Question Number 178576 by Spillover last updated on 18/Oct/22
$$\mathrm{If}\:\mathrm{a}>\mathrm{b}>\mathrm{0}\:\:\:\mathrm{prove}\:\mathrm{that} \\ $$ $$\mathrm{b}<\frac{\mathrm{ae}^{\mathrm{x}} +\mathrm{be}^{−\mathrm{x}} }{\mathrm{e}^{\mathrm{x}} +\mathrm{e}^{−\mathrm{x}} }<\mathrm{a} \\ $$