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प्रश्न
If y = x3 – x2 + x – 1 calculate the values of y for x = 0, 1, 2, 3, 4, 5 and form the forward differences table
उत्तर
Given y = x3 – x2 + x – 1
When x = 0, y = –1
When x = 1
y = 1 – 1 + 1 – 1 = 0
When x = 2
y = 8 – 4 + 2 – 1 = 5
For x = 0, 1, 2, 3, 4, 5
When x = 3
y = 27 – 9 + 3 – 1 = 20
When x = 4
y = 64 – 16 + 4 – 1 = 51
When x = 5
y = 125 – 25 + 5 – 1 = 104
| x | y | `Delta_y` | `Delta^2y` | `Delta^3y` | `Delta^4y` | `Delta^5y` |
| 0 | – 1 | |||||
| 1 | ||||||
| 1 | 0 | 4 | ||||
| 5 | 6 | |||||
| 2 | 5 | 10 | 0 | |||
| 15 | 6 | 0 | ||||
| 3 | 20 | 16 | 0 | |||
| 31 | 6 | |||||
| 4 | 51 | 22 | ||||
| 53 | ||||||
| 5 | 104 |
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