How to prove that the continuity of a function on every point of domain by analysis approach?
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I have my real analysis final tomorrow and there are multiple choice questions. I'm wondering about a fast way to tell if a function is uniformly continuous or not. I know and understand the definition of uniform continuity, and I understand its difference from continuity, but I'm realizing I don't really know how to tell if a function is uniformly continuous or not (on a given interval or on R).
One of my classmates suggested that a function is NOT uniformly continuous if its derivative diverges in the given interval. Is this true? Can I just think of the graph of the function and if its slope does not eventually settle to some point, is it not uniformly continuous?
One of my classmates suggested that a function is NOT uniformly continuous if its derivative diverges in the given interval. Is this true? Can I just think of the graph of the function and if its slope does not eventually settle to some point, is it not uniformly continuous?
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