Question

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

score 73 · Answer 1 · 2026-05-14 05:17:32

73

Views

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

Published on 14 May 2026 - 5:17

score 650 · Answer 2 · 2026-04-08 18:30:41

650

Views

How to maximize this expression?

Published on 08 Apr 2026 - 18:30

score 287 · Answer 3 · 2026-05-11 03:17:48

287

Views

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

Published on 11 May 2026 - 3:17

score 413 · Answer 4 · 2026-05-10 15:26:44

413

Views

Upper Bound for a Sum

Published on 10 May 2026 - 15:26

score 72 · Answer 5 · 2026-04-16 17:05:18

72

Views

Cauchy Schwarz: Proving this inequality

Published on 16 Apr 2026 - 17:05

score 357 · Answer 6 · 2026-04-16 05:30:14

357

Views

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

Published on 16 Apr 2026 - 5:30

score 36 · Answer 7 · 2026-05-14 11:34:03

36

Views

Lagrangian Optimization Linear in Constants Comparison?

Published on 14 May 2026 - 11:34

score 120 · Answer 8 · 2026-05-10 15:29:07

120

Views

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

Published on 10 May 2026 - 15:29

score 72 · Answer 9 · 2026-04-16 21:05:58

72

Views

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

Published on 16 Apr 2026 - 21:05

score 81 · Answer 10 · 2026-04-15 13:34:15

81

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 15 Apr 2026 - 13:34

score 830 · Answer 11 · 2026-05-14 12:41:04

830

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 14 May 2026 - 12:41

score 343 · Answer 12 · 2026-04-18 06:20:08

343

Views

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

Published on 18 Apr 2026 - 6:20

score 324 · Answer 13 · 2026-04-13 06:39:12

324

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 13 Apr 2026 - 6:39

score 136 · Answer 14 · 2026-05-14 16:02:25

136

Views

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

Published on 14 May 2026 - 16:02

score 220 · Answer 15 · 2026-05-14 07:03:39

220

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 14 May 2026 - 7:03

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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