List questions from cauchy-schwarz-inequality

Published on 16 Apr 2026 - 3:32

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How big does $r$ need to be, to ensure that $x^4+y^4 >r^2$ for all $x^2+y^2 =r^2$?

Published on 13 Apr 2026 - 16:21

61

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$\lVert tx +y\rVert\ge 0$, for all $t\in\mathbb R$, implies that $\,|\langle x,y\rangle|\le \lVert x\rVert \lVert y \rVert$

Published on 15 Apr 2026 - 4:59

47

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How to bound $(\frac{a}{x}+\frac{b}{y})(x+y)$ for large $x,y$ and positive $a,b$

Published on 12 Apr 2026 - 20:39

521

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prove $\frac{x}{(ay + bz)} + \frac{y}{(az + bx)} + \frac{z}{(ax + by)} ≥ \frac{3}{(a+b)}$

Published on 14 Apr 2026 - 4:37

54

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Need a hint on how to solve this inequality

Published on 16 Apr 2026 - 22:33

64

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Prove using squared number property

Published on 13 May 2026 - 2:49

103

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If $f$ is continuous and $3\geq f(x)\geq 1$ for all $x\in[0,1]$, show the integral inequality.

Published on 10 May 2026 - 18:45

82

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Inequality involving a kind of Harmonic mean

Published on 17 Apr 2026 - 14:12

90

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Finding maximum value of squared sum

Published on 11 Apr 2026 - 17:50

1.9k

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Kantorovich inequality and Cauchy-Schwarz inequality

Published on 14 Apr 2026 - 5:36

179

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What kind of "geometric" regularity $f'^2$ gives on $f$

Published on 14 Apr 2026 - 4:58

80

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Maximum length perimeter of a box whose diagonal is 10 unit long.

Published on 14 Apr 2026 - 21:14

121

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Remark 16 in Chapter 2 from Brezis - Functional Analysis, Sobolev Spaces, and Partial Differential Equations.

Published on 10 May 2026 - 15:22

128

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Proving $q:\mathbb{R}^n \to \mathbb{R} \text{ with } q(x):= x^TAx$ totally differentiable

Published on 14 May 2026 - 11:16

List Question

Prove Cauchy-Schwarz inequality

How big does $r$ need to be, to ensure that $x^4+y^4 >r^2$ for all $x^2+y^2 =r^2$?

$\lVert tx +y\rVert\ge 0$, for all $t\in\mathbb R$, implies that $\,|\langle x,y\rangle|\le \lVert x\rVert \lVert y \rVert$

How to bound $(\frac{a}{x}+\frac{b}{y})(x+y)$ for large $x,y$ and positive $a,b$

prove $\frac{x}{(ay + bz)} + \frac{y}{(az + bx)} + \frac{z}{(ax + by)} ≥ \frac{3}{(a+b)}$

Need a hint on how to solve this inequality

Prove using squared number property

If $f$ is continuous and $3\geq f(x)\geq 1$ for all $x\in[0,1]$, show the integral inequality.

Inequality involving a kind of Harmonic mean

Finding maximum value of squared sum

Kantorovich inequality and Cauchy-Schwarz inequality

What kind of "geometric" regularity $f'^2$ gives on $f$

Maximum length perimeter of a box whose diagonal is 10 unit long.

Remark 16 in Chapter 2 from Brezis - Functional Analysis, Sobolev Spaces, and Partial Differential Equations.

Proving $q:\mathbb{R}^n \to \mathbb{R} \text{ with } q(x):= x^TAx$ totally differentiable

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