Solved: Estimate the error by halving.In Prob. 7

Chapter 19, Problem 19.1.98

(choose chapter or problem)

The derivative f ‘(x)$ can also be approximated in terms of first-order and higher-order differences (see Sec. 19.3):

\(f^{\prime}\left(x_{0}\right) \approx \frac{1}{h}\left(\Delta f_{0}\right. -\frac{1}{2} \Delta^{2} f_{0}\)

\(\left.+\frac{1}{3} \Delta^{3} f_{0}-\frac{1}{4} \Delta^{4} f_{0}+-\cdots\right)\)

Compute f ‘(0.4) in Prob. 27 from this formula, using differences up to and including first order, second order, third order, and fourth order.

Text Transcription:

f ‘ (x_{0}) approx 1 / h (Delta f_0   - 1 / 2 Delta^2 f_0

+ 1 / 3 Delta^3 f_0 - 1 / 4 Delta^4 f_0 + -cdots)

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