Please, carefully show that
$$ e^{\pi} > \pi^e $$
You are not allowed to use a calculator!
thanks
2026-04-02 17:27:18.1775150838
question about an inequality in calculus
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Consider the function $f(x)=x/\ln(x)$. For $x \geq e$, this is an increasing function on the domain by taking its derivative. Since $\pi > e$, $f(\pi) > f(e) $and this gives the inequality.