Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Exercise 6. Prove that if f [a, b] R is continuous, then f([a, b]) is a closed and bounded
interval.
Exercise 7. Prove (using the definition) that f(x)=√x² +1 is uniformly continuous on [0, 1].
Exercise 8. Prove that if f: ER is uniformly continuous on E, then it is uniformly continuous
on all nonempty sets A CE.
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Transcribed Image Text:Exercise 6. Prove that if f [a, b] R is continuous, then f([a, b]) is a closed and bounded interval. Exercise 7. Prove (using the definition) that f(x)=√x² +1 is uniformly continuous on [0, 1]. Exercise 8. Prove that if f: ER is uniformly continuous on E, then it is uniformly continuous on all nonempty sets A CE.
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