Explanation The given equation is: P n ( x ) = f [ x 0 ] + f [ x 0 , x 1 ] ( x − x 0 ) + a 2 ( x − x 0 ) ( x − x 1 ) + ⋅ ⋅ ⋅ + a n ( x − x 0 ) ( x − x 1 ) ⋅ ⋅ ⋅ ( x − x n − 1 ) Now, substitute the value of x = x 2 in the above equation. P n ( x 2 ) = f [ x 0 ] + f [ x 0 , x 1 ] ( x 2 − x 0 ) + a 2 ( x 2 − x 0 ) ( x 2 − x 1 ) + ⋅ ⋅ ⋅ + a n ( x 2 − x 0 ) ( x 2 − x 1 ) ⋅ ⋅ ⋅ ( x 2 − x n − 1 ) P n ( x 2 ) = f [ x 0 ] + f [ x 0 , x 1 ] ( x 2 − x 0 ) + a 2 ( x 2 − x 0 ) ( x 2 − x 1 ) Now, calculate the value of a 2 from the above equation: a 2 = P n ( x 2 ) − f [ x 0 ] − f [ x 0 , x 1 ] ( x 2 − x 0 ) ( x 2 − x 0 ) ( x 2 − x 1 ) = f ( x 2 ) − f [ x 0 ] − f [ x 0 , x 1 ] ( x 2 − x 0 ) ( x 2 − x 0 ) ( x 2 − x 1 ) = f ( x 2 ) − f [ x 1 ] + f [ x 1 ] − f [ x 0 ] − f [ x 0 , x 1 ] ( x 2 − x 0 ) (

10th Edition

ISBN: 9781305253667

Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden

Publisher: Cengage Learning

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Chapter 3.3, Problem 21ES

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To show: That the equation a2=f[x0,x1,x2] by using Pn(x2).

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Chapter 3.3, Problem 20ES

Chapter 3.3, Problem 22ES

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Chapter 3 Solutions

Numerical Analysis

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That the equation a 2 = f [ x 0 , x 1 , x 2 ] by using P n ( x 2 ) .

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To show: That the equation a2=f[x0,x1,x2] by using Pn(x2).

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Chapter 3 Solutions