For the following data develop difference table and find forward differences and backward differences
| I | xi | yi |
| 0 | -1 | 16.8575 |
| 1 | 0 | 24.0625 |
| 2 | 1 | 16.5650 |
| 3 | 2 | -13.9375 |
| 4 | 3 | 28.5625 |
| 5 | 4 | 144.0625 |
We are given a data table: | I | xᵢ | yᵢ | | - | __________ _______ _____ ____ _____ __________ ___.
______ _____ ____ ___ ________ ______ _____ ____ _________ ________ ________ ___.
___ _________ _________ ______ __________ ______ ____ ___ ______ _____.
____ __________ _____ _______ _______ ______ _________ ___ _____ ________.
______ __________ ___ _____ ____ __________ ______ __________ ____ ____.
_________ ___ _______ __________ ____ ___ ____ __________ _______ _______ ________.
____ _________ _______ _____ __________.
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Obtain Approximate the value of (3.7)-1 using first three terms of Taylor's series expansion.
Find out to how many decimal places the value 22/7 is accurate as an approximation of 3.14159265, where the latter is value of, calculated up to 8 places after decimal?
By decinnial census, the population of a town was given below
Year (x) : 1971 1981 1991 2001 2011
Population (y): 112 132 158 189 226 (in thousands)
(i) Using Stirling's central difference formula, estimate the population for the year 2006
(ii) Using Newton's forward formula, estimate the population for the year 1992.
(iii) Using Newton's backward formula, estimate the population for the year 1980.
If values of the function
find the Lagrange's interpolation polynomial of f(x). Also, find f
Determine the smallest roots of the following equation:
to three significant digits using
Explain what is the role of interpolation in solving numerical problems?
Find the values of the first and second derivatives of f(x) at x = 76 from the following table. Use 0(h2 ) forward difference method. Also, find Truncation Error (TE) and actual errors.
| x: | 76 | 81 | 86 | 91 |
| f(x) : | 5.3147 | 5.4346 | 5.5637 | 5.6629 |