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Su94Ex2sol - 1 4 Su 94 EGN 3421 Exmn 2 Name Ptohlem 1{25...

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Unformatted text preview: 1.} 4: Su 94 EGN 3421] Exmn 2 Name Ptohlem 1 {25 pts} A spline fit through the points (1,“), {2,4}, and (3,9) is required. Find the coefficients 11;, e1, :13, h}, and e; in the function 3132+ by: + to 1 .6): 53 . {EH-i=1, g‘eu‘ ea 5'+;‘=&J *‘1’: “fla‘fi‘ve fifi‘i am we! at “i “1} vow-H = “t be “-H ”LC-‘1. #15; «rut =-t (.1 :.—H Sing-2,3. cure, EUR-.11“ f: ‘9‘ 7'- estate.) #51 qfl‘tiriblye, 12‘ 1‘... *1 _ '4‘ 2. 1— LB]- ...LL a ‘4: HQL if 5L 1&1 (LL EL 5-1. 1‘- '4 G l 1 1. It “I. D I ‘I 1g :1. 1‘ '4' 1 '1. l-II #5 Cl 1, i. a r4 G I. 1' D G '35 1 3 1 cf ‘ I C" D O - o q ‘1 *1 E‘) tLLifl } LL11: £45.34 51-h? I i b - . ““1 1-9 h ‘ ... Cl. '—'I CL 1-1. 'L- L in 1...: Su 94 EN 3421] Exam 2 Name Problem 2 {25 p13} Find the equation of the Newton Divided Difference polynomial 1which passes through the points {-1,I}], ELI}, {Lil} and {2J1}. Assume xu=-1, x1=fl, x;= 1, and 53:2. Show that the polynomial reduces to the product of the three linear faction: (1+ 1]{x-1](x—2} since the roots are located at x=-1,1 and 2. _ 5:, ’9‘ hi“ *2: '4 1L; ‘1; L 1&1“: fl. A ¥ 3 a —1 (I? ”Z. «.1 i i c: z -1 1 1'- 1 o c: 3 z a g-E-i'ijlal 2: qfilwiS-LRE -' 1‘0 '3 Z.- fi-I"‘ILI: D“£"'"‘] shank gum-etw _ — 0-1. -_-1. T‘Lflqt‘I teen sueml= “194% .. o—e - c:- 1‘5- *1. "2.,“ ‘[*21*1,M = filtlltflv‘rih in] - ~z~a - -1 11.5%: V-L'l" QY}; X; X I 7- 2i 1 r I 7131" l'gifitnl 1, n l {rpm _ .I *3‘ 3L 9:. i 1—D $31 1.. 1 1‘- :x-k QET‘3,“LL,$W -§;"E_}LLIK1K¢, - 1- ['IE 1:. 'I. - iii-Ixe- 1“L*1‘ Ans. r3m= he WWWH-Kfi n z£t+'}”1{i*il¥ HMHMt-I‘} = (3+13LZ-‘11‘ + t1 *1] = manta“ +1.“) '- (nominate?) Sn 9‘4 EGN 3421] Brain 2 Name Pram- 3 {25 pts} The exponential fix] = e" is to be approxhnated by a linear function. Esrahlate the exponential at 1:0, 1, 2 ,3 and find the equation of the least squares line based on the four data points generated. Find SSE, SSE, EST and the coefficient of determination 1.". Prepare a table to show how the coefficients of the normal equations were obtained. Prepare a second table to show how SSE. 55R. and SST were calculated. n. Y :‘D'DJ'G'I‘T‘ C}: 31149.“: is: 111273 Hf = _‘ Licl’t *-I {a e H; GL1: -1913, I] L_. ligJEfiI‘ihH‘Li ”I: - 53"?- = fl : QB‘S‘H '- tam-rec: Am. SSE=3L11M 5511 = moan, SST =215.1e||,1-’ = QES‘W Su 94 EGN 342i] Exam 2 Name Problem 4 [25 pts} Ifinfl the equation of the Iagrange interpolating polynomial through the points in the table below. Esthnate the value of the function when x = 2. Hun, a 2:1 Lind has L3H} Mom: iii-SlLK*S\} = guemu-E) n-a‘i hfiltivil 8 LI“): xix-nix-Sfi = ,mpngx-sa B-EHS-o‘ui3—Sj 1L L'JL‘H = iLx-I] i 1-31 l§-D‘1LE-tHS‘-5) Hat-Mk3} Lia gag-1“}: l' zt-ni'fi ”'33 " ltfif-s) 'r is; ' 7- [Elli-l} S :1, B 4:17-23? 2 u: E :3. 3 Ilil‘lIOII'll...IQOIQII'III'IOII‘llIi.I'llI'llI‘llI‘lllil'I'FlI1‘I'lil'lI‘I'lI‘I'IIII'II‘I'IiI‘llflfliflfliliilfliilil‘lflill-PI'II‘I'I Ans- £300 :31, :u-e'luvs’) 'Eiu-nii—S‘m + Q “Haw-3] ' .‘L E QatL‘j = ‘3- So 94 EGN 34% Exam 2 Name Problem 1 [15 pts] Find the equation of the Newton Divided Difference polynomial which passes through the points {-1,fl}, {1);}, [1,1]} and {Lil}. Ame xu=-1, x1=ti, 11:1, and x3=2. Show that the polynomial reduces to the product of the three linear factors {X+1}{x—1}{x—2} since the roots are located at x=-1,1 and 2. IiI‘I'Ii9"iFI'Ii9"iPIJFI‘Ilflilfliilflilfll‘lfll‘lil‘lilI‘lllQI'Ii‘IJFIJFl'II‘IlPI'II‘I'III'III'IiI'IOI‘IOII'IIP'IOIIUOI'IOIIOOI Ans. f3{x} = 511 94 EGN 34% Exam 2 Name Problem 3 {25 pts} The exponential fix) = e’I is to he approximated by a linear function. Evaluate the exponential at x=il,1,2,3 and find the equation of the least squares line based on the four data ' is generated. Find SSE, BER, EST and the coefficient of determination 5 Prepare a table to showr how the coefficients of the normal equations were obtained. hepare a second table to Show how SSE, SSH, and 851‘ were calculated. Use three places otter the decimal point in all intermediate calculations. Su 94 EGN 342i] Exam 2 Name Problem 4 (:25 pts] Find the equation of the Lagrange interpolating polynomial through the points in the table below. Estimate the value of the function when x = 2. Ill-fll-ilIiI-lII-IIII-lill'lIiflliillfi-Iilliiliilifi-IilIiiIOIIOIIOIIiIIiIiiIiiIIOIIOIIOI-IOIIIOIIOOIIOIIOIIOOI. Ans. tau) = [3(2) = ...
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