Calculate a bound for the truncation error in approximating
where
and (fact n) denotes factorial of n
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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 |
Express A³fi as a central difference.
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 |
Explain what is the role of interpolation in solving numerical problems?
Calculate a bound for the truncation error in approximating
where
and (fact n) denotes factorial of n
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?
Obtain Approximate the value of (3.7)-1 using first three terms of Taylor's series expansion.