Question: 7. Let A C R be a compact set. Let a be a limit point of A. Let f be a real-valued function that is

7. Let A C R" be a compact set. Let a be a limit point of A. Let f be a real-valued function that is continuous on the set A \\ {a}. Prove that if lim f (x) = -co, then f attains a maximum on A \\ {a}. x-a Hint: Use the extreme value theorem for compact sets

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