math119lecnotes-set010

math119lecnotes-set010 - r L 5.1? . New? ’WC WA” 44%...

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Unformatted text preview: r L 5.1? . New? ’WC WA” 44% 16mm? Prablm : Given, (X;U)-——->! ¥ )6 §O<;y) ) ( .3: )———> .ngLsm Wm»). \) EH «a,LS.t)/Y~ This look; WPLLOa’tQA ) 17m} 5&‘5 omit/«01293 gwkle we make. WM. 0; Ha, marl: 01C As a, -FMMO{Z(;6¥L olfi x and, «6 , W, aufimaafi 0‘: 1c (/5 by (bx V ‘by V £793!" 7‘ W0!- "3 j/ \ygmdg +?.‘i all: , cum {mat/ms (bx (Mott Cb! €ch 051 sMJc)auASo =5§45+5g ‘ 00d; HQ MMlHHLCa/‘tww; ) Owd, fax/koflkfi ovd; As and, 0% m \ _ 2:221 152.9. EEK. Ely.)on (L7 dflc “(WX (as—{‘23 ‘35)ds + "bx'b+:+‘33”bt 3ch 0» G. {xx/minim» 0.81 5 move )+L& 0.? {i «‘2; 4,049 %cm by (at) M=gé§ds+g§d£5 So) simcp. 412. cho “Waggon; (umd (a) M be equaflfielmrt CMFN RULE #2 (6.14) { 2i:2£2¥.+3§.%$) a KWkS. We WW¢¢Q Ccm be aQso mum“ ‘64? (M, mod:er mlJcIPUCaiW form (Totes X Columns) , (2’s gallows : 9+ "M. 1; '2 (9.14’) (/3? 2. ’05 73$ <S3<£ %% “0* Ly 2t Seamakbj, one cow, gwaaflze We Tales to move, Wig/m {two vmles )‘ 2.3. I 7Cor 3C(x(s,€))~3(s.(:))2—(s,£) ) E (as M300?» —— ~ A,» Mg;th 44M: 01c 5m. AAFE‘mHaQ A's Lb, 43%] +2) MP Hm, eta/32. 0.; defied/m Ham. (4 M 1/wa [e . A WHIQ 9"0 — Yam COMM mums ward: o‘crchm, 03W 9cwa firm/ks M 61112, 5m «alum qfaolms 9.531172. How swsiJchc {9 Hu 'L-mkfls VoCu/mQ ’50 SMaQQ VMCO’KSWWM radial)? SCUM, . The Volwvuz, Ls 193 ’HA—Q {WKOE‘IOWL V(f,L)—'=th‘zk. The m? in» VOLu/wz «6 55am Lt, Am. oUererwHaQ 01V = (91/ dd" 'l'rfl 7m ‘bk, =2mkau~ #eralh, , m .SoY‘ (73k) =(1,s) ’Hnls @1116; oL'V' :IO'TLGLY"+‘TLd—k. (‘95) W5 ) 0L alumnae 0.? one l‘M H‘e Tact)“ PWas 0.. M3}. qvoWe, :Lo HAMBS W MCI/W“? é-2o ‘ Exam/PIC 641-» Ldsls COWHW Adka ’HAK malflsm‘s 91C 3) Jake W 03C Hm Ffem‘ows emeLe. Suppose we Med/Mm 1“ WLHA. cw, War 0;. no wove, Hum 1% ) Mal, (IL «{ch an. awov 0.51 m vwove meiz EsWa/ke Jdu. pencMaaa armor Numb; 9k Hm. VOW - Wmslaidwa H42, Mats Quito aka/Ha we kcwc 1%.ls 0.02 meal 0.005 . Hm) 5m a = auroLr-rmvzdk __, 14r+45 ’V wr‘h Y‘ hr ’ ’wc km ‘ $ 2X0.02+O.005’:O.OHS’) and, So Hm W'Y‘ on M volume ix.) 643341054: 452‘ . Two mofe 2xmf>fes 420“?er same, 1% m “m HEM, “3.643444- A Exmplc (ml. The. WOOL 01C a, smFle (413.) gamma“) EDWAAklM/M Le. FP=2T[\/:%:l , whore 2 i: Hes WU» awd, % is Hm accdmaizion 01C 3min]? wk Hte told/C2 Ivoko