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math119lecnotes-set008

math119lecnotes-set008 - imm W" LL" §é>-l...

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Unformatted text preview: imm- W " LL" §é>-l .. Imhodum M Ko’ciuai'mau . Um mow we, We wax/Rad axe/9,34% errb. Veblems 1». mom 4, Wm Wk 6&2,ka mJuA/l: am 0%- q-(Zwotm «081 one. VQMG/LLP— . In, m YzaQ Wat, M g’cuahkx: Ana/M, “@me mkfimw W1&A)bem Magi. pww’ #Wmm m mptimieol Wd‘ms 01C Mcva campefiuj )wownezs. 4m: W qua/«£6431 ca» «Hum 52. 471160364 cu; W? cm Wave 0% ¥aotwsjmd [xx/flu}; wmj «:6 4A2 (64 RM mmpk a; fivjtumddm 0+ W value/Um. Fer Jpn/em) (a) Hoe, WWWW 'w/ a, 1,00% W 016 slow—s2 claws on, Hue, posialm Comm“ 793,-} MHzeEm£__L.e./4 Was; 0:) 4k. kayak 0.; Ha. W's 9%;ch above meow 88a. laud). WA cm Hm, [aka-M12 M “42. lowaiholz. and, :‘M A}: a. .FWO-vamaHesfi M'wm. We, (la/LL ML] We. ow» dLWiEm <o§ ,gwokm 9 a, M1330 Vanmnge, J‘: 4; ‘J jgevamm WtodaoisHsEaQQ W wpueos m (1». WW 4.13m“; (76, Wfla 4,) )M—r‘ [—vfi T(X,y,%)£) (0T jusb W. 50.5) (4 no.9 nos ‘) EMMA” (one. real W) As before} m mg; mm W 18mm was 0,; a 52k mam WQWIMMOWQL/PWWWMWMW’QQFM 120.2 M WaL Ru, “Wars . 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W 04.47141; talcum n‘l'ko}: {o , CL Wald/vied fepremm QFHA-L WfoMs. LF‘HCMW ‘Hu. TaFk o¥Hu§aE 2=§(x,5) muck dzsakbes M Taiwan 94301» WuQaL Laure ‘L’o coma mm)?” a, 3D Hot,ka mullet be 1:93 MW. Mséeal,aoa,«uwdl k/ww,«am. WAN-LEA, W q, Efgoxgpw W )rwlmlok {A a, 2D represwim 0% Mfeaism, Ham (/3 M M? 5‘, W [We/g tfePrW mskam Windy); «mam? 0&6“? we!» a, W mullet mam mflbug on q, M W . Tm. Hm. CMQ 91C a [MIL Tisha, qcrow. ’HNL Xy—le} a, 34mph, 01C all), M Owesfll owtow» PE}, gives a, vowed 101m _ 9;;me.1tmoem thog) Yeheswima WWW (lg-Hanahfllahécflj). [email protected];, GMfi/ng, 45W» Foam)m C is QSCLML. . memé’ . A-eFMoonJcowm 32943”: GCVQM. abuzz—MK ma Am am Wows cum. (1/ Why ‘6 D» M rem/59. 04143;) W “.012, Hm loud owwes egg; WSFW ’62 k W 2% =4 «92 sows owe 322 mam Sod‘is—H (9‘!) {(X,y>:kx, rem. Noha mu: m We; macaufi a W g=3[g)-mm? LI- A EXWXe (9“ - Fukwt H“- |€Wzo~ came; out Hat/{351° $172ch Le: 31% I9:: 'JECX7‘j)=9~X-—3j+l. éol'u. Ham 2x—33+1 zk Camsk) 7 01‘ %=%X+é<'-k> A Example 6.1 . Sketch +ke leueQ we: of. 3C: IRE-HR came”. by ¥Cx,3) = xz+371 M fem‘shur/{Z 2E5 WPK. ————~———-—' refused/s Writ; (LI/role; wu—LHA. W 42% HA1. 0T1?» ami— Mug [I Tim 40W o.(1{1 In RZ,M$I:M.CL xfifao Hu. (“’3‘ egg”; L5 4km o; w pom 3.4:. {(2,3)go .rTLM) k/ Cow. 01!ng Jcakz man—macaw, yahoo. - Harem) M [M W WFWEF ’t'o kzo mask; as: 4&2 ”/2192. {Dog (931) )wk/Lok, C: MW “Maxim zxcqai—M [M W‘ A 50"». Hm x2+51=k9rwkiak A Emele 6‘5. Sknkok Hme level Se’c a; @112 . The (ampk a; Hvié {0% liv€< in [R4, mot so we cam’i— meow. Bud rm cam, @{d'm Hue 16W}. 39): ‘. xl+52+21=k Is 0L. {lamllv a; EFW (Wfl) 5% 123, A _._.