Ivan Shishkin, Rye (1878)

Problems/Real analysisUnreviewed

Integration and limit

by Anduril·
50
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
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  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Let f:R+→Rf : \mathbb{R}_+ \to \mathbb{R} be of class C1\mathcal{C}^1 such that ∫0+∞f\int_0^{+\infty} f converges.

  1. Give an exemple where f does not tend to 0 at +∞+\infty
  2. Assuming that x↦∫xx+1f′(t)2 dtx \mapsto \int_x^{x+1} f'(t)^2 \, dt is bounded, show that ff tends to 00 at +∞+\infty.
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