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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 .
{EHi=1, g‘eu‘ ea 5'+;‘=&J
*‘1’: “ﬂa‘ﬁ‘ve ﬁﬁ‘i am we! at
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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]{x1](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 gEi'ijlal 2: qﬁlwiSLRE ' 1‘0 '3 Z.
ﬁI"‘ILI: D“£"'"‘]
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teen
sueml= “194% .. o—e  c:
1‘5 *1. "2.,“
‘[*21*1,M = ﬁltlltﬂv‘rih in]  ~z~a  1
11.5%: VL'l"
QY}; X; X I 7 2i
1 r I 7131" l'giﬁtnl
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1‘ :xk QET‘3,“LL,$W §;"E_}LLIK1K¢,  1 ['IE 1:. 'I. 
iiiIxe 1“L*1‘
Ans. r3m= he WWWHKﬁ n z£t+'}”1{i*il¥ HMHMtI‘} = (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 ' tamrec: 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: iiiSlLK*S\} = guemuE)
na‘i hﬁltivil 8 LI“): xixnixSﬁ = ,mpngxsa
BEHSo‘ui3—Sj 1L L'JL‘H = iLxI] i 131
l§D‘1LEtHS‘5) HatMk3}
Lia
gag1“}: l' ztni'ﬁ ”'33 " ltﬁfs) 'r is; ' 7 [Ellil}
S :1, B 4:1723?
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‘lﬂillPI'II‘I'I Ans £300 :31, :ue'luvs’) 'Eiunii—S‘m + Q “Haw3]
' .‘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. IllﬂlilIiIlIIIIIIlill'lIiﬂliillﬁIilliiliiliﬁIilIiiIOIIOIIOIIiIIiIiiIiiIIOIIOIIOIIOIIIOIIOOIIOIIOIIOOI. Ans. tau) = [3(2) = ...
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 Spring '11
 klee

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