____ 5‘ L_ § 6- 3 _ 9on5ai DeriVaidves ‘ G5 A wow 9- RZ-‘R am by (Xaa)r~++=wm be dLFfW—Haied Qw “Ewe $HW§9¢W¢L wafls; («1) Keep 13 Cowskcwt and, diffwmfiate, '3? w.r.t. 70 (Like, a, {30E «:4: ow: Vania/He) }Rem0,b clenched 5-7: (a) KQP 7C COM/SW Md. dLFFQ-WMHCLE‘B Nihj } u g? We. Outfit??? of £0 )Swaefimes) GALA. 3:5; (61- 7%) 'H'uz, 5'“th Pantiai’, Dmthwes 0; 1c (PDE). . H072, is HAL formal), mac} '. The 13133 01C {3 Out “We PDWf (a, b) maimy ‘ a b 1' if. Ohb :1 ’eVYW ' £(a+k,b)~-FCQ;E) M £913 MC ) b0 k cub 2 E 4,19 = M 7C(4)b+‘1)*'§(4)5) wet ) (33 < ) ———T——— 4‘4 4'ng lim‘d‘s extsk ) 0+ coUJLse, _ I W. Albfim 4;»me 11»me of. Mmfitdccm We am, « jfiwm‘iax «Ii-H» can/x3 017M. 2 ’ " ‘ A Emele (2-4 , Cowsidzxr £093): x ekXy ) k = mush FCILGL {1:5 PD'S a): QM. “\Hafifi POLK/b (’95) . 50% 7f =23 = em“ emu = (”‘aflem‘ k , = 3;; :: X6 XB- kX = kxzeva- ‘ l A Exwfie 6.5. Comiobw {(3,3) = (79-1—33) /3. PM %§(0,o). Sol’n. Prom/3 cw umab. we, obi-M ) ....2_ iii .1." J— X3+13,g) 3- 8X1 z: XZ ) ‘BX 3 (64—43325 bw/mgortmwbdzj ) Jdcvs 97mg wk Ha. origin, Ha. MMWMZG, §orm2.50mmmdfir§m{7w‘ (Di—9.9. 0 gym). 1% M=% (All/3:1, A “bx h—ao In. k—m LL I WM. HOSE ogm%m)mwa/1~) W M ruflo, 97C , Ne/x’c we. WE’iAR/r Mmficivcs of: W and”, M MC‘QQ, W Chadd» $013+!» 6!, {MC/(7m 9.? £1410 waiver/1:195 F01” swag. Comicflyr %§(m\g).1¥{s q, fol.- cu: MJM A): :éa (A Wfiable rm “0:! Jew HAL (9513- w‘M- 7”: qua. ‘WC 1 3 = “Bi-F , W 19.1)~ «5.12%. x 3 7M ’bx 3x7- 1 ”Ed : ”37'; u n n ‘3 .~ (W a. mixed, 19.1%); 23 0x 959x ’ Hum, Me may otlfimfajze, .Fxx aaam. want. x (AMA, 36*: 31:3: ) Xxx ('1‘me M goM)fl/>tflha_m ‘HNL WPWLLMES uésb‘ We Cow. swmme c229. N; ‘w, ‘Hu. 100me Mm: 1 w -1- v. 21,: ., .7 -£(X)3) L i AM (9 —9 ..' A "bx 45x7. (7 — > 537 >79 1 2f. 3: "but 3226 if: (33 3x73 3px ”' 2 ”l R "o 2 1- 3 (2 3 1‘5 ~93” M =04 _. 7’31 I 3x737- rajz'Bx TlML cruis’c'um monks M ‘HAZ. gr/We cwlz 'Hu. quasi-5m) ?' ! 6‘7 Do Hm, mLxeoL Mozifveg equal and» Oer 2 01‘) 19* mm W223, Do MR '?.'D.'s fibre/mi WM owls” 01C Aifilamkiafmi Eukw Sad “N” 0755)) amt 4'); £00k over 100 46'0”” to 1044 a, oombréxa/MPQ) Th}; 43M: (V9113 WWW) by HA-SOwaLi (1373) M W W (W) by G‘?ew(1984)_ m 0‘th 'ww: 44w“, sailed by 41% {admin/5L Theorem: ConsidM a, it“; {3: (RI—HR for wLqu/L. 'Hrw. RD]: EU 1C5, M £7 exist m a, kaorkwd out (0%)) m swiping», M 18' (A miliwuouo 6147(475) . The/w {yxgmw fixis’cs mat %’s "Y quay; '{70 fiy(a,b’) . E and“ version ; I; g Ls 0; Gem (1" (twice Canifmugueg 1(ij b 6) £9 7C“ J gm. Hmbfiafldawumtxsmm) Hue ‘wmtex example produced 53 342%: M £wm47bm. 7 7. —| z -1,‘ C ltcx,v)={x JC%(%>”3 h“ (7) J 4:; X'HEO’ O 7 “E szo ) ‘9) SM, M £y(o’o) #49 (0/0) +693) = 993093) mlwze % 22.; bomdzd,btk M’C "ice/um}; Wémm WWOTM 94. (0,0)) m Swot» M £303,» 7E'%x(?’o)" Q How TN: gep's meme D?D THEY cone: 0-? NTTH T373 