IMC 2003 · Problem 2

Day 210th IMC · Cluj-Napoca, Romania

Statement

Evaluate the limit

limx0+x2xsinmttndt(m,nN).\lim_{x \to 0+} \int_x^{2x} \frac{\sin^m t}{t^n}\,dt \quad (m, n \in \mathbb{N}).

Official solution

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