EDB — 15Z

Exercises

1. [15Z]Prerequisites:[15W]↺↻. Let \(f:ℝ→ℝ\) be uniformly continuous; show that

   \[ \limsup _{x→±∞} |f(x)|/x{\lt}∞ \]

   or, equivalently, that there exists a constant \(C\) such that \(|f(x)|≤ C (1+|x|)\) for every \(x\).

   Solution 1

   [160]↺↻