EDB — 19Y

[19Y]Say which of these functions \(f:[0,1]→ℝ\) are Riemann integrable:

1. the characteristic function of the Cantor set.

2. \(f(0)=0\), \(f(x)=\sin (1/x)\)

3. \(f(0)=0\) and

   \[ f(x)=\frac{1-\cos (x)}{x^ 2+|\sin (1/x)|} \]

4. \(f(x)=0\) if \(x\) is irrational, \(f(x)=\cos (1/m)\) if \(x=n/m\) with \(n,m\) coprime. [ [19Z]↺↻]

5. \(f(x)=0\) if \(x\) is irrational, \(f(x)=\sin (1/m)\) if \(x=n/m\) with \(n,m\) coprime.