Give an example of a function that is uniformly continuous on R but is not bounded on R.

Question

Give an example of a function that is uniformly continuous on R but is not bounded on R.
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Solution 1

Sure, an example of such a function is the identity function f(x) = x.

Step 1: Define the function Let's define the function f: R -> R by f(x) = x.

Step 2: Show that f is uniformly continuous on R A function f is uniformly continuous on a set if for every ε > 0, there exists a δ > 0 such that fo Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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