Sp94Ex1sol - EGN 3421} EXAM I Sp 94 Name i4 E i SHDW ALL...

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Unformatted text preview: EGN 3421} EXAM I Sp 94 Name i4 E i SHDW ALL WORK! Problem 1 Consider the function fix} = x5~ 1. If "-H. A} Find an expression For the differeneeii'txfli - f1 [x1] where flix} is the second order truncated Taylor Series expansion of FIKTahout some point xfl. Leave your answer in terms of no] and £1. E] Evaluate the expression from Part A} when xfl= 1 and XI: 1.1 “fiat-'5: from, es‘ungxaw e Vises”: 11-h)?" "a: zit-get) + 5!». Lifil 3* L a - c3 * lei“ {it-1“) Lt Problem 2 The function fix} = xl - 11]};2 + 9 has a root located between 2 and 5. Fill in the tables below for the first three iterations of the Biseetion Method and the False Position method. Express all ansvarers to four digits after the decimal point. Iteration xl x“ x, fixl] I‘txr] ea 1 2 5 33.: w: “slu. soar; ~ 2 2 is? 21.1"; as —C'$._‘-131,g3. —c:. {‘11.} 3 3.75" "thi- 5415 Ninth: 4111111 04?. Biseetion Method “*1” and- i+ts¢\\an 1 E. = To. _. “f. d l A r r z ‘l S - 3'- 3 I: _ 1411.; —"—"— 1.- 2. 7 s Here‘txeo 5' a“; : BALE; _2_—"1§ a {LII-L "b. .t'L'S' Iteration sl 3:“ xr fixl} fixn} l‘{xr} en 1 2 4 2.1: as to? rasfieoi - 2. '2'“ 1- S - ,7 _ let-E; -b “ac-i113! 3 b "l 5W _‘fi‘qur‘ “3,5 ._~_1_,_qfl ' 1 Cot-*bg 2% H H c, .. F 1.‘t'dl.‘-l H ‘ .. ~fi—1fieb. — we: .’ e—ee-e-o. Line"? 3 -t‘-l-bhflfl Anglos c», Gb‘tfl False Position Method tat-turnkon 1". 1‘? = 1‘1.‘ ELM-32 $___“‘*Ft_.1§ = E'Lflgy LZL—H): EH15 martin“: my ‘15 , _ ‘ _ a fiesta” Z, t..- ~ 2,7,3 .. ;_L5fiqm\,<o_zjflg 1 1:1 Hr tc‘in -I.-?;_‘-’~.“tb'l. Men—'- E-fi: 7“: -s-Tfi jflfl —._. "- Z-“s-hH-§-.1_-L§ __ .ueufi ___—_ 1: Wc,oq%3 h“ 1.5% Ht Histfi H qt ‘3“ “Luau member» 3 t ._ “1 F Home. A _ r a r 1.3-4'1-35'3 - Kan-Fame) H Lea-H. - F ‘ 1.?IED 1:3— — wee-1E Lewi-Zmfit‘f lathe-an: ti, *— Wvbfl—i—S a __ E E; . _ Beau-he aware. Prob! 3 Consider the function fix] = x3 + x - 1. A} Use the Simyle flue Point Iteration Method and fill in the table below. Be certain that the glint} function you choose satisfies the condition I g’(x) I s: H for all s. | l 1‘i xi+1=EEXIJ {I [l 1 1 t the 2 0.5 Chg _, t. ‘ it“ +13—t‘0 $:*‘: = ‘14. :31,-_%L1‘j: 1. ;+'*. 115.11 at“: t. ._ 1— .21 1: 12*I" 01"1 can}: -‘L‘A — K = 1 .. L 1' L -v— e‘ 1" 1C).“; .. {K drip} iii-1 fin“. l3'Li)|:zL_ «it flat -m"1‘-"'m ?. L it“! 1 1 -. l _ f i; L _o.E ll] Use the Nemon-Raphson Method and fill in the table below. i K; file} f’fxi} 31+: o o _1 1 I " l "l 0.15 “ten: 1‘: ‘9”3’ } s'nzfigf'u stilt-t3 TH = in - Eixa) -; O ._ {—1. I 9%.“; " xe=1fi¥fi~fl - t— ‘t = cos" Preblem 4 Evaluate the following determinant: NEIL: Hip-ta»- UlNi-Im l —2 T 7 Be sure to show the results of intermediate steps. b I n— I. 3 l_-. G I 2-, "i Z. 7 4- q *9 1 or ‘4‘ Z 7 e -e 49 ? b I 1 ' G b ‘E‘ 'H a —e we 7! 7., *1 S 0 z. -B -‘e ‘-“ _ Z ‘3 "b" = 4.13:3) P -H re hi u m] a {a -é- -l‘t w “u? *fl 1: la a ‘f z j; “I z ? 0 1% 1‘1 - IE- '1‘? = j; b ,4 z 102. 5:1 4&3” :6 Sq ‘.' Problem 5 Solve the system of equations below by using the inverse matrix. x-i- z=1 Zy- z=1 33+ y+4z=1 #5.“; wkis't R= E: a I 1~=("" 121(1 l ' ‘I '51“ _ E 1 5.1% B _| a _ P: = i—“aak '3" “" =1L¢fi+5bt§ =5 l—nl ‘9 '1 -‘ ’3: I. 4. c' I; q "-3 '15? a (I i -1 F1 1 1 an! H 7' L s. 1 -1 3: -3 l 1' -b '1 2. ...
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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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Sp94Ex1sol - EGN 3421} EXAM I Sp 94 Name i4 E i SHDW ALL...

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