(a) Consider the table below for an arbitrary function y = = f(x). I |1|2| 3| 4 | 5 6| 7| 8 f(r) | 9 37 243 1017 3109 7749 | 16767 32713 5897 i. Draw a forward difference table for above table. Use your table to give the numerical values for: ii. Af2 iii. A²fa

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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(a) Consider the table below for an arbitrary function y = f(x).
1| 2 3 4| 5 6 7| 8
f(x) 9 37 243 1017 3109 7749 | 16767 32713 58977
i. Draw a forward difference table for above table.
Use your table to give the numerical values for:
ii. Af2
iii. A²fa
iv. Aºfi
v. What is the degree of the polynomial from which these values were obtained
from?
(b) Find the specified higher order forward differences specified with the given en-
tries:
i. A°yo given that yo = 20, yı = 50, y2 = 90, y3 = 100, y4 = 150, y5
250.
200, y6
ii. A'yo given that yo = 79, yı
218, y6 = 250, y7 = 300.
iii. A*y given that yo =
120, y2
150, уз
190, Ул
201, y5
160, y1
400, y6 = 410, y7 = 460, ys = 500.
200, y2
240, y3 = 300, Y4 = 350, y5
Transcribed Image Text:(a) Consider the table below for an arbitrary function y = f(x). 1| 2 3 4| 5 6 7| 8 f(x) 9 37 243 1017 3109 7749 | 16767 32713 58977 i. Draw a forward difference table for above table. Use your table to give the numerical values for: ii. Af2 iii. A²fa iv. Aºfi v. What is the degree of the polynomial from which these values were obtained from? (b) Find the specified higher order forward differences specified with the given en- tries: i. A°yo given that yo = 20, yı = 50, y2 = 90, y3 = 100, y4 = 150, y5 250. 200, y6 ii. A'yo given that yo = 79, yı 218, y6 = 250, y7 = 300. iii. A*y given that yo = 120, y2 150, уз 190, Ул 201, y5 160, y1 400, y6 = 410, y7 = 460, ys = 500. 200, y2 240, y3 = 300, Y4 = 350, y5
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