# Tagged Questions

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### Rational and trascendental numbers: $\pi$, $e$ and $\pi+e$ [duplicate]

The numbers $\pi,e$ are trascendentals, but if consider: $\pi+e$ then is rational, trascendental? Thanks
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### question about an inequality in calculus [duplicate]

Please, carefully show that $$e^{\pi} > \pi^e$$ You are not allowed to use a calculator! thanks
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### Relation between e and pi [closed]

I found the following relation $\pi=3+\frac{1}{5+\frac{1}{7+\frac{1}{9+\dotsb}}}$ known and $e=3-\frac{1}{5-\frac{1}{7-\frac{1}{9-\dotsb}}}$ Can we relate these directly?
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### Occurrence of $e$ in intersecting circles.

Consider two identical circles that share a radius such that they intersect. The radii of the circles are $\pi\over 2$. If this new shape sits such that its major axis is horizontal and the shortest ...
Integrals is definitely not my strong point, and I'm having trouble proving that: $${\int_{-\infty}^\infty (e^{\large{\pi}n})^{-\large{x}^2} dx = {1\over\sqrt{n}}}$$ It has similarities to the ...