Ivan Shishkin, Rye (1878)

Problems/OtherUnreviewed

A two-sided bound

by Dattier·translated by visitor·
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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Let a,b>0a, b>0.

Is it true that:
b212(1+b)3(1+a)4⩽b+ln⁡ ⁣(ba+1b+ba+1)−b2b+ln⁡ ⁣(1+aa)⩽112ba4?\dfrac {b^{2}}{12(1+b)^{3}(1+a)^{4}}\leqslant b+\ln\!\left( \dfrac{ba+1}{b+ba+1}\right)-\dfrac{b^{2}}{b+\ln\!\left(\dfrac{1+a}a\right)} \leqslant \dfrac 1{12ba^{4}} ?

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