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$a < b$ and $c<d$ imply $a+c < b+d$

score 162 · Answer 1 · 2026-03-25 18:54:47

162

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$a < b$ and $c<d$ imply $a+c < b+d$

Published on 25 Mar 2026 - 18:54

score 111 · Answer 2 · 2026-03-29 18:50:25

111

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Can I prove there is no real solution except $x=0, x=1$, without using the function $W(x)$?

Published on 29 Mar 2026 - 18:50

score 1.6k · Answer 3 · 2026-03-27 21:55:48

1.6k

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Proving $E[\max(X^2,Y^2)]\le 1+\sqrt{1-\rho^2}$

Published on 27 Mar 2026 - 21:55

score 133 · Answer 4 · 2018-12-08 07:48:59

133

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Spivak, A Twice Differentiable Function

Published on 08 Dec 2018 - 7:48

score 195 · Answer 5 · 2026-03-25 03:22:18

195

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Find the minimum value of $\sqrt {2x^2+2y^2} +\sqrt {y^2+x^2-4y+4} +\sqrt {x^2+y^2-4x-4y+8}$

Published on 25 Mar 2026 - 3:22

score 127 · Answer 6 · 2026-04-11 18:17:55

127

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Choosing suitable weights for AM-GM

Published on 11 Apr 2026 - 18:17

score 280 · Answer 7 · 2026-03-25 04:43:23

280

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Find the value of Δx for which the value of Δy/Δx is within 0.1 units of slope.

Published on 25 Mar 2026 - 4:43

score 1.1k · Answer 8 · 2026-04-12 21:07:00

1.1k

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Absolute value of a martingale

Published on 12 Apr 2026 - 21:07

score 120 · Answer 9 · 2026-04-10 19:51:52

120

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How to show that exactly one of the following inequality systems has a solution?

Published on 10 Apr 2026 - 19:51

score 50 · Answer 10 · 2018-12-09 04:55:31

50

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Show that there exists $T>0$ such that $\frac{e^{t}}{t^{1-\alpha}}-\int_{0}^{t}\frac{e^{\xi}}{\xi^{1-\alpha}}d\xi<0$ for all $t\geq T$

Published on 09 Dec 2018 - 4:55

score 401 · Answer 11 · 2026-04-03 12:35:55

401

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Bounds for the rank of the sum of two linear maps

Published on 03 Apr 2026 - 12:35

score 197 · Answer 12 · 2018-12-09 07:19:43

197

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Prove $\Delta \text{ABC}$ is a right triangle with $\left | \text{k} \right |\leqq 3$

Published on 09 Dec 2018 - 7:19

score 90 · Answer 13 · 2026-04-11 16:27:55

90

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geometry inequality

Published on 11 Apr 2026 - 16:27

score 124 · Answer 14 · 2026-03-25 07:45:53

Prove that $\frac{3a^3+7b^3}{2a+3b}+\frac{3b^3+7c^3}{2b+3c}+\frac{3c^3+7a^3}{2c+3a}\ge 3\left(a^2+b^2+c^2\right)-\left(ab+bc+ca\right)$

score 117 · Answer 15 · 2018-12-09 19:48:09

117

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Show that $|y-y_0|<\text{min}(\frac{|y_0|}{2},\frac{\epsilon|y_0|^2}{2}) \implies \left\vert \frac{1}{y}-\frac{1}{y_0} \right\vert < \epsilon. $

Published on 09 Dec 2018 - 19:48

List Question

$a < b$ and $c<d$ imply $a+c < b+d$

Can I prove there is no real solution except $x=0, x=1$, without using the function $W(x)$?

Proving $E[\max(X^2,Y^2)]\le 1+\sqrt{1-\rho^2}$

Spivak, A Twice Differentiable Function

Find the minimum value of $\sqrt {2x^2+2y^2} +\sqrt {y^2+x^2-4y+4} +\sqrt {x^2+y^2-4x-4y+8}$

Choosing suitable weights for AM-GM

Find the value of Δx for which the value of Δy/Δx is within 0.1 units of slope.

Absolute value of a martingale

How to show that exactly one of the following inequality systems has a solution?

Show that there exists $T>0$ such that $\frac{e^{t}}{t^{1-\alpha}}-\int_{0}^{t}\frac{e^{\xi}}{\xi^{1-\alpha}}d\xi<0$ for all $t\geq T$

Bounds for the rank of the sum of two linear maps

Prove $\Delta \text{ABC}$ is a right triangle with $\left | \text{k} \right |\leqq 3$

geometry inequality

Prove that $\frac{3a^3+7b^3}{2a+3b}+\frac{3b^3+7c^3}{2b+3c}+\frac{3c^3+7a^3}{2c+3a}\ge 3\left(a^2+b^2+c^2\right)-\left(ab+bc+ca\right)$

Show that $|y-y_0|<\text{min}(\frac{|y_0|}{2},\frac{\epsilon|y_0|^2}{2}) \implies \left\vert \frac{1}{y}-\frac{1}{y_0} \right\vert < \epsilon. $

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