Hoe {De/matume in flood-ML . The wow 'v: (35% by 8(1): @113 ) min. G Md. ME cms’ramfic and yd— 1" Hue, ousfomw *TOWL 'Hae W as: ‘Hua. eauvH/L. Sw|of>ose €= 2m WK 0. {Blaii'vc embor Of 1 0/9) b M e homo” 4M, Lu. 3: MES-1 if" 5‘200k 5 ) 501'“, . The 5?th "(v/lathe ower ow’r” Wm; M Hm, WWW)WQQA3MW€W$£WWE€ Simce. (F = 9:“, (Ly/'1.) we : $4421!) + ) we). so i: = _l.( 93 — Eli) rr' 2 e 3 «Hm; we .3 L+kis,wedm'+ hMeaflreaAj How-emf) 8 £5 a, {WC/{2m 0.1: “r ; me_Fore., d3: 3kmch :d. an T“ air a “2G” 1*"ng M E y E , M So 91 z; 311 + mafia“ “any T 1 Q GMEr“ 1'6 7" :.L7<001+0.Ol =0015 =25Z ‘ A Exmrle, 6J3 . 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TWS obbwhzd (:14. 011W 1 Hae mace/AW M @99ch .Jtor {1a, (/XMBWE 0.9 a, W Maxme or minim to Mchék; g-_—._§Cx,3) 04; {mo VWH8974A>W me We "Co We aTW W aka/Mich Ala, Hut MWWMOX Of a. podd‘ (xo,50)=gi 1C<x°+h’%ofk) :‘FCX"\19)+%§(K9130)J1 +%@mj.)'kx +~~~ ; (6.1:) 2%(ayh +%(a)-k + 135: t» Md, k/ oodeL be posiéive ,% mall/1cm A_F<o acu’Qd M1? be, {TM {or MikfmAj In, and, k. (TM SW WW Wes «fa 6L W ~—~ A£>O Cadet mo’c be, fimmkad {w Gin/bike.” h, Md, [6, victor‘taufi ) So HM; Ag < 0 (MAX) A§ >0 (WWW) 00w be at»mede Em afielng k M k, M Lg me 3% Hub rips. of, (this) eqwdHro 29w o We gum-W26 Hue, above 0A ¥ounwg I ‘ 6.27. 13, 4:0 (36 61, Max 0? a. min (or 6L $‘Eaib‘omamd EOE/WE) d: is mace/aw hm): (we) %(a)=%£(§;)=o , 9+ dflgr—o J o1r Vjczpzo W,” W M m 422, molx‘l'fiws o OK—buk MwJCo1CMou£ MMWEi/aqrmxoram‘m? To OM,wa We questing M :30 back, +23 “we Tat/3L9? sewers Cents) Md. look, wt Ha: QU‘i‘rfAn/r W: M 2x33 22/; W A B c RAH : Afi+2BM¢+CIJ +.-.) Fa ' =L OY‘ “exam? 0( .E, (617) =Ao<2+28d +C '77 W This is a qua.de 1>obnowiafl Em, oz M So (QOWL \L'ES &E Edam; {20$in vague; A>o M AC—BZ>0 ) OWL ale was madam W3 lg. A<o M Ac—B7'>o. Thus) we, «3va HQ geupmg 6.13 COWCLuSl‘m (La M e [759) I C > ’a‘ ) 2 Let {:3 R2.» R Q 0.? onn C L and gm’pPose (6.”) ‘ 71mm. ((1)2, as aloud), an, if ai (PO fi>o MA '32?“ 9110.. ’3___2’-F_.>Z>O thL (Bx—Z (3:77, . Freqwzmily 4L» WW: one, huh/Sb Hm. max or 1mm 04 a 0,? kwo or YWOTE vaLa/Lzles swbl'eot—E , W~ Lola's see. mm M: meow, on. 0.. 55mph Mmrte : A EXMW?‘S___@_‘£- Find, a. fihkionqx‘y \ooflw’c 0; Ha, qu/wohkw 36093) —.-.- 1x74 35?- subject.