Find an example of a sequence of continuous functions {fn} defined on the interval [0, 1] such that 0 < fn(x) < 1, | fn(x) dx converges to 0 as n o, and that { fn(x)} does not converge at any point x in [0, 1].
Find an example of a sequence of continuous functions {fn} defined on the interval [0, 1] such that 0 < fn(x) < 1, | fn(x) dx converges to 0 as n o, and that { fn(x)} does not converge at any point x in [0, 1].
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 20EQ
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![Find an example of a sequence of continuous functions {fn} defined on the
interval [0, 1] such that 0 < f(x) < 1,
| fa(x) dx
converges to 0 as n → ∞, and that { fn(x)} does not converge at any point x
in [0, 1].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe03f381f-6d19-454e-9ddd-1b07a7b32431%2Fbc8ee9d9-8c70-4900-ad97-f2b64985135e%2Fip77l6d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find an example of a sequence of continuous functions {fn} defined on the
interval [0, 1] such that 0 < f(x) < 1,
| fa(x) dx
converges to 0 as n → ∞, and that { fn(x)} does not converge at any point x
in [0, 1].
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