math117 lecturenotes3

math117 lecturenotes3 - @7] g 1.7- EEQuences 8th Their...

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Unformatted text preview: @7] g 1.7- EEQuences 8th Their Uses, . 7.| o What is q, "se uence" —) I—t‘s )wsk m ” input-Le, \isk” 0.? numbers (1‘11) ‘ a’l )q27a’3J"‘)Q Wm 13¢ a, $pecL§CeoL order and, suck M 4km {/5 (fig an firm 7L. More preaufifl) “’69 ‘ A 564% 04 Wall Wm :12me "NI/L056 aboan is N . In block 9%) m—flE’Zfl—fia /‘ a): k— GLY‘eCLQ. Wer5i.e., 0— W M 3 RM . Accoww‘t? ‘to IHvis dag!" , ‘Hne. owlTPuk Should he clawkd, by no») #jwsl: Jam. HA2. output «a? a. ‘gck .F I‘o Mom by acm- How, am. «ohm (1.7.1) 1;, $0 warm Hat we 91mm Me “:wa E —" we do éemse M m 0.5; .Fmdamui‘afi MPW [MI W W 0,?- SW “Md. For Wstmr—a) h ' ‘M— ‘H/Le qua/«km WWW AmmpL-m GEE/l5 do W€ CCWL almwl: .52qu 7 l Lu. smpblwa 04 oovdrtywog sew £0? ouzucd ‘75). kmwwW; Swims 01C hacth ancazs‘v. A Exmplgi‘ Mo%—£o—dbaibai WSCML o§__S_t|3M§£§. A $1M15¥k We W gar 4 W (wLaQQS 41cm.) «om WW W PkgsalcaQ qwkibj ———e.<&. ) A, «Mina:— m- 0» W~ A; ear/Mb” (ism/ta: ) Ware. M rwwre faroasw L9 Wed 0% b3 WED. “RPM . 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You wWL 22m dooth sicfinalc mot Mr L... or SYDE 251, I W594}; rm, ECE 342 (as and. ca), 55 530, AExcvwelgi. £2915 2:59 (23% V” H“ Pkwy?" ‘ W “HAL {9%,} Wm M” [QM J: a; E ‘“ Seqmu “4 %L='L LLOOOOOO O 13‘: YL<O I 76 5 --O--O- fi-C-O-t -- r-1--r—-c--|----) w{3_ fig: Into. 4» -u —2 3°14 4% This is 00.932201, Hae umIL’c sX-qo Sequence (g9? remake obvious from. he grapk)‘ A A Exmpk 3. AmH'tef ’VC’Vj WSQfV-Q Sec]qu 2/.) He one Edam: . Ax {xwz,wm€keam+emw g" 1 i given. by 1 if he ', x = i \ ~-~-o-o—+~c~—i--o~-r-t-o----~-> 7" o oHnethSE. = n This is CaMwL Hue. Kroner):st Dania. Saw . (menu. seam/r A Example 4 . In man-j Mkmkical moduli; Of. rpluahx'mfl Phil/nomad. 41: in W fixed: )0“ oralwr .Qor ‘er 50mm to exisk, a. condition oxfi the. fine. spr)=o ( {a valuable , L fixed) Mush be. Saiisfied. . Thus , Hm mun/labia p I}; obtat‘meaL 63 TequL'n‘Mfl, pL=rn1£ )neN]; fixak 15, p is 3mm 63 Hm seqmu {fan} «1W =3— . *7". L.“ A .53 5-3- 363st 0.81__S_9_qvences. The conceal; I 8.1 34: Lim‘dc. 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' R 030 r‘uE‘Ls ufise<dlem€ 6d: M befiiwwkufl') «A: to m Hm. whim (1.9.1). Imam) me am W. m genome“? (13.1) tit—>0 an new, “MMTM I’i—WstoOaAnRués’tOWM”.W +kewwow—>x‘/aMad.)wt¥hzo<\wa$lsicfiw;5o‘d=mvkzs‘dz “~01: 43,01» will. O‘E. (1.8-1) CIA I’Phl-fll‘wral’m (MED 9; £0 area;— wm Mm W3! 