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2. Give examples of functions, which satisfy the following conditions, and justify your choice. If no such functions exists, explain why. a. A function f(x) such that f(x) dx converges, but f f(x) dx diverges. b. A function f(x) such that both ſ f(x) dx and f f(x) dx diverge.

2. Give examples of functions, which satisfy the following conditions, and justify your choice. If no such functions exists, explain why. a. A function f(x) such that f(x) dx converges, but f f(x) dx diverges. b. A function f(x) such that both ſ f(x) dx and f f(x) dx diverge.

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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Give examples of functions, which satisfy the following conditions, and justify your choice. If no such
functions exists, explain why.

2. Give examples of functions, which satisfy the following conditions, and justify your choice. If no such functions exists, explain why. a. A function f(x) such that f f(x) dx converges, but f f(x) dx diverges. b. A function f(x) such that both f(x) dx and f f(x) dx diverge. c. A function f(x), such that 0 ≤ f(x) ≤ 10 for every x = [0, ∞) and f₁ f(x) dx diverges. d. A function f(x), such that 0 ≤ f(x) ≤ 10 for every x = [0, ∞) and f f(x) dx converges.
Transcribed Image Text:2. Give examples of functions, which satisfy the following conditions, and justify your choice. If no such functions exists, explain why. a. A function f(x) such that f f(x) dx converges, but f f(x) dx diverges. b. A function f(x) such that both f(x) dx and f f(x) dx diverge. c. A function f(x), such that 0 ≤ f(x) ≤ 10 for every x = [0, ∞) and f₁ f(x) dx diverges. d. A function f(x), such that 0 ≤ f(x) ≤ 10 for every x = [0, ∞) and f f(x) dx converges.
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