The following inequality
$$(*) \quad \frac{x}{\sinh(x)} \leq e^{-x}, \quad \forall x>0$$ or $$(**) \quad \frac{x}{\sinh(x)} \leq e^{x}, \quad \forall x>0$$ are true ?
thank you in advance
2026-03-27 08:39:39.1774600779
The inequality is true?
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Seeing as you provide no context, I'll simply answer the question: no, it's not. Try substituting $x=1$ and the inequality won't be satisfied.
https://www.wolframalpha.com/input/?i=1+%2F+(sinh(1))+-+e%5E(-1)