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Consider the function: 1. Using the laws of Calculus, provide the expression for f'(x)- which will be our basis for analytical (theoretical comparison) 2. With x=3.98, x=3.99, x=4.00, x=4.01 and x=4.02 find f'(4.00) using: a) 2-point Backward difference b) 2-point Forward Difference c) 2-point Central Difference d) 3-point Backward Difference e) 3-point Forward Difference f) 4-point Central Difference 3. Compute the relative error (%) for each method

Consider the function: 1. Using the laws of Calculus, provide the expression for f'(x)- which will be our basis for analytical (theoretical comparison) 2. With x=3.98, x=3.99, x=4.00, x=4.01 and x=4.02 find f'(4.00) using: a) 2-point Backward difference b) 2-point Forward Difference c) 2-point Central Difference d) 3-point Backward Difference e) 3-point Forward Difference f) 4-point Central Difference 3. Compute the relative error (%) for each method

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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Problem 1: Consider the function: f(x): et 1. Using the laws of Calculus, provide the expression for f'(x)- which will be our basis for analytical (theoretical comparison) 2. With x=3.98, x=3.99, x=4.00, x=4.01 and x=4.02 find f'(4.00) using: a) 2-point Backward difference b) 2-point Forward Difference c) 2-point Central Difference d) 3-point Backward Difference e) 3-point Forward Difference f) 4-point Central Difference 3. Compute the relative error (%) for each method Numerical Solution
Transcribed Image Text:Problem 1: Consider the function: f(x): et 1. Using the laws of Calculus, provide the expression for f'(x)- which will be our basis for analytical (theoretical comparison) 2. With x=3.98, x=3.99, x=4.00, x=4.01 and x=4.02 find f'(4.00) using: a) 2-point Backward difference b) 2-point Forward Difference c) 2-point Central Difference d) 3-point Backward Difference e) 3-point Forward Difference f) 4-point Central Difference 3. Compute the relative error (%) for each method Numerical Solution
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