1. If fn converges point-wise to f on a closed and bounded set then the convergence is uniform. True False 2. If fn converges uniformly to f on I and gn converges uniformly to g on I then fn+gn converges uniformly to f +g on I. True False 3. If fn converges uniformly to f and each fn is increasing then f is increasing. True False
1. If fn converges point-wise to f on a closed and bounded set then the convergence is uniform. True False 2. If fn converges uniformly to f on I and gn converges uniformly to g on I then fn+gn converges uniformly to f +g on I. True False 3. If fn converges uniformly to f and each fn is increasing then f is increasing. True False
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
100%
Do 1, 2, 3,
Determine if each statement is True or False. Justify all answers best as possible. Explain.
Transcribed Image Text:1. If fn converges point-wise to f on a closed and bounded set then the convergence
is uniform.
True
False
2. If fn converges uniformly to f on I and gn converges uniformly to g on I then fn+ gn
converges uniformly to f +g on I.
True
False
3. If fn converges uniformly to f and each fn is increasing then f is increasing.
True
False
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