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# Su94Ex1sol - Su 94 EGN 342“ EXAI'L’I 1 Name C at...

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Unformatted text preview: Su 94 EGN 342“ EXAI'L’I 1 Name C) at —1 'i.‘ 1. rm .5 Problem 1 {25 pts) Consider the function fix} = x“ - 2. A} Use the Bisection Method to estimate the root which is located between x=ﬂ and x=]ﬂ. Continue the iterations until the approximate relative error [in magnitude} is less than 11]%. Fill in the table below. Enter all calculations rounded to the 4th place after the decimal point. XI x" xr leﬂtl1% ﬂ ll]I e _. S H3 1-; 313.3331. 7.3 EC! E113 'r‘JL. LESS—l 7.57; 8.2: 6.513 ‘3. {3‘11 ‘5 B] Use the Newton-Raphson Method to estimate the root of the some Function, starting at x: 1. Continue until the true error (in magnitude] fath helow 11.5. Fill in the table below. Enter all calculations rounded to the 4th place after the decimal point. 1 xi fﬁii} f, [X;} E]- 0 1 — l. 0.3 1. E. 3. '1 Lf 1 i“. t' r at I 3 ?.eee0 d3 ngf3=\$rL33 t S *1 = -c:-.z.ﬁcm S4. in Sri‘Kr) = {~1‘1i —Cn L‘lﬁﬂ} : CI )(L:S“h \$1“th :3 \$15: 5-1-13? :15 I 1 = 15-5" \‘ﬁuoo = 33.3333?- 1.5 air.) = T. S if} _ E, = “ﬁl- DLf 16 “in Srt'ﬁr) =r (_ o-zﬁan) («3.94 1a.“! 7 c *L17.§J )1“: EC} :3 ﬁr: 13-5112} = B‘TS "'2. E& '2 'rl-SF \ﬁ‘aa : a}: 8.75 H3 “Her "‘ GKQJS}: 33\$ «.2. ‘~'- D.DEBE #annxr‘} : (—9.93 Lb‘PL-D. nﬁné) 4 CI XL!- 7.5’ XUZ'B‘?S :3 sir: j'S‘f 9,?3 ._. enlist! I : v.6“?z'5 \$0 ea = \Ent‘S-— e.7§\ *IIDD \$415 I3 K) = Naif - Su 94 EGN 3421} EXAM 1 Name Problem 2 {25 pts] Consider the function the} = eh. {Round all calculations to 4 places after the decimal point.) A] Estimate 1' (13.5} using the ist, 2nd, 3rd and 4th order tru ncatcd Ta ylor Series Approximation expanded about 15:1]. Ans. Z [lst} a. S {2nd} 'ZJse-ts'? {3rd} 2.?0‘63 {4th} B} Calculate the approximate relative error in going from an estimate based on the 3rd order truncated series expansion to the estimate based on the 4th order truncated series expansion. fins. eh = D- ‘5 C] Calculate the true relative error in the estimate heated on the 4th order- truncated series expansion. Ans. e-.- = 0.563 I" Work Area m SAM: e ELM -= High i‘k‘ss: tut—L) ":e TEE, aka-say .- -. O a EIE‘O‘E") ‘ e e 1e, Krasw-ﬂ -: t+1f£L\$l : Z. glue} 7. shinni- Ruth“) gsdﬁjt 2.”: ' Rae‘s s a {ﬁg 1 _ '51.. Rick?) g 'r ‘“ _ - Lkdtbﬁ- gxkad-y} ar Zea l,UC‘hcgﬂﬂyL Z “'r ZECHLSF = 2.5 \$3”) 1 Stun 3; ‘19:“) (rag; 3‘. = Sam «r gem (an—x3 {p a 3 gatﬂ‘ﬁ" '-'- ;Ltn-51 1- i 9. (G's-0‘) 3 = 2.5 + ** (0.12.3) : Llama? ":3 a. 1"“: u" a Siam + 2 1m trig“ u: :— 1"" Rah“? wet (EL-K93“: 1‘1 Sr LD.‘S = ‘1 H \ ¥3{Q.S‘J ‘r E ea (aggro) ' 3 “- 2.9%? + “Egmﬁbrs‘; = 2.7083 ‘3) e '4 2. " p: TOE-3 196\$? : G‘o‘sti 2."?«3'53 CF) 1 eat-[0.3) " 9. QT: 62, - 2.?u33 = 0.0:.2-37 Su 94 EGN 3421} EXAM: 1 Name Prat}le 3 [25 pts} Solve the following system nf equations using the inverse matrix in the emulation. x + 3' + z = 6 2x - 3' - z = -3 5!: + 4:; - 2.: = T I}: do a -—i - 3 Am A1=ljé ‘3 3'3 I. x: f,j.