Is $3x^2+7$ uniformly continuous on $[0,1]$?
My argument: Yes, Since $3x^2+7$ is continuous on $[0,1]$ and $[0,1]$ is compact, any continuous function on compact set is uniformly continuous. Am I right?
2026-03-29 20:49:41.1774817381
Is $3x^2+7$ uniformly continuous on $[0,1]$?
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Yes. This is indeed a direct consequence of the Heine Cantor theorem.