Taylor Series - Th9. "thar iiinls Em QnE:-Dfl cf» a....

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E 1' d " = Hmf 1 1. 9H») + 5: {finicky + 5P“;th i fish“) . L1 The, ' arrar t.‘ vs nuabhrrm’c‘ifi Ekkfifi afl$?an‘sxcn 35} {run 055.21% it: Can 5‘3 \nl'ra Lflflfinnifi‘fi‘a 1'; q- ‘ri‘i" = 311% 4r ‘r‘mm-xua +_____,«r {mum cm: 3“ n‘. {hi-IL] EL *‘1- in Lima) {Pi-*1 flirt {n+1} a ‘r '9 if. \Hffli “H (mm: “3 +-*---~-- T . H 9hr.“ 4r ’11“ r» 1% ‘r‘ni rtmawnéifli 4.1!?“ tam-El ‘5 cthtn Haw} _ m t in q a. *jci:j {x-F‘uan?‘ + gin-r15} Law-U“- 1. r. at; 1. 11cm“) 4: -.-_—-q_.—- [n+131 Fur“ fill: 3L1“) : Sr‘f-l'ilqw'fim 5"??“"~ it 1': Lh=fien *5 El fiarfl. tan-“s *fini' 1‘11 ‘5 E'C‘Lfl : at,” +1. I?- ‘I :. g‘HIE—gii‘f‘“ In aNN-xtr u—‘I-DV é‘; *hgi Tfihaxnaxr ’1‘ .5 kafinkgth 1-2: Wt . J 3|ch n Lakxn n mtrfi'?‘ E t fi‘rtfixfiéb’tm n13 ‘ ‘Frnrfi (lamb—rug] aha, lapmnaafi- Was-ram “fire-.3: I"_—g—| in-Hirmu £=n\mmr~?§ 3 H- n‘: Var-5 dafir‘s-acmi #:- Sttfif} I anmlhfln {II-L1.) U, arm-HQ x44.qu :u'fir 3 Whin EEK “human Lanai) wt; Filer-s. “gt at: we.“ :35. 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M THE, Tmfiknr- Sarxtg E$?&flgign DST. 3kth {:‘anx‘ an 9mm =~ Ia,EIL {_mLK‘-m) Gigaa5r *“i ?01'\.* ‘KH'LG ab Fun—.— sm= mm + Q‘Lmtx—m ra“LmL~I-I~'.‘IL I 2.1 . fie {51%;} = E. ’ Ho} :1 I. ’1‘“ SIan-) = E“ I fi‘ta‘) :1 1 VIII ‘1 ‘— J“ I 'I - It: J s [5") " I I I : I I : I ' I I I I * =5. 1" - _ z. 5 ‘9— ' “r K 4 "f- + I: a, _*__ I w h :51 K = z 1 i I K, (“Lam L}?Ln$.'fin 125; EL “had: tiff: ) K=D " ‘59? 71-. c} 1' CI :} EL ‘_ 'l i‘ G if c. .i, __ 9.5 :15 '7‘ 1 a 1+ an: I: 0-5 *r 3-“?! *' 11 55“ The. 5-.) - M :‘r JI'VT‘E Ingnnfi'fit Efifi't‘fa “Nada ‘5 *iqu‘HLIL-‘Ft For $= I I _ I _ 3:: EL =- I + I + I + l + Th1 Edi-n $5: 1&1 miwrkct sec-I23 afiu-‘Eu‘k'é: 3:7’32'3'2’25 =1-ta~t%1?_,:1?r 5341*) 'r {EL ' inlalfiglfllfi fiuqqafit we, 451 )C, DST Q. QHQQN— is =— :3. arth %rqnggfiaa T573:an banana». E$?on%ucfl- . in *5 mahma‘ia 6,10. 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Arr-1Q. fiXb—Nxdfl ivth an; flkx-J’in Bu}; ‘3 T '1 ET :- 5rr-J‘EL ugh-1t '- a11¢=ixr~n¥g Q9142, *FJ‘L. \lG—KJQJ art-41 Wain-1e, in amt Hertha-J5- Qa‘fiflm'fXQJ 14mm. swag rgxflxga 1¢¢3¢$ are, GL1. 1 SELL‘S‘, wanCLLS} SELLS) 1.51 ‘1 1+ 9—1 = 9-2“ ; :_c_15* (12.5; 1,) ELLE “1“; it, “-= 0.8 — {113' : racial“; ‘1 6.1€?n 3 0.9.: “L1: __ fl_anc‘%\1§ *_-_ “Giolgélfir i“ tr?) ‘3)13 ) 5.8 («L-.31 QT = D.'b-D-'JctfiEfl§ : g_QDy-HDQZ,§ {CLEFRDEL‘S' “PD 0.3: t fight-k Wit. krd‘t. warm: ET 5M5 Wat maxi Ti\:~"t\“:~ Efra 3 J ‘31:... 