ed. Proof omitted.) iformly continuous to

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Assume the following statement:
If a function f: (a,b) → R is uniformly continuous, then both f(a+) and f(b-)
are finite.
(This is true. Take as granted. Proof omitted.)
Can we change the term uniformly continuous to continuous in the assumption?
Justify prove if yes, give a counterexample if no.
Transcribed Image Text:Assume the following statement: If a function f: (a,b) → R is uniformly continuous, then both f(a+) and f(b-) are finite. (This is true. Take as granted. Proof omitted.) Can we change the term uniformly continuous to continuous in the assumption? Justify prove if yes, give a counterexample if no.
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