Suppose the following data points are generated by a smooth function f(x): 1/3 1/2 2/3 0.7075 1/6 5/6 1 f(x) 0.8415 0.8339 0.8105 0.7692 0.6229 0.5144 Find the best approximation of S, f(x) dx using the composite Simpson's rule. 0.7387 0.7147 0.6600 0.5109

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Exercise 4

8:59
A docs.google.com
Exercise 3 *
Using the centered three-point formula for the first derivative and the function f
defined in exercise 1, then the approximation of f'(0) with h= 0.05 is:
(а) —2.010040
(b) 3.102171
(c) -2.010038
(d) 1.139627
a
C
O d
Exercise 4
Suppose the following data points are generated by a smooth function f(x):
1/6
1/3
1/2
2/3
5/6
1
f(x) | 0.8415
Find the best approximation of f, f(x) dx using the composite Simpson's rule.
0.8339
0.8105
0.7692
0.7075
0.6229
0.5144
0.7387
0.7147
0.6600
O 0.5109
Exercise 5
dx
Consider the integral I =
The approximation of I by using the
composite Trapezoidal
Transcribed Image Text:8:59 A docs.google.com Exercise 3 * Using the centered three-point formula for the first derivative and the function f defined in exercise 1, then the approximation of f'(0) with h= 0.05 is: (а) —2.010040 (b) 3.102171 (c) -2.010038 (d) 1.139627 a C O d Exercise 4 Suppose the following data points are generated by a smooth function f(x): 1/6 1/3 1/2 2/3 5/6 1 f(x) | 0.8415 Find the best approximation of f, f(x) dx using the composite Simpson's rule. 0.8339 0.8105 0.7692 0.7075 0.6229 0.5144 0.7387 0.7147 0.6600 O 0.5109 Exercise 5 dx Consider the integral I = The approximation of I by using the composite Trapezoidal
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