0 As 4 4W gay/P )m ng Mat/1&2. wede Hm, Mowing of HQ PIA/lane, “wad/g to". When mesa; Haul” Jfi-JceM/uio Hm MEG memecm, 41m): WWW“ betmfimoLo mice Mode ow swaflcvawewtsk. For M9W,Ucb>on/r W 41.315 ', J——0< (0" 'g , or 0.0; < 0.1. - ‘ ‘1 41-250, 55%-0< l0 ; 0004 < 0.01 -3 _ h=lSooj 72%)- -0 <10 ) 0.0006 < 0.001 $0 an. game ms Mame/wt C(1me to ow; $61M {can} wuok News ’69 mfia‘w‘ué awn: 52): (L863) "The, defl'ni‘lzl‘ovt of Configmi. ‘ A sequence {an} ansz t, a, [amt a. (an—)0. an new) «F no mediu- wal e we choose artth WWW myme, COM fend. am. N Swo “Wk [aw-“J < lO-m 46 Soon an n) N- (N dzpé/Mfls on m) 1'98W5.vn.AsMo\mjcl‘-a.bmshmsjwm&a \2 inward, in HM. cowa 0% [tube [2: am figflf‘, ) wot aw.qu an (1.9.1) gems “to amasl- . 2. The Hut): vague ’Yzezal, rho-E be. one 0&2 Hm Wt; {Av Hut, savanna. For imam ’rke [mi-E 01F .10: av: n—wa is O,buJ.-o Is not number 0.; ch$€amq{%}. 3‘ USiha Hte 692410.33) “to {Moo-e me 04: a. Samoa, 4‘5 Vang deFL'mib. Theme amz. a. Couple qf.‘ slmlolg examldesam Page gm 03c Suppl/’73 L.H.#2) we Hat's abouk «‘17 ({bur us. We QW 166mm Lvow- JCo CQQULQOUX Umuzs in am mt Mam. Leaflets #9 g 1.9 _ CanaJcing Limits (HEM , 438—443) K CM L6U?PL..L.N. p.110) 0 More exich wSawa ’Hneorems 0n “ka5 ) prawn gov us 55 maizkemakiams 5 we use “1%, dong mild“ Algebraic Mampufiwfiom ) as ~Hues 91C Qmpmfiow. (You. We aQTeadj Showsz +912wi in sdnoo! /' go -H«Ls lg a, CIUCck review E The 0*” a, SW zme SW 0,81%8 . MOVE. Vac/Wag ) q. an—>Q, amok bat—>19 ax) ’YL-‘>00 «than. and; bah—a aib av.) n—mao. 0o AExmple 1. 42M Jer limi’c o4; {3—H} . 11:! Sn Scum. 6" = 8—2" 7-32.,L ~33. 42 r ‘ MMLW‘oh ” Sn 5% S < 30"“ ‘ ) NOW, M “90° ) Md! '90 , NW?— 3. is no}: aggedbeal by Hue “M411: v Ham 5' ii — Z: —-—> —.?; M 41.6%" A 5‘ 1x, 5‘ s i; elm—96L Md bat-ab cw mace ’me awbh—e ab an “96°- Nore ~‘ 0, M‘$\m1\an@ , I: 2 av: )Cqu +ke product rule W6. in —Hn‘s Cage)onng 4N8 mad, bio. A Example 2.. Compm Hm We a“: { 3+” }¢¢- 214+! 50”»: Hm we W n=| 3 . = éj—Y'. = "rT'H climate W#u24£wu 0"” 1w 2+4. (“Q6 ) w ,: 3 l For now-’4‘Mlk a; *wntiwugw, 430:; fa)” {3 MAL“ Wart» 04 8: km no break? ” Is: 411% Confimwsqkq)m LP amfwu M ’YL—aoo) Hm)“, .g-(mm) ——> ¥Cq) cu; “+00. AExmpLei. gm um limi’c 03c \ Eh! Sink) [A 0k WWMM ,Fd') mat. 75h _ '75 1: Do W5 and 2) 2n“ 1*”; -———> .7: ova 1” m E] Herpc¢253 (thug) we find SW(TC:—>_——)5l;m(%>=l Wan->06 A l I}: avg—>2 and. GIL-+2 am new ) Md, I§ aébngcm “Ham bm-e ’L Cum-#00 {$0. 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math117 lecturenotes3 - @7] g 1.7- EEQuences 8th Their...

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