Ivan Shishkin, Rye (1878)

Problems/Real analysisUnreviewed

Intégrabilité et limite

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
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Soit f:R+→Rf : \mathbb{R}_+ \to \mathbb{R} de classe C1\mathcal{C}^1 telle que ∫0+∞f\int_0^{+\infty} f converge.

  1. Donner un exemple où f ne tend pas verd 0 en +∞+\infty
  2. En supposant x↦∫xx+1f′(t)2 dtx \mapsto \int_x^{x+1} f'(t)^2 \, dt bornée, montrer que ff tend vers 00 en +∞+\infty.
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