EDB — 15Z

Exercises

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

   $$\underset{x\to \pm \infty }{lim sup}|f(x)|/x<\infty$$

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

   Solution 1

   [160]↺↻