(A) Explanation Given: The given table is, x –6 –2 0 2 6 f ( x ) 19 3 10 3 19 Formula used: The Newton’s formula for the interpolating is p ( x ) = a 0 + a 1 ( x − x 0 ) + a 2 ( x − x 0 ) ( x − x 1 ) + ⋯ + a n ( x − x 0 ) ( x − x 1 ) ⋯ ( x − x n − 1 ) (1). Calculation: The ratio of the change in y to the change in x for each successive pair of points is the first divided difference. The ratio of the change in first divided differences in the numerator and the change in two successive values of x in the denominator is the second divided difference. The Third divided difference can be obtained in a similar manner. The divided difference table is as follows. x k y k First Divided Difference Second Divided Difference Third Divided Difference Fourth Divided Difference –6 –2 0 2 6 19 3 10 3 19 3 − 19 − 2 + 6 = − 4 10 − 3 0 + 2 = 7 2 3 − 10 2 − 0 = − 7 2 19 − 3 6 − 2 = 4 7 2 + 4 0 + 6 = 5 4 − 7 2 + 7 2 2 + 2 = − 7 4 4 + 7 2 6 − 0 = 5 4 − 7 4 − 5 4 2 + 6 = − 3 8 5 4 + 7 4 6 + 2 = 3 8 3 8 + 3 8 6 + 6 = 1 16 Table 1 The first number from each column of the divided difference table is the coefficients of the interpolating polynomial. From Table 1, a 0 = 19 , a 1 = − 4 , a 2 = 5 4 , a 3 = − 3 8 and a 4 = 1 16 and from the given table x 0 = − 6 , x 1 = − 2 , x 2 = 0 , x 3 = 2 and x 4 = 6 (B) To determine To approximate: The value of f ( 5 ) using the interpolating polynomial.

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134668574

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

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Chapter B.4, Problem 18E

(A)

To determine

To approximate: The value of f(1) using the interpolating polynomial.

(B)

To determine

To approximate: The value of f(5) using the interpolating polynomial.

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Chapter B.4, Problem 17E

Chapter B.4, Problem 19E

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Chapter B.4 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. B.4 - Consider the points in Table 1. (A)Let...Ch. B.4 - Given the following polynomial and table,...Ch. B.4 - Prob. 1MP Ch. B.4 - Prob. 2MP Ch. B.4 - Prob. 3MP Ch. B.4 - Prob. 4MP Ch. B.4 - Prob. 1E Ch. B.4 - Prob. 2E Ch. B.4 - Prob. 3E Ch. B.4 - Prob. 4E

Ch. B.4 - Prob. 5E Ch. B.4 - Prob. 6E Ch. B.4 - Prob. 7E Ch. B.4 - Prob. 8E Ch. B.4 - Prob. 9E Ch. B.4 - Prob. 10E Ch. B.4 - Prob. 11E Ch. B.4 - Prob. 12E Ch. B.4 - Prob. 13E Ch. B.4 - In Problems 1320, use the interpolating polynomial...Ch. B.4 - Prob. 15E Ch. B.4 - Prob. 16E Ch. B.4 - Prob. 17E Ch. B.4 - Prob. 18E Ch. B.4 - Prob. 19E Ch. B.4 - Prob. 20E Ch. B.4 - Prob. 21E Ch. B.4 - Prob. 22E Ch. B.4 - In Problems 2130, find the interpolating...Ch. B.4 - Prob. 24E Ch. B.4 - Prob. 25E Ch. B.4 - Prob. 26E Ch. B.4 - Prob. 27E Ch. B.4 - Prob. 28E Ch. B.4 - Prob. 29E Ch. B.4 - Prob. 30E Ch. B.4 - Prob. 31E Ch. B.4 - Prob. 32E Ch. B.4 - Prob. 33E Ch. B.4 - Prob. 34E Ch. B.4 - The following table was obtained from the function...Ch. B.4 - Prob. 36E Ch. B.4 - Prob. 37E Ch. B.4 - The following table was obtained from the function...Ch. B.4 - Prob. 39E Ch. B.4 - Prob. 40E Ch. B.4 - Prob. 41E Ch. B.4 - Prob. 42E Ch. B.4 - Prob. 43E Ch. B.4 - Prob. 44E Ch. B.4 - Maximum revenue. The revenue R (in thousands of...Ch. B.4 - Minimum overage cost. The cost C (in thousands of...Ch. B.4 - Prob. 47E Ch. B.4 - Prob. 48E Ch. B.4 - Prob. 49E Ch. B.4 - Prob. 50E Ch. B.4 - Voter registration. The number N of registered...Ch. B.4 - Voter registration. The number N of registered...

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To approximate: The value of f ( 1 ) using the interpolating polynomial.

Solution Summary: The author approximates the value of f(1) using the interpolating polynomial.