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Question Number 178576 by Spillover last updated on 18/Oct/22

If a>b>0   prove that  b<((ae^x +be^(−x) )/(e^x +e^(−x) ))<a

$$\mathrm{If}\:\mathrm{a}>\mathrm{b}>\mathrm{0}\:\:\:\mathrm{prove}\:\mathrm{that} \\ $$ $$\mathrm{b}<\frac{\mathrm{ae}^{\mathrm{x}} +\mathrm{be}^{−\mathrm{x}} }{\mathrm{e}^{\mathrm{x}} +\mathrm{e}^{−\mathrm{x}} }<\mathrm{a} \\ $$

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