fi (x) %3D е*, f.(x) %3D хе-* — е-*; [0, 2] |
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
Show that the given functions are orthogonal on the indicated interval
![The image shows two functions and an interval specification:
1. \( f_1(x) = e^x \)
2. \( f_2(x) = xe^{-x} - e^{-x} \)
The functions are to be considered over the interval \([0, 2]\).
These functions are commonly used in calculus and mathematical analysis to demonstrate growth and decay, as well as transformations involving the exponential function \(e\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b020904-503e-46f0-a83a-8c74ba785f01%2F63e8e963-6d84-4a7d-bf6e-fe02c3708cb2%2F9mh2dik_processed.png&w=3840&q=75)
Transcribed Image Text:The image shows two functions and an interval specification:
1. \( f_1(x) = e^x \)
2. \( f_2(x) = xe^{-x} - e^{-x} \)
The functions are to be considered over the interval \([0, 2]\).
These functions are commonly used in calculus and mathematical analysis to demonstrate growth and decay, as well as transformations involving the exponential function \(e\).
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