STUFF :2? § 6.4- :“fiLO‘F SWCQS ma. ane, Lineazr APFroflma/{im . iii: Om mea/Mb‘to WMT%wm t: W Q5: Ewo VW‘B': (HM, {aim in ‘to W Ha. cmyakas-é cm) . N1; follow W083 (13:19) and, reduce. M Problem ”Co 213— valuable a» {cl/lows: .La Maura M E=Cxww 6» PM AoWa-xeao ) (*7 3%,?) =3€C’%>3)+£(my)(x—xo) +§fi§wwé<~xo>2+ T T T o Now anon M ‘Huz. aJoove st ale/woke Fumdsfis o waxfixcijgo eXkQ/vui ¢¢OKO¥HWW0LT6UZMTM Wow «3, G“) 7C("°’3) = ‘Rxnafifl + gcxvlyo)("3'16to> + 3: {3500230) (7—30.),fl'é‘" £<qu5 = $557») + fifwn (3-30) + % flyéxwoxymfim (W) fiKCXOI‘J) = gxxowo) + 1C (mm) (1.930) + yxx ,L 70-79 Z ‘ 7- + 4755‘“ > +2 {(5%) (K Wm) fifimfiofl "L + I‘D This 19 ‘HM— eerusm 0g fie "Eater We; ‘53 +wo Vain/Haj 4t ca,» be SMFICFCA 6L “We L33 “bruit/n? ,besidg/a (X.,3°)=Po) %m ><--7<o 1: h and, 46"430”: k (cw i: mama) Onyx/r Wd~ (6.2) becomes (63) my) = we) flaw + gnaw +Ji[1cxx(P.)h + 21ngcz)klc +¥yyca)k] + II. @Re/Mank. In, comfaie’ce @4033 milk M m waist/{ole cam @e cam Ha. jCirsl: lime 9&3) ,«he. (6-4) §(*»a)~7fl0’) +,CCP) +1C<P>L 'HA-L. Linea/r ApFToXl/mwhm 9.31 .F a»: (P: (X909) -<W€ Show. 962. 4:1:9 amwdcrix, mew“? PM, 6L MW >IPE 1/: also Hut. 1* mm we“ potdwomiafl. :wvdlaflj a; we W Hue, Sam M OJCCQZ) we £3ng Ml”maim Twflrr looLonmioJL M So am. a . If M SW (6.3) szvafizs (and we Wm'I: Mk. how Hw) mbe $Mm>,am\ sv'me, O(M=O(k)= OCH) ax) h M k——->O We may wmée (as) 0.x) .FolLows ) ) (9'49 A? :jcmm hawk + 005) a» LL40 _ x y WWWWWWchMWMm§WM [0’ WWW 0!} {1 ,Wefluj Lé—‘Lo A; = ¥Cx)v>-¥C><~aos = Haw-mo) = ¥CXo+k)vo+‘o)—¥wo)r I“ alm'wa so we. Ma 41a}, ((9.4) {/3 Hun makmaé exwus'uw 0;. Hm om-Mwsimafl «Magma A-S: :: DCICXD)AX + OCAXZ) m Ax~+o . As we, know l l l d; :: .ngXOMLX O [:M— ‘Hkflv W15 AK-fio t Has difgormiafl 0.} 410‘) ) owl '50 i’c ‘v: Mfullrivv/Qg Haustble 4m}; 0w ‘Hu, We an h~>o amt keo E1. (bu—i) 13st (as) / df = i on +33% m MW“ 03° RM)- A Example 6.4, . dongx‘dzf 51'. (RI—”K“ film by 519(0):?(8Xy) ¥Cnd cw. 4+“)me vww é]c\C(1.1}-o.1>. 301'“: Howe 11=1o+0| ~01=O -—-Ol Thug/urchin Xo=i.o ,gozo I ' ) amtww. (6.4) ‘tblaek £004“) #1CC')°) +.£(l,o)(0.l) + —Fy(l,°) k. = I + \-(Oul\— I‘C—OJ) zt Company, IWLHV a, Wdor’s VJ“, : {(I-I,-0.I)=l.lxe_o‘uz QC)“- A A Exmple (9.7. “TM, Ffecsww P) voLumV) cud, Jcamparabm VP ©§ one mole as: iriaafl, (345 (959}, Hat 3424 ’Fressm gi’iiv- E1 (1.) cleft/rues Wic‘L’cbj a {mchen 13(1)") gum [9‘5 PCI'Iv-g) 122/: GM so (mu/L3, 'Hu. flALf—FM‘A’Q. 0L?=_,_P.0U'+?_EAV =£gLT 510w T CDV V ‘Vz W Lib (v =5ng _?4‘},/; $3550) v 3) Lonw/r Ms M” , 41-931 77” I11 V Tip/”W0; M$° Egg—9X ~10019~0-025=00‘H P T' V ”W1C?“ “*2 F’essw M703 {all . A NB This W of echWa/{es 60m Huz. ”W and ukba " 01C €om mt WW“? rowyu caQwfldI/mc 0’0 132): au. [alga 03C Row (MM okayflm Lw PLU$‘C°’Q VMeS 44‘1wa OHM validates) . ...
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