1. Approximate the first derivative of f(x) = 5e²³x at x = 1.25 using a step size of Ax = 0.2 using the following methods: a. Forward Divided Difference (FDD) b. Backward Divided Difference (BDD) c. Central Divided Difference (CDD) d. Use analytic method to find f'(1.25) and compare the errors. Which method had the best approximation? Approximation Method | First Derivative Value | Error(%) FDD BDD CDD
1. Approximate the first derivative of f(x) = 5e²³x at x = 1.25 using a step size of Ax = 0.2 using the following methods: a. Forward Divided Difference (FDD) b. Backward Divided Difference (BDD) c. Central Divided Difference (CDD) d. Use analytic method to find f'(1.25) and compare the errors. Which method had the best approximation? Approximation Method | First Derivative Value | Error(%) FDD BDD CDD
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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please answer number 1 step by step. thank you!
Transcribed Image Text:2.3x
=
1. Approximate the first derivative of f(x) = 5e2³x at x = 1.25 using a step size of Ax
the following methods:
a. Forward Divided Difference (FDD)
b. Backward Divided Difference (BDD)
C. Central Divided Difference (CDD)
d. Use analytic method to find f'(1.25) and compare the errors. Which method had the best
approximation?
Approximation Method | First Derivative Value | Error(%)
FDD
BDD
CDD
2. Use the same conditions in #1 to find f"(1.25).
Approximation Method Second Derivative Value Error(%)
FDD
BDD
0.2 using
CDD
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