- t: M comm SIX—P321. m. This problem. is So <.tv’w.;a>[e Had: 34: ccw. be {educva to HA2. cam-e. 0*: one-vmlole m‘ In {our/E’sénu x mot. 3 Mel: Seth‘ng Ha. ocm-«JYME, we. can. wake. 414.2. (m av: 5 == l-SLx M6... swbsh‘hta U: mite £095) to fix}: a, a, 0; Ha Sole Vania/He x) 31%) == 2x2+ 30-2201 .1 sz—lzx—fi . 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We I3» (4») M4 05') M ‘I I‘ll Vedas-1- 47:)aud-MW Hm}; M must be Pmflhfi ’ta eacb. elixir—— «711.21%(‘4 2x4.on ‘Huz. of E¢(9-"7) ' . For zxample; 0‘? Hal; mede See. HEM) Pp,655vé5'q) M Hae assignments. $9.4 _ m bowie 1159p; \ 6.25 b WC. saw in Calm J. Hut ‘Huz. 46MB 1;ch2144-9. ff.(3c)d,x of a, single vWLe .{ :[o,b]—»fi é: aim {:QMM 01C Ha, of HM, View sm515w+1v2 ‘ we Gkofl aw {was to £wo-kub892. fi/vfims (er coda/r {Coed-6) 1506.3) 0W some R 01U’ke m. For smktcdky , we 96% W M Jrke. fefxm, mm Hm)» Mind. 435 a, mafia/male, g ={(x,3) [aflgxgbl jet/293552} , =L‘a‘”‘"] x Dahlia] ‘ WC VDOW M 471410 99/179 E‘|)bl3 M [4-2: by a,=x,<x‘<...<xm=bl NOTAT‘fon The Yer/Lawuale R cow. 6?. (2de an H». prod-La: :4“ M ’C‘wo 9dr; ['4.,b,] az=fio ) 4;; M caSZLfi‘Ha-L Mask" as: M ’fcmfigbm- 47kg mxm ow WW. 3. cud-4,5 o1( Ax; = xi ‘x’i-l and, A . = .. ‘ - 33 31' ’33-! OWL jamki'E-l‘dw @099 w: 6W. an 164M. ‘7‘?” “msz , [e gammy?" R:[o)l]x[2,3] and. 161': 2 be 0 x°=°-0) X1=0.§ ) X2: 0:? ’30-‘20 1 QVI’Z‘Z ) ’52:,2J‘i‘ ) 3352\7 I ’34:.3‘0 5L9“ 9. W main, is 9‘5 Clio. (augech MEW Ma w m Axis M H41. 43%) ; Hug. «Q50 shows (93 mm Ha; Vaflw 01C a): some. mam (amid: Mind. 5‘} mot, an, m exmlple Mam ya in 1mm (0.! )(2-I)1(o-s'>C0-2) + (°«‘+)(2‘7~)7'(°'S)(9~2) + (o)(2-$)26>-$)(0-3) + (owxznfzwsxoa) + (o'e)(z>‘(ols>(o‘2) + (o'e)(2-4)‘(o-s>(o-2) + (0.5) (2.7)2 (0-3) (a. s) + (0‘7)(2-s)2(o~3)(o-3) + (03) (2tl>2(0-2)(°'2) + (I) (2~s)‘(o-2)(0-2) + (0'9)(2'é)‘(0'2>(o-3> + (M) (2-9)2(o-=>(o-3> =3.12%3. Newt: M +41“. HM. lama: cu: Hue. ” {pmfim (Moi-ed by [my )Jcmts to 2-2110 ; ’Hu'us [MK 21Xl‘a‘175 Hum. we Call ‘Hu. mm: Hue. double ‘mkgxd oF__.;L m 12: M m (0‘29) M Z Z 'Fég’yg‘»): 7" {+0994de - R "Tmeo 1:1 5:: Q3m.we 4112. MD. 6Mols +2: dache aHu; double. .Tke mosh aneuan ones am: {R4 2' [gamma ; Lanywdy L14: Ls Hm alode 0+ Entered-rim. ’Hmu‘: {alts you. a - M 3“. m mew/a mH~ a. Ana/we Magma. g 0 Moe}: a} We 45% 5.41: does ME maker how- we [proceed Cw M $656 0; «We Mask. For insfcwco.) {at 'va be M Pam-Eton a; Hue, )c‘5 cqu 113" {m q]; Hm 3's. Since M #JOL‘MJES M cuuz anab'x-Hofi) [2,17 15;]. cape/MW mm’qia, 1. ar- . J 749. =x£ ) 1&%=y;5. I; MR. [65 "TEN—>0 {Link} me. 13:21:: Lecwa = a»; (64» Z .21 mug.) magi) R Utxu—m lImyu-w i=1 1:! J jive.) Jaw £(m ZHKLgpAgan; Hui->0 ~=t who 1=1 :ngfio +(x32})&7)A>2 (6-20 = frrtflmfiy d». Conflde fixed) 4414.