] [Backwards difference approximation of first derivative] Using Taylor's theorem, in lecture we derived the forward difference ap- oximation to the first derivative. In a similar fashion, derive the backwards fference approximation f(xo)-f(xo-h) 1 = f'(x) = ²h f"(E)
] [Backwards difference approximation of first derivative] Using Taylor's theorem, in lecture we derived the forward difference ap- oximation to the first derivative. In a similar fashion, derive the backwards fference approximation f(xo)-f(xo-h) 1 = f'(x) = ²h f"(E)
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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Question
Taylor's theorem
![[3] [Backwards difference approximation of first derivative]
Using Taylor's theorem, in lecture we derived the forward difference ap-
proximation to the first derivative. In a similar fashion, derive the backwards
difference approximation
f(xo) – f(xo - h)
h
assuming that f € C²([a, b]).
= f'(xo) — 1/ h ƒ" (E)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fd47556-f3ce-4f39-818d-be563d9523c8%2F14a9cec5-cfe4-41d3-9755-f52cb517a3a1%2Fx8irrsw_processed.png&w=3840&q=75)
Transcribed Image Text:[3] [Backwards difference approximation of first derivative]
Using Taylor's theorem, in lecture we derived the forward difference ap-
proximation to the first derivative. In a similar fashion, derive the backwards
difference approximation
f(xo) – f(xo - h)
h
assuming that f € C²([a, b]).
= f'(xo) — 1/ h ƒ" (E)
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