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प्रश्न
Find the missing entry in the following table
| x | 0 | 1 | 2 | 3 | 4 |
| yx | 1 | 3 | 9 | - | 81 |
उत्तर
Since only four values of f(x) are given the polynomial which fits the data is of degree three.
Hence fourth differences are zeros.
i.e Δ4y0 = 0
(E – 1)4y0 = 0
(E4 – 4E3 + 6E2 – 4E + 1) y0 = 0
E4y0 – 4E3y0 + 6E2y0 – 4Ey0 + 1y0 = 0
y4 – 4y3 + 6y2 – 4y1+ y0 = o
81 – 4y3 + 6(9) – 4(3) + 1 = 0
81 – 4y3 + 54 – 12 + 1 = 0
136 – 12 – 4y3 = 0
4y3 = 124
y3 = `124/4`
∴ y3 = 31
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