Question: Consider ????(????) = ???? 4 for ????0 = 0, ????1 = 0.2, ????2 = 0.4, ????3 = 0.6, ????4 = 0.8 Calculate ???? (????2)

Consider ????(????) = ???? 4 for ????0 = 0, ????1 = 0.2, ????2 = 0.4, ????3 = 0.6, ????4 = 0.8

Calculate ???? ′ (????2) from the following three-point formula

(a) ????0 ′ ≈

1

2ℎ

(−3????0 + 4????1 − ????2),

(b) ????1 ′ ≈

1

2ℎ

(−????0 + ????2 ),

(c) ????2 ′ ≈

1

2ℎ

(????0 − 4????1 + 3????2),

(d) ????2 ′ ≈

1

12ℎ

(????0 − 8????1 + 8????3 − ????4)

Determine the error Compare and

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