- 59 MS 'w I‘F ,meewL) we. Lee “Tau—>0 756mb, we 3d.- (exactse) 57. (9‘22) JR 1LC">'6)4"“*3 =J H55)“ ‘1‘: - “Lat M, accmAARA-g'to (L21) we. km . The {afms ((9-2!) auoL (6.7.2) o; ‘Hmt acoutale infeéxafl. ctJLe, Cow ’1ka (meaning we Jo {Cm-E one MA Ham AM. W).Iw eruLs .fasbu‘on W is Web W W Lu. Jche mug ante/8rd. _. ewe mm Is 6:. am! And “we COWS , 97L cow-use ) we problem eat M 300mg," M . There is at, long; 5004:! 9,; mwes comma M amsw +0 “vi/s qua-143%) cud we. aLou'h We. H12 +LML ‘(zo «:30 0W 34:. So 'Ine shew. LimiJc omselves’h: H's-Hr? 0. km: {arth Tewflts : _ If He domed/n, o; {mkefimiim E \S a rector/wag oqu is} .F is (9‘23) conkinuous an EA , ’HWM. item-Utah, is flawed) Md. W; Wraith (ices no’c maHe/r. . L3 Guido ‘r‘ub‘mi Ln 1907. I} “12 domain» af— Me Takm is {he aw argpg,e33.§ ; K3423) va : / / e 24) m b 4“” 5 413 /// C ‘ zj ( §(*I9)dy)dx : 35:47,“) ~-'-‘-+‘--——-—-|-- I Q 5 A T ., Here. 13%,»! amt; 4’.(">~<B$42(’° Viewing) .5- g». Scmilaflj, a4 “42. dovuaim 01c Wkearai‘wn L: is 04 Ho. We D={(X»a) l %(%)é¥$4)2(5)}06¥34j (6'25 ‘1 43(5) a 2W8, The». arm reams 9.? ’Huz. {plat/n.2, -—-s—u.oL_ M Hue. disk. skewn— Lu, M W Below -——H4.ak ch. be. dual/bed. bo+k wags) Epe~3 fefi‘wns Thy/n.) of courage.) we cow. {4,53 .eWux .— _-—-. @514)” (L‘2§)_W , we use 4% We)» m! I A Compuke §(x33+mx) dxdfl) wow ‘1' ’"={O‘»‘.1)(Oéxélg3 0535*} Sara. gleghola, ‘H’Le, we ‘ "l". Edy"? 3=¢£0=X IVs obvious H1.an we Our 2" l] l‘ (hTH/ 3:440:17 wmdm‘dc aTUPe-I czaion- rm . __-_ _.,x o§ a Hwa, m? (9.24), we got (9‘ Lg }(X33+mx)4xdj : jam/2 (j0(x3y+mx)oeg)%x T O T‘/z. s~ (a =... .1] fi+Xwa dx=...=l+I—I,A 2. 76 2 O A Example 6-55. Gem};th 1x31414417 , mm D ism . D (234mb 0°C #33 fthme Wosed. by He x-maoL a-aXIA)OMd, “12. W ’g=4-X7‘. Sel'n. Sketch D; M ‘1 u D={(x,3)[ oé x52 ,‘ 053$4-xz} fTI[ N059- M we W 3:4—X7'=) x:é/I:g_') M 40mmuQiT‘efiMD “4.40% o3r_’Ta|ae,2: D={(x>7)195X$JZ-T; 0é3$4}' ...
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math119lecnotes-set010 - r L 5.1? . New? ’WC WA” 44%...

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