Geometric and Calculus Proofs of Some Inequalities

HOSSAIN, SARMAD (2023) Geometric and Calculus Proofs of Some Inequalities. At Right Angles. pp. 99-102. ISSN 2582-1873

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Abstract

There are many visual and calculus-based proofs of πe < eπ and ba < ab(for e ≤ a < b). The aim of this paper is to give geometric and calculus-based proofs of these inequalities. We show in addition that ba > ab for 0 < a < b ≤ e and ab ≤ 1 < ba for 0 < a ≤ 1 < b. To show πe < eπ , Nelson ([2]) uses the fact that the curve y = ex/e lies above the line y = x, while Nakhli ([1]) uses the fact that the curve y = ln x x attains the global maximum at the point e.

Item Type:	Articles in APF Magazines
Authors:	HOSSAIN, SARMAD
Document Language:	Language English
Uncontrolled Keywords:	Mathematics, Geometry, Calculus
Subjects:	Natural Sciences > Mathematics
Divisions:	Azim Premji University - Bengaluru > University Publications > At Right Angles
Full Text Status:	Public
URI:	http://publications.azimpremjiuniversity.edu.in/id/eprint/5218
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