Beyond $pi^{e} le e^{prime$: Proof Without Words of $b^{a} le a^{b} (b ge a geq e)

摘要

Using elementary properties of calculus there are at least two [1, 2] visual proofs of π e B A for e ≤ A B . It seems to be an interesting problem to visually compare a b and b a where the argument does not depend on the shape of a graph more complicated than y = ln x. In this note, using elementary function and an elementary property of calculus we give a visual proof of.