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Example of continuous function which is not locally lipschitz

Continuous function - Conditions, Discontinuities, and Examples

SOLVED: No explanation is required for the following examples.(a) Give an example of a continuous f:[0,1) →ℝ that is not bounded above.(b) Give an example of a continuous f:[0,1) →ℝ that is bounded but does not achieve its minimum.(c) Give an example of f:[0,1] →ℝ that does not achieve either its supremum or its infimum.Give a rough sketch of each example.

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CONTINUITY definition and meaning | Collins English Dictionary

Continuity in a Function