Advertisements
Advertisements
प्रश्न
If u0 = 560, u1 = 556, u2 = 520, u4 = 385, show that u3 = 465
उत्तर
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
APPEARS IN
संबंधित प्रश्न
Using graphic method, find the value of y when x = 48 from the following data:
| x | 40 | 50 | 60 | 70 |
| y | 6.2 | 7.2 | 9.1 | 12 |
The following data relates to indirect labour expenses and the level of output
| Months | Jan | Feb | Mar |
| Units of output | 200 | 300 | 400 |
| Indirect labour expenses (Rs) |
2500 | 2800 | 3100 |
| Months | Apr | May | June |
| Units of output | 640 | 540 | 580 |
| Indirect labour expenses (Rs) |
3820 | 3220 | 3640 |
Estimate the expenses at a level of output of 350 units, by using graphic method.
Using Newton’s forward interpolation formula find the cubic polynomial.
| x | 0 | 1 | 2 | 3 |
| f(x) | 1 | 2 | 1 | 10 |
Find the value of f(x) when x = 32 from the following table:
| x | 30 | 5 | 40 | 45 | 50 |
| f(x) | 15.9 | 14.9 | 14.1 | 13.3 | 12.5 |
Using interpolation estimate the output of a factory in 1986 from the following data.
| Year | 1974 | 1978 | 1982 | 1990 |
| Output in 1000 tones |
25 | 60 | 80 | 170 |
Use Lagrange’s formula and estimate from the following data the number of workers getting income not exceeding Rs. 26 per month.
| Income not exceeding (₹) |
15 | 25 | 30 | 35 |
| No. of workers | 36 | 40 | 45 | 48 |
Using interpolation estimate the business done in 1985 from the following data
| Year | 1982 | 1983 | 1984 | 1986 |
| Business done (in lakhs) |
150 | 235 | 365 | 525 |
Using interpolation, find the value of f(x) when x = 15
| x | 3 | 7 | 11 | 19 |
| f(x) | 42 | 43 | 47 | 60 |
Choose the correct alternative:
If f(x) = x2 + 2x + 2 and the interval of differencing is unity then Δf(x)
Find the missing figures in the following table:
| x | 0 | 5 | 10 | 15 | 20 | 25 |
| y | 7 | 11 | - | 18 | - | 32 |
