Question

Finding $\min_{x,y\ge0} (x+y)$ such that $\sqrt{x}+\sqrt{y}\ge c$ for a given constant $c\ge0$

score 69 · Answer 1 · 2019-08-01 09:42:30

69

Views

Finding $\min_{x,y\ge0} (x+y)$ such that $\sqrt{x}+\sqrt{y}\ge c$ for a given constant $c\ge0$

Published on 01 Aug 2019 - 9:42

score 648 · Answer 2 · 2026-03-27 00:55:08

648

Views

How to maximize this expression?

Published on 27 Mar 2026 - 0:55

score 284 · Answer 3 · 2026-03-26 01:25:11

284

Views

Find the minimal value the hypotenuse of a right triangle whose radius of inscribed circle is $r$

Published on 26 Mar 2026 - 1:25

score 410 · Answer 4 · 2026-03-25 03:16:36

410

Views

Upper Bound for a Sum

Published on 25 Mar 2026 - 3:16

score 70 · Answer 5 · 2019-08-06 14:38:14

70

Views

Cauchy Schwarz: Proving this inequality

Published on 06 Aug 2019 - 14:38

score 354 · Answer 6 · 2019-08-09 20:55:31

354

Views

Prove inequality with logarithms:$\log_{a}{\frac{a+b}{2}} + \log_{b}{\frac{a+b}{2}} \ge 2$

Published on 09 Aug 2019 - 20:55

score 32 · Answer 7 · 2019-08-11 01:30:41

32

Views

Lagrangian Optimization Linear in Constants Comparison?

Published on 11 Aug 2019 - 1:30

score 119 · Answer 8 · 2026-03-25 03:19:43

119

Views

Range of function $f(x)=\sqrt{4-x^2}+\sqrt{x^2-1}$

Published on 25 Mar 2026 - 3:19

score 70 · Answer 9 · 2026-03-25 13:56:50

70

Views

proving $ \mu^T \Sigma \mu \cdot \textbf{1}^T \Sigma \textbf{1} \geq (\textbf{1}^T \Sigma \mu)^2 $

Published on 25 Mar 2026 - 13:56

score 80 · Answer 10 · 2026-03-26 06:15:17

80

Views

Problem II.3.13: How to prove $\sum_{k=0}^{m}|(x | u_{k})|^{2} \le \|x\|^{2}$ for an orthonormal system of an inner product space

Published on 26 Mar 2026 - 6:15

score 827 · Answer 11 · 2026-03-27 02:40:27

827

Views

maximum and minimum value of the function $ f(x,y) = x^{2} + y^{2} + xy + 3(x+y) $ at $ A = \left \{ (x,y): x^{2}+y^{2} \leq 1, x+y\geq 0 \right \} $

Published on 27 Mar 2026 - 2:40

score 337 · Answer 12 · 2026-03-20 17:19:07

337

Views

For positive $a$, $b$, $c$ with $abc=1$, show that $\sum_{cyc}\sqrt{a^2-a+1}\geq a+b+c$

Published on 20 Mar 2026 - 17:19

score 321 · Answer 13 · 2019-08-14 20:50:09

321

Views

For positive reals $a_i$ and $b_i$, if $\sum a_i \geq \sum a_i b_i$, then $\sum a_i \leq \sum\frac{a_i}{b_i}$

Published on 14 Aug 2019 - 20:50

score 132 · Answer 14 · 2019-08-20 08:30:48

132

Views

How to solve this? (Argument of the complex number in complex plane)

Published on 20 Aug 2019 - 8:30

score 216 · Answer 15 · 2026-03-25 23:42:48

216

Views

Under what conditions do we have $\int_{0}^{\infty} |f(x)|^2 dx \leq C \int_{0}^{\infty} x^2 |f^{\prime}(x)|^2 dx$?

Published on 25 Mar 2026 - 23:42

List Question

Finding $\min_{x,y\ge0} (x+y)$ such that $\sqrt{x}+\sqrt{y}\ge c$ for a given constant $c\ge0$

How to maximize this expression?

Find the minimal value the hypotenuse of a right triangle whose radius of inscribed circle is $r$

Upper Bound for a Sum

Cauchy Schwarz: Proving this inequality

Prove inequality with logarithms:$\log_{a}{\frac{a+b}{2}} + \log_{b}{\frac{a+b}{2}} \ge 2$

Lagrangian Optimization Linear in Constants Comparison?

Range of function $f(x)=\sqrt{4-x^2}+\sqrt{x^2-1}$

proving $ \mu^T \Sigma \mu \cdot \textbf{1}^T \Sigma \textbf{1} \geq (\textbf{1}^T \Sigma \mu)^2 $

Problem II.3.13: How to prove $\sum_{k=0}^{m}|(x | u_{k})|^{2} \le \|x\|^{2}$ for an orthonormal system of an inner product space

maximum and minimum value of the function $ f(x,y) = x^{2} + y^{2} + xy + 3(x+y) $ at $ A = \left \{ (x,y): x^{2}+y^{2} \leq 1, x+y\geq 0 \right \} $

For positive $a$, $b$, $c$ with $abc=1$, show that $\sum_{cyc}\sqrt{a^2-a+1}\geq a+b+c$

For positive reals $a_i$ and $b_i$, if $\sum a_i \geq \sum a_i b_i$, then $\sum a_i \leq \sum\frac{a_i}{b_i}$

How to solve this? (Argument of the complex number in complex plane)

Under what conditions do we have $\int_{0}^{\infty} |f(x)|^2 dx \leq C \int_{0}^{\infty} x^2 |f^{\prime}(x)|^2 dx$?

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