =2A-2F(2). From Apperediio B: Páixl>zj = ia-a(o9772)= 0.0456. Cb) Pfx>ag=i- Pixsapei- F(2)=1-0.9772 = 00228. 4-2) (0) Pflxi>27= Pixpajepixccas = 1-Pjx<e) + Pêxe-ed. Lo (a. e), (2.47) amd Qupuudiy E | to gt Pglxi>ad= 1-P( 228) +P(CEdx) = F(=*) , , +(t) = FC) +F6) Ft=Li=Ft03+0 03] = FC)-Fls) erro. sua - 09987 = o. 426. | (b) Pjxdej= -pjrsajo FEL) = = Fl) = e-b-rty]= FU) =o. seia. Í - - z z CD x Elm) dy = Lie id fiada | | - | L2:80 é Pl +) E se -(x-a, Vet o (x 9,320; to Var | to VIP On Lebting E=(x- ro vm he pra night. | fi ha a rt Ha Aran density fundtica shi i SA EM x E (x) dy = 39 EH) (Continuad) (am). Dia gosto fica corn, -c o Fx us. (-A0)/4Z «de= de Sã 65 fã E (x) dg = [20% eo Ga nto x-a 3 f(x) io a e o *º “x Rs | z F= 7 , e dz. On ig (C-52) Mei tecoras Kore, onda é 28 VE = 6 Z | E Éx-5) (4.) Repito nasirtes Covuagond to $X< 90003 amd tx>nsoas Frastian ruqpetao covefirndo + | P$xX<900] Cefto uso) F(900) + [1-F, (100)]. | Farm (2-7) tha berma PÊ neaiotm mjgadid ) = | | p(istcicco ietrioco) 41 p(tcezteso) = I+F(-as)-e(2.5) ! = I+[i-F(a.s)]-F(2.5) = 7 A-2F(as)=a- a(0.9938) | =00/24 a 124 Po ama (b) Pinsaiate. negucdot 3 = RÊX<I00) rrix>iico3 - | ! E (900) +1-E E (t100) = rio fedo ) 4, p(ttee mtos jas0 ) | [ro = 188) 614 E)=1- FOR + -P(1.25) = a -p(305) C-Ftras) = 2z-o. 2099 -o.8904 = 0.1057 o 10,57% ane naquelas +o CMI Continued) (a-af-gt=0 a x=a,t É (0 Pitu<x<s2.0) = FE C2:0)- Belt) = e(2ste 1.6 . FÍLEChE op = F(o)-F(-0.5) = F(Lo)-[i-F(o.S)] = o. BEIZ +O.GUS -Lo =0.5328, (b) P$-d.6s (X-LE)< 06) = PiLocxxcza)=E(2.2)-RCh40) - p(EEcts 1.6 -P(tecte) = F(15) -E(-45) = A F(LS)-s = a(o 9332) -LO = O 866%. a. (n) PáINBO-68 <XL 1980468] = E (2046) -F (1912) = P( 2088-2000) p (LRC). p(ra)-F(-22) = 08849 -[-0.986/] = 0.80. - - - So - (b) Pixz20807%= 1-Pix<20s03 z I-Fe (2050) = (- p(3eenaeto) 2/-F(L.aS) = a.tos6. (a) Pjlto<x<2103= E(20)-R(t60) = p(ME=ãee). p táo-200 ), Flo.S) -Fl-2) = Flos)-[1-F(2.01] = 0.6945 ro.quna -1 = 0.668, (b) P$xDaBif = o PfxtastG == (281) = 1- P(2BIDRC) 2 ip (e5S) = |[-0.1394 = 0,0606. Hawu Pfo imepsroblo 3 - PE 0.05)" (0.95 P = 06634 P$u imganabte 3 = a (0.05) c6.95)” = 0,.2793 =—Sund q P$Zimagunalto)-=-0r051S PES mepinalto | o-o-go sm, Pit imeperabito ) = 0, 0004, PÍ5 mepuablo j= 000002, PÊ6 imegnalh) zo, PÍ7imepnattijzo, am P$8 mepuabiitoo. “3 (Continue) (a) E.6x> eaawz (b) Pispactty 1 Camp so imopanabh 3 to (taste qt Ee = 02793. “Noavar (0) P$B om frometimal 3 = Pjo imopeoth? 0665 = 0,663%, (a) PÍt a meu imopurabte 3 = P$O inoqunable ) = 1-0. 665% = 0.3366, Lama a sas aaa 911345678 x (ED) (0) 2, =[Oy* et) dy = EJíxe (r-o/b À b -x>b 2 4 2 co de [7 - € TS + €1/6% Ji) = (a+b) +be.) ) | i b - Rio L=[" x f(x) dx = elf xe “a. Ur . a ld | - - a/b -x/b! [x 1 oo. bs O. ns eo fel Lis cepesll, Je (eb (e) T-L*=(arb+b*-(arb)t a b?. pa CER») Fa tra: df 0/4 - alga) E Lira “45 2 se OA a +]-º co hem “26x a(xa o x=a +Jb/z. By aula + budtiçi ler) | =iPet -pmes o. conJa/r. | Septametio : Tha morde io Yha point ul £,00) io map imum. Thus co na mualiitim hat a pumba £.00 commel hort ra Ham eua auch main amd Faretos hora ma tram mu méde. EE) toa uaa pra Roy miga ditaibadim, giram ly (2:5-9) with a=0 au = “oo, pro protobitin. (a) P$x<iF= (1) = Det 90025 s10,25 %%. (b) P$x>saj=4- E(52) = Lite eg DL | í = 40 dort6 a odz %. | Ros fê 0 dat = fo * (b/r) du . | b?