Consider the function f(x) = eª sin(3x). 1. Compute the exact derivative f'(x) using analytical methods. 2. Use the Central Difference Formula to approximate f'(1) with a step size h = 0.01. The Central Difference Formula is given by: ƒ'(x) ≈ f(x + h) − ƒ(x – h) 2h Compare the results obtained in parts 1 and 2. What are the implications for the accuracy of numerical differentiation methods?
Consider the function f(x) = eª sin(3x). 1. Compute the exact derivative f'(x) using analytical methods. 2. Use the Central Difference Formula to approximate f'(1) with a step size h = 0.01. The Central Difference Formula is given by: ƒ'(x) ≈ f(x + h) − ƒ(x – h) 2h Compare the results obtained in parts 1 and 2. What are the implications for the accuracy of numerical differentiation methods?
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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Transcribed Image Text:Consider the function f(x) = eª sin(3x).
1. Compute the exact derivative f'(x) using analytical methods.
2. Use the Central Difference Formula to approximate f'(1) with a step size h = 0.01.
The Central Difference Formula is given by:
ƒ'(x) ≈
f(x + h) − ƒ(x – h)
2h
Compare the results obtained in parts 1 and 2. What are the implications for the accuracy of
numerical differentiation methods?
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