1. Consider the function 1 f(x) = 2€ (-2,0] 2a+3 Divide the domain into 9 evenly spaced points and determine at each point (where possible): (a) The first derivative using forward differences (b) The first derivative using central differences (c) The second derivative using central differences (d) The third derivative using central differences (e) The analytical value of the derivatives; compare these with the approximations of (a)-(d).

1. Consider the function 1 f(x) = 2€ (-2,0] 2a+3 Divide the domain into 9 evenly spaced points and determine at each point (where possible): (a) The first derivative using forward differences (b) The first derivative using central differences (c) The second derivative using central differences (d) The third derivative using central differences (e) The analytical value of the derivatives; compare these with the approximations of (a)-(d).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Please solve Parts D and E ONLY!

1. Consider the function
f(x) =
a = (-2,0]
2a+3
Divide the domain into 9 evenly spaced points and determine at each point (where possible):
(a) The first derivative using forward differences
(b) The first derivative using central differences
(c) The second derivative using central differences
(d) The third derivative using central differences
(e) The analytical value of the derivatives: compare these with the approximations of (a)-(d).

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Step 1: Determine first derivative using forward and central differences, second derivative using central

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Step 2: Determine the first derivative using forward differences

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Step 3: Determine the first derivative using central differences

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Step 4: Determine the second derivative using the central differences

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Step 5: Determine the third derivative using central differences

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