The unequally spaced data given in Table 2 were generated fromf(x)=3xcos(x)
Table 2
| x | 0.1 | 0.2 | 0.3 | 0.4 | .0.55 | 0.75 | 0.95 |
| f(x) | 0.2985 | 0.588 | 0.8598 | 1.1052 | 1.4067 | 1.6464 | 1.6578 |
a) Calculate f''(0.1), f''(0.95) andf'' (0.3) by using the appropriate divideddifference
(forward, backward and central) equations which will give the mostaccurate result.
Compute the true percent relative error for each case.
b) Evaluate the integral from a=0.1 to b=0.95 using acombination of the trapezoidal and
Simpson’s rules; employ Simpson’s rule wherever possible to obtainthe highest
accuracy. Compute the true percent relative error.
