EDB — 16F

Exercises

1. [16F]For each of the following functions, say if it is continuous, uniformly continuous, Hölder (and with which exponent), or Lipschitz.

   • \(f:(0,1)→ ℝ\), \(f(x)=\sin (1/x)\).

   • \(f:(0,1)→ ℝ\), \(f(x)=x^{1/x}\).

   • \(f:(1,∞)→ ℝ\), \(f(x)=\sin (x^ 2)/x\)

   • \(f:[-1,1]→ℝ\), \(f(x)=|x|^𝛽\) with \(𝛽{\gt}0\).

   • \(f:(0,∞)→ ℝ\), \(f(x)=\sin (x^𝛽)\) with \(𝛽{\gt}0\).

   Solution 1

   [16H]↺↻