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Question
If u0 = 560, u1 = 556, u2 = 520, u4 = 385, show that u3 = 465
Solution
U0 = 560
U1 = 556
U2 = 520
U4 = 385
Since only four values of U are given
The polynomial which fits the data is of degree three.
Hence fourth differences are zeros.
Δ4U0
(E – 1)4 U0 = 0
⇒ (E4 – 4E3 + 6E2 – 4E + 1) U0 = 0
⇒ E4U0 – 4E3U0 + 6E2U0 – 4EU0 + U0 = 0
U4 – 4U3 + 6U2 – 4U1 + U0 = 0
385 – 4(U3) + 6 (520) – 4 (556) + 560 = 0
385 – 4(U3) + 3120 – 2224 + 560 = 0
1841 – 4U3 = 0
4U3 = 1841
⇒ U3 = `1841/4`
U3 = 460.25
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