Give an example of a continuous function that is not uniformly continuous. Be specific about the...

Give an example of a continuous function that is not uniformly continuous. Be specific about the domain of the function.

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Colby Messinger answered 1 year ago

1) There is a continuous function from [1, 4] to R that is not uniformly continuous....

1) There is a continuous function from [1, 4] to R that is not uniformly continuous. True or False and justify your answer. 2) Suppose f : D : →R be a function that satisfies the following condition: There exists a real number C ≥ 0 such that |f(u) − f(v)| ≤ C|u − v| for all u, v ∈ D. Prove that f is uniformly continuous on D Definition of uniformly continuous: A function f: D→R is called uniformly...

Prove that any continuous function on a standard n-dimensional cube In can be uniformly approximated by...

Prove that any continuous function on a standard n-dimensional cube In can be uniformly approximated by polynomials in n variables x1, . . . , xn.

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Give an example of a continuous function that is not uniformly continuous. Be specific about the...

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