Sp95Ex1Bsol - Sp 95 Exam 19: Name EGN 342i] SHOW ALL WEEK!...

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Unformatted text preview: Sp 95 Exam 19: Name EGN 342i] SHOW ALL WEEK! Problem 1 (25 pie) Consider the function ffx) = lfx. A} Find the 3rd order truncated Tayler Series Expansion er fix} about the pt x0 = NZ. 5) Use the 3rd erder truncated series it) estimate fix) when x = ‘3in re 3 plaees after the decimal point. C) Find the true relative error (in %) in the answer to Part B) to 2 places after the decimal point" ....................................... Aiffix} = 13) ewe} = C)eT= —% Sp 95 Exam 1 Name EGN 342D SHDW ALL WDRK! Problem 2 (25 pts) Given the function fix) = x3 v _fi , use the Newton Raphaon Method to fill in the x table below. Round all calculations to 4 places after the decimal point, exoept the last: column which should he rounded to 2 places after the decimal point. Stop when the magnitude of the approximate relative error is less than 1% or after 5 iterations, whichever comes first. Sp 95 Exam 1 Narno EGN 342i] SHOW ALL WORK! Problem 3 (25 pts} Tho following data points come from an unknown function for). (0,1), (La). (2.5), (3,19) A} Find tho valuo of “a” if tho oooffioiont I33r in tho Nowton Divided Difforonoo Intorpolating polynomial f3{x} is 1. E} Find fgflt). Tho table below may help in your solution. A) 3- = l E) iii!) = Sp 95 Exam 1 Name EGN 342D SHDW iiLL WDRK! Problem 4 [25 pts} A) Cemplete the table below tn find the coefficients of the Newton Divided Difference 3rd order interpolating polynomial, Le. 1‘33) = be + 131(39on + b2{x‘xn:'(x'x1) + b3[x'xn){x'x1)[1"x) B} Use 130:} to estimate f(l). hu=—, h1=—5 b2=—1 b3: fail) = Eitfi't'l 1 EmJ-h-ufln‘j 5? “1‘5 (D r. 'I 1 .. u 1 ‘11 * K‘Lfl'i—E .‘H‘i E 59“”): -L L I 1'“ 1L3 ‘— “It 3 ‘2’) 773193.53: z-*-I,fia.i\,r 1b Bfo.fi1~ Maia") = new <5 gran-Law *_ 1 MM” Q": {in} ‘1'“: Sfifl'bw" —§3£D'L} u lpil- r :3- tr 0* .4 1 a- an. .4: (tic-h"! lib-H 5‘4 L1: 69 E1-fltfi 1. EuLuTH-HS Qui= 13-15 _ c, ‘L 1 SI '51-]: 313' «r E “1 *+1'1'; vsrLii'} thlL? J 3' a I "-" 91%;} I 1; ¥L$:) fi‘ltri a I ‘15 1% ‘ 1.1fifi5 -5thg mflfiosa 1-" 1.136 ‘13 gawk? “a! (:1 He] 3) Zea-:55 ' CI lb mat _ “I, HHJL 10.9‘1 O.‘-tb fies” P?) : Tu L - 1'- 3 I. {F 1'1‘! fl EL A i ' 9- 3—0.. (1+0. 1" 'L 2 Z '5 m 3 3 H b} = ‘3' :1 1+ CLL'I 1.. flu”: ‘- ‘m. + Mai-fin) +51, Lat-flak mm + ‘93 tumult I‘m mph) 11 1 4r t‘fl‘tfl‘) 1 ng—LH‘MLH .- 1 +19% r11 + 1t?“ an? +1.1- ¥—‘f- ark I. 4 4 Ir E614 EWKD E‘LH’H 1 Ea\a¥xfihs '3? ‘15 C) $ 4 1 '4 1*“ 1£¥EL 1' 3 $191: 1 L. ‘- (6.1L «Juer 321.13 *1 11. L 1‘f.*31‘~\-11 3:12”: Eququfihnék SKD?I'!.$ L13: MnNtTV’r jN-E @‘f.'-‘L’ 1 = 2¢x+h\ F 1"?— = Hair‘b Q‘Lt-fi'; 1 = H$'%\ 1:3 $=s H‘r “L11, ‘kt—“Lii-L =- L‘htgxc. a. H+m=3 1L-L‘f.*3 .—_ :2. Ann (L‘— ...
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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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Sp95Ex1Bsol - Sp 95 Exam 19: Name EGN 342i] SHOW ALL WEEK!...

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