EDB — 1BZ

Exercises

1. [1BZ]Difficulty:*.Suppose that \(f:ℝ→ℝ\) is continuous and bounded, show that

   \[ \lim _{y→ 0+} \frac y𝜋 ∫_{-∞}^∞ \frac{f(x)}{x^ 2+y^ 2}\, {\mathbb {d}}x = f(0) \]

   (Hint. start with the case when \(f\) is constant.)