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Use Taylor series expansions to verify that that if a bounded " exists, then the following expression is correct for some -3f(#) + 1f(w +h) – f(w + 2/h) f'(=) – 2h

Use Taylor series expansions to verify that that if a bounded " exists, then the following expression is correct for some -3f(#) + 1f(w +h) – f(w + 2/h) f'(=) – 2h

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use Taylor series expansions (Hint: Start with the Taylor expansions for f(x+h)f(x+h) and f(x+2h)f(x+2h), and combine them, together with f(x)f(x), according to the right-hand side in the exercise.) Exercise 1: Use Taylor series expansions to verify that that if a bounded f" exists, then the following expression is correct for some f'(a) – -3f(#) +4f(x +h) – f(x + 2h) 3 2h
Transcribed Image Text:Use Taylor series expansions (Hint: Start with the Taylor expansions for f(x+h)f(x+h) and f(x+2h)f(x+2h), and combine them, together with f(x)f(x), according to the right-hand side in the exercise.) Exercise 1: Use Taylor series expansions to verify that that if a bounded f" exists, then the following expression is correct for some f'(a) – -3f(#) +4f(x +h) – f(x + 2h) 3 2h
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