Solved: Estimate the error by halving. In Prob. 5

Chapter 19, Problem 19.1.96

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Consider \(f(x)=x^{4}\) for \(x_{0}=0, x_{1}=0.2, x_{2}=0.4\), \(x_{3}=0.6, x_{4}=0.8\). Calculate \(f_{2}^{\prime}\) from (14a), (14b), (14c), (15). Determine the errors. Compare and comment.

Text Transcription:

f(x) = x^4

x_0 = 0, x_1 = 0.2, x_2 = 0.4

x_3 = 0.6, x_4 = 0.8

f_2’

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