9‘3!“ arm-’5, Ea. a4¢\qug$ Wham Arm-a ’H‘J‘K HIM-“b “‘5 ‘J \‘Lh sub 1". fig. a??¢n$m£fi% TaxafirxJE Qr'rz'x?‘ r151u2'. *0 'r‘n‘k ¥¢E~L¥~an0~3 thhfi%.fiu a"? an 15%,“;qu \aqfi-m QKr-x #9:: {snatL—I "HJQ. «TH-Kc m‘rxnn Ci:- _ "Ifirxm‘x- 1'8} (-19 1 net-J arc—ML — 2:313 ua‘qu' nix» ua‘iug 'H" *5”; 11¢W?‘i JEN-“‘6- flm UH"- anéfl' ¥¢an¢cfira§ Ta‘h‘xut‘ gifki‘: K": fi‘t‘hmu‘ffi Ch gdfithan “QEQQ Gk} bahi “fill J whiz. a??ru+xncfiffi fi‘Ka’h-HJ‘L emu-r grram Jami? Snug] ’r: aahmu‘m 9:th x5 '9. = Emu-Jr H L20 fi-F'i gar-W) \r'w .HMQH "“Dradxa-QS fi+gfi?1i J n 1‘, *1qu 1 ‘xfinvsy— SrgCL'I-E"; 5‘r' {1.13 ‘) 0.75_; t —D-_3%333:‘> C “11.353”; ‘2: ‘5 0.1 5 fl - 2iI and: = QLLLI‘E j—Q‘mii‘: m Elumgg : 53-92115" 0.15,“ ._.__________ 0.3J1'3 L 9*Q-jgci13i ('?-{2‘T13?¢}g} : -Q.D+‘"}bo'?3 (1 I-‘iéycfl'éfifigj 0» "m b‘E-E'JS EGN 3420 Exam 1 Name Fa 2WD SHOW ALL WORK! Problem 1 {30pm} For the fimcticm fix} = %35 shown below. EIFBJHW'I Us. I a} Findfgfic), the semnd order truncated Tayiur Series expansion affix] about My =:rI:. b) Use: fglfix) to approximateflfl). c] Defining flfi) as Lim flx) = mm??? I arr—>0 3—” Use L‘I-Iopitai's rule to find fifi) and the true ermr ET at Ft}. = "Jim-xi '1‘. ‘9 5mm} = 91%;; a: Q‘Lmnvx; Jr i‘km Int-X, )1 2 fl 3*. a; 1-. .. Z. 5.. Li) -‘."x [ii-smut.) arccsgk+ca$1LJ .. (innafieamfifitzfi) It"! 3.: . 1 -7{ bm‘fi -_ ‘Lfi La‘sf. 4r lism‘i 3-: TE. 1:.in :' {hunfi :t} ‘7 fit”) ' fi'gnfifi’ ‘5:on _ _. W1 ? II a, 1. ‘1 £M~ ~n amt: -z~n: warr' +Lfi’5m'fi’ = 1 I” "'1' '5: mt.) = Q -~ - L 1 “(infiaru1(g~n3 rr "—1. an i "d —1 C —W\}" L? rd _ ‘fx ‘r 1 Lit-WP) a fi' 1.1;“ I ‘93 in“): -_‘_{o-fi'} +l_(D-cr}L fi' 1. “I .n — L...” _ l cpl) 903'} :- LH'" S-L'It} =- LII-I" '5 '3- 'i'Fifl jég 1 y‘alfl 1 fl E1: {riofi-QLLQ‘) = ‘- l EGT‘J 3423 Project 1 — Taylor Sari-as Expansion Writo a MATLAB program to do the following: 3} Find the truncated Taylor Serios expansions fnljx}, H =3,1,2....,3$l3 about the point x” =3 for flfx)=oo5x. Graph filx}, n=3,1,2, 4,3313 along with fix} ovorthe intorval 3 :1 x :1 Err. 1:} USE fix], n=3,1,21...,9,I3 to approximato f[rrf3)=coarrf3=3.5 by fillingintho table below. Express all answers to 14 places [Fonnat "long" in MATLAB] after the decimal point. I f[rrr'3}=cos{2rf3} fiEF-rfl} 3.533 33333 333333 I .333333333 33333 3.533 33333 333333 1.333331333333333 3.533333333313333 3.451333344333912 fl - 353333 33333 3333 9 353333333 333333 c} Repeat Steps 1 and 2 for :::u = 23M. f{;'r.f3} film”) E?.