List questions from inequality

Published on 07 May 2026 - 7:36

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Prove or disprove the following inequality

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Proving that: $||x|^{s/2}-|y|^{s/2}|\le 2|x-y|^{s/2}$

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Show that $x\longmapsto \int_{\mathbb R^n}\frac{f(y)}{|x-y|^{n-\alpha }}dy$ is integrable.

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Solution to a hard inequality

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Is every finite descending sequence in [0,1] in convex hull of certain points?

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Bound for difference between arithmetic and geometric mean

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multiplying the integrands in an inequality of integrals with same limits

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207

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How to prove that $\pi^{e^{\pi^e}}<e^{\pi^{e^{\pi}}}$

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Proving a small inequality

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Continuity of composite functions.

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How to prove the following inequality (log)

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Prove that $ \frac{1}{1+n^2} < \ln(1+ \frac{1}{n} ) < \frac {1}{\sqrt{n} }$

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An inequality involving $\int_0^{\frac{\pi}{2}}\sqrt{\sin x}\:dx $

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Spivak Calculus 3rd Edition Chapter 1 Problem 4 (vi)

Published on 10 May 2026 - 10:37

List Question

Confirmation of Proof: $\forall n \in \mathbb{N}, \ \pi (n) \geqslant \frac{\log n}{2\log 2}$

Prove or disprove the following inequality

Proving that: $||x|^{s/2}-|y|^{s/2}|\le 2|x-y|^{s/2}$

Show that $x\longmapsto \int_{\mathbb R^n}\frac{f(y)}{|x-y|^{n-\alpha }}dy$ is integrable.

Solution to a hard inequality

Is every finite descending sequence in [0,1] in convex hull of certain points?

Bound for difference between arithmetic and geometric mean

multiplying the integrands in an inequality of integrals with same limits

How to prove that $\pi^{e^{\pi^e}}<e^{\pi^{e^{\pi}}}$

Proving a small inequality

Continuity of composite functions.

How to prove the following inequality (log)

Prove that $ \frac{1}{1+n^2} < \ln(1+ \frac{1}{n} ) < \frac {1}{\sqrt{n} }$

An inequality involving $\int_0^{\frac{\pi}{2}}\sqrt{\sin x}\:dx $

Spivak Calculus 3rd Edition Chapter 1 Problem 4 (vi)

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