+(u-a? dt Fe u-a, di uu to : x-a | = dê. bit! Ex) = 7) TR -+[7+ (70 Es - | La ttem(tE8), | “uh (C-15) hoo bum ud, * -Lim(u-b) -a, 3/2 Ge Et) = E - , X>b b Jam q (u-b) =o, x<b 45 (Cmtinued) . . -6/4 z P à faituno) - P(3 failuno )= 1—-€ Lie córm + sega (UPA 67 hS + a — ls -ãe = 0. p6S6 grem (2.5-5). (6) Same ua (09 avant um 12 8 usesão : Pa gnáicant dom time =t- E fre e8p0) + (8/0 da + (ezai (8/47 1 = Ze? = 61429. -x%/a so ED re xe , PÉ fatae detuetim 3 = o Elxidy = fre ea mao 2 “4 =- === 0.001! 40 vía = fm(1000 ã ER -: ( feon/a ama VT - 3.169 vob. ED, (glB)= É P(X n D,)S(x-L) = é . | = Bo s(n-1) +88 Ed Gtx-a) + do 60x -3) LE (H8)=f "Ele|BpdE - o um + £2 u(x-2) +, rasa -3. x Loo : io | l no 1x8) Etuta 10 nto/iSo e ! 80/150 | | as/iso | 60/1506 [| i ! I | | 10/1590 | | | o | 4 o 0 1 2 3 xo 1 2 3 x : xE62) wuk B=fa<x<b) (2.6-2) (acena pixsxha<x<sb3 Parirhoiil.. Rlula<x<b)= | Pia<X<b) +8 (Continuad.) | 04 x<a tm Elxlasx<b)=0 became. | Pixsana<xsb]=P(0)=0. O) | | 4 asx<b thm Pixsena<x<bj=Pjacxsa : | Fetr) - Fela) amd Pjacxabja Eb)- Elas se Elxla<x<b)= Eem-R (4) , QEtx<b (2) Be Ch) - Eee né) (Cmtonuad) 94 x2b +ham PÍXSKNA<LXSbI = Pja<x sb] ami Í [Ec b)-Fela) <x<b)= elis . zb.(9) ftxja ) = per Eta) "0 XE Ps term bemina (1), (2), eta (3): | Elxje<xeb)= o | | x <a BON - E x 6 asxx<b , “Eb- E) o 21.0, ; b<*. By difjucantintio (1) flxlacxsb)= 0, | | ea = nto fam a<xx<b | EO tento z0 | x>b, 4663) The vp prassimo g lui vm frttm 2,6-2 pla. 5 pocsficatig , hat az20o am bzco so +9 4ECI)(Continud) slulzo<x) = 0,|| - Six (2) | [EC dm Nevrna, hora, 2o e Leg: | 1) = zoo e. o 0, | Ao : Simas, so 10 | f SC dy = 1-J lida, =1- Elzo) 20 =00 . . xX<a6 agsa<s t) | | | | 0<x | | | %<o | y | -(20)/400 | = =e .(w) da postais 4 copio | diputôme Leve Song Ham 26 usanho, qium Hal [dae mena got fo mao | wr woe (7) width (1) to o P$x>26/x>10], | pixcac]eaote fo jltInoão) de | 2 || o z to | ce x ç O, I ' ãoo | as | dt E = w'/v00, diz p du /200 1 (e-4s) do get d Pjx>ac)x>204= ef é = | (aef/400 -0.69 a = 6 =x 0.50/€. 50 cmd usa ef o ! (26)/400 | Ecs) (Contimund) (4) E (XÍD=D,)= O LUCK) +ORUCK-100) 4 0.7 U(H-t000) EXE O ÓCX) + 0.2 5CR-100) roótx-t000). (bl f(xiD=P,) = 0.58%) + 0.356 (x-100) +oiséfa-1000). (e) ElxID=D5) = 0.8 6(x) +0 15 6(x-100) + 0.05 dlx-1000). (d) Pix=foj = Pixzolp=D,3 Pid) + PixzoldeDaJPimi +PÊx=olD=D;IPEP;I =or(oz)+os(ors) +0s(025) = 0455. Similoty, Páxzioo) = 0.255 amd pixetoooj “<2-0:24 Tas Eta) 0455 b(X)-+ 055 blx-100) +0-aG0-bta-(000) uu nesutto of part cd) of solution fo Problum 2.6-B' (a) Pihoj = 0435, (b)TSfWoj=0.25S, ama (Cc) P$Floco) = 0.190, -(2P/a * Ge) E sem c2.c-n) with b=takm so Hat EG): 1-€ =osves =t/ryass, we home: F(x|x<t2hm)= 17285 [1 - 372 x<t2 km, amô Elxlxstahm)zo, x>1.2 hm, e , 3 Pixzochm|x<takm] urnas [1 ee = otrro. sem) ua gta ; - 2x7 (Re6-12). fetx) = (-* 2) utx) + Soofi-e J -33/: 3 = ixe *uco. ECHIX Sta km) = gta) cum, veia khm, (Over) 53 +67) (Continuado) da fix x <t2hm) = Ro asa xt e Cuto, e<takm x> 1.2 km se