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6. A function f : R → R is said to be bounded if |f(x)| M, for some M > 0. Give an example of function f: R → R that is bounded and an example of such function that is unbounded. Also, give an example of function where sup{f(x) : x € R} €R but max{f(x) : x E R} does not exist.

6. A function f : R → R is said to be bounded if |f(x)| M, for some M > 0. Give an example of function f: R → R that is bounded and an example of such function that is unbounded. Also, give an example of function where sup{f(x) : x € R} €R but max{f(x) : x E R} does not exist.

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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6. A function f : R → R is said to be bounded if |f(x)| M, for some M > 0. Give an example of function f: R → R that is bounded and an example of such function that is unbounded. Also, give an example of function where sup{f(x) : x E R} € R but max{f(x) : x € R} does not exist.
Transcribed Image Text:6. A function f : R → R is said to be bounded if |f(x)| M, for some M > 0. Give an example of function f: R → R that is bounded and an example of such function that is unbounded. Also, give an example of function where sup{f(x) : x E R} € R but max{f(x) : x € R} does not exist.
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