# 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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