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e big O form of Taylor's theorem about r = a to show that if f and its first three derivatives are uous then f(a +h) – f(a) f(a +h) – f(a – h) - f'(a) + O(h?) f'(a) + O(h) but %3D %3D h 2h 0. (These formulas are useful for the numerical calculation of derivatives.)

e big O form of Taylor's theorem about r = a to show that if f and its first three derivatives are uous then f(a +h) – f(a) f(a +h) – f(a – h) - f'(a) + O(h?) f'(a) + O(h) but %3D %3D h 2h 0. (These formulas are useful for the numerical calculation of derivatives.)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Use the big O form of Taylor's theorem about x = a to show that if f and its first three derivatives are continuous then f(a + h) – f(a) f(a + h) – f(a – h) = f'(a) + O(h²) f'(a) + O(h) but 2h as h → 0. (These formulas are useful for the numerical calculation of derivatives.)
Transcribed Image Text:Use the big O form of Taylor's theorem about x = a to show that if f and its first three derivatives are continuous then f(a + h) – f(a) f(a + h) – f(a – h) = f'(a) + O(h²) f'(a) + O(h) but 2h as h → 0. (These formulas are useful for the numerical calculation of derivatives.)
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