=_f(;re’3}—fi[rrf3) 0.50m flflflflfl DDGUU —D.2D?1U6T81 1 8655 0.5 ODE] Dflfiflfl Dflfiflfl 43.92 I 986658?6323 0. SUDU UUUGG DUDDU 111302245 5035965? Uiflflfl flflfiflfl UDGUU U.flflfl13fl353fl6995 USDDU Dflflflfl flflfiflfl 1 5 0.50% DDDUG Dflfiflfl 6 El'. SQUID UGUUU UGGUU [1.51391] UGDUU UDUUU '--J fljfiflfl DDDUUDDDUU E} _ fliflflflfififl DUDUU DD DEUUGUUU UGUUUDH — E] d) Repeat Steps 1 and 2 501' 3:0 =m“2. fWJ) ET =f{2rf3)-fi.txf3) flfififlfl'flflfiflfl'flflflflfl fljflflflflflflfiflflflflflfl fl.5flflflflflflflflflflflflfl -fl.fl23 598? T55933G QEDDWUWUHUWD -U'.UZ3593T755933U' {15 Wflflflfiflflflflflflfl fiflflflSEfiEZflfiflfi fi3 USUUUWUGUGDGQU — 0.5mnmmnmmn H.50flflflflflflflflflflflfl H.5mflflflflflflflflflflfl '15 UDflflGflflUflDflflfi , 0.5flflflflflflflflflflflflfl flSDflfl-flflflflflflflflflfl “fie—cu“ I - TM“? “aims Emman 051‘ Grim : Lag»: . [I 1 I L 5m can ‘5 1' firm“) r 9‘\ m Qua-m + ‘r “aux-m +._... + firming} cm)“ . 3 3', T For “fig :13} “RV-10}: STU-fl -*r 59W) )L +- 55“qu jil+__.__ + 5?“an in 1.]: n: T" 3mm: 1' glL})= 'll 1- (-G)7{ —_ I 2.1 2.3. 1. 3-. 1. Editor“): 1—3: +5323. :. 1-}: LE 35‘» z. I gr: - 1 ‘1 .1. 1 H ‘10!" '1"!- a- it) 1 _ 1' J‘ I L +35% ThiPfiR-DQQ} WE TL 95' apc‘jfiu‘ *E‘uh {Lau‘flLtg Tu\a\ur Efifi'xtg Dar H‘H 1- E551. fibndfi ia=a as. chxfi'in ‘33 _ L *4: b "I: {ThL‘i-‘j '- ‘I l a“ _ " L + _____ 1- in (nqfljti 1"") 1“. H1 in 1- .fl .. : 0.5 —I -: -r:_5 I ‘FI'. - "1 31E. Ill-q} * Jafrfi'fil ; Dfiufgfgjggbq 2.’ ET: firm—$1,015} .- mi - a.-f~§1h%%etf :- anafiilfle I» -n- I ' If I fibrin - r -' (F33); + Nb.) = 0.50:7qbag 1i - ~11 -c>q Deficit-ale fm=msm and nth Order Truncated Series {n=fl.1.2,4.fi.fl.1fl} f{x}=cn5x fir]=m5{x} and ant] r .- I I _ -.__T:.-I_.._ _ .-__;.-_._ Inf-3%- _. F— aun-I. _ -_ fm=¢n$m and nth Order Truncated Series {n=a.1,2.4.s.a.1n} fm=ou5m and mm fix)=uu5{x} and nth Order Truncatad Salinas {Hi-{111 .2.4.E.fl.1fl} fwflmsix} and mm ...
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This note was uploaded on 06/09/2011 for the course EGM 4320 taught by Professor Klee during the Spring '11 term at University of Central Florida.

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Taylor Series - Th9. "thar iiinls Em QnE:-Dfl cf» a....

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