|'= 2,2: 3 War]: Area ﬁﬁiﬁ ﬂu: _1 ‘1 _ I'll-I t 1. 1. '21:; 3 "m'\1-1-1\1\a -3'3\=1u-3=13 Sui-1 a“: :— em = L G: (97: I .. Rt 1%. “a I +3 a *9. 13 "‘ '7’ 3 )<+\$\ \$3 1 +3 7 _‘ L ’3 . 1% 3%: 8‘4 Su 94 EGN 3420 EM 1 Name Problem 4 (25 pts} Solve the following system of equations by Gauss Elimination. Start with the augmented matrix and perform a series of elemental-3,r eonr operations on the matrix until the forward phase of the Gauss Elimination is complete. Finish the solution using hack substitution. II + 2x; + 3K3 = 3 2x1 — 9x; = —1 X1 + 6H; + {52513 = ﬁ (one): ‘1313 113:3. 1' °“q"" "i o «Ni-“Lil-‘f' i in [a b G q: 3 £3 H l 1.. '5, i 3 G ‘| ‘Slqln’f‘f a a 3: 3 a: l 'L 3: 13 D 115' 1 o HUN 0 -|.'3:LI.IL_._I ‘i-q is. it} .-1 I 'L 3 '13 a. 15 l I. Him]? 0 0 1 ill“ ifs iii-iii =1 3‘ 3 a Bo‘sn. )tisi ﬁL: 1. ‘ = L I a 11(13' ‘2; 1’ z, Su 94 BEN 342i] EXAM 1 Name Problem I {25 pts] H3 _ 2. Consider the function ﬁx} = a A} Use the Bisection Method to estimate the root which is located between x=ll and x=lt}. Continue the iterations until the approximate relative error {in magnitude} is less than “1%. Fill in the table below. Enter all calculations rounded to the 4th place after the decimal point. X] K II xr ledli ﬁ’ {II U] B] Use the Newton-Raphson Method to estimate the root of the same function, starting at x=1. Continue until the true error {in magnitude] falls below {L5. Fill in the table below. Enter all calculations rounded to the 4th plaee alter the decimal point. i. Xi f, (xi) ET I} 1 Su 94 EGN 342.1} EXAM 1 Name Problem 2. (25 pts} Consider the function ﬁx] = eh. {Round all calculations to 4 places after the deeirnal point] An} Estimate EELS] using the lst. 2nd, 3rd and 4th order truncated Taylor Series B] Approximation expanded about x=ﬂ. Ans. {1st} {2nd} {3 rd} [4th] Calculate the approximate relative error in going from an estimate based on the 3rd order truncated series expansion to the estimate based on the. 4th order truncated series expansion. Ans. e. = Cl Calculate the true relative error in the estimate based on the 41h order truncated series expansion. Ans. eT = III-lil-li'I-lil- a an a Work Area Su 94 EGN 342i} M 1 Name Preblem 3 (25 pts} Solve the fellewing system of equations ush'lg the inverse matrix in the solution. x + 1' + z 11 - 1' - z 51 +4113,r -Zz Ans. A_l=( 5 K: 51’: :1:— ll il [I :3: OIIii-Iii.Iii-Iii.IiiI-lllI‘ll-lIII-lIII-lIII-ll-I-ll-I-lIII-ll-I-l-ll-l-lll-II-l-Il-I-Illg.lg.ti.ti]ti]ti]ii‘ijiujqullgllqlligllglli Work Area Su 94 EGN 342i} EXAM 1 Name Problem 4 [25 pts} Solve the following system of equations by Gauss Elimination. Start with the augmented matrix and perform a series of elementary row operations on the matrix until the forward phase of the Gauss Elimination is complete. Finish the solution using haek substitution. X1 + 2K1 + 3‘33 = 3‘ 2x1 F 9x3 = —1 X1 + 631:; + 6X3 = E 5.15 x1 = 5 x3 : 5 X; = Work Area ...
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