The following table represents the prices of copper futures (in USD) from theperiod of time from 14.06.2020 to 06.06.2021, where t is time since 14.06.2020 (measured in weeks) and f(t) is the corresponding price:
t
f(t)
0
2.6655
1
2.7120
2
2.7800
3
2.9255
4
2.9355
5
2.9220
6
2.9110
7
2.8445
8
2.9070
9
2.9570
10
3.0365
11
3.0810
12
3.0590
13
3.1215
14
2.9785
15
2.9900
16
3.0800
17
3.0720
18
3.1305
19
3.0565
20
3.1635
21
3.1890
22
3.3125
23
3.4210
24
3.5285
25
3.5340
26
3.6370
27
3.5675
28
3.5240
29
3.6800
30
3.6070
31
3.6315
32
3.5565
33
3.6265
34
3.7885
35
4.0775
36
4.0925
37
4.0755
38
4.1400
39
4.1130
40
4.0680
41
3.9905
42
4.0400
43
4.1680
44
4.3360
45
4.4680
46
4.7485
47
4.6545
48
4.4810
49
4.6775
50
4.5290
51
4.5375
Let L(x) be the third Lagrange polynomial for the function f(x) with the nodes
X0 = 0, x1 = 12, x2 = 42, x3 = 50.
(i) Find the value L(22) of the Lagrange polynomial at x = 22 and the relative error in the approximation f(22) ≈ L(22):
(ii) Find the value L(51) of the Lagrange polynomial at x = 51 and the relative error in the approximation f(51) ≈ L(51):
All calculations are to be carried out in the FPA5,and the computational results are to be presented in two standard output tables for themethod of the form
xk
x0
x1
…
xn
yk= f(xk)
y0
y1
yn
Lk(x)
L0(x)
L1(x)
Ln(x)
Total, L(x)
ykLk(x)
y0L0(x)
y1L1(x)
ynLn(x)
∑kykLk(x)
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