Question

Solve $| \frac{2+z}{2-z} | < 1$

score 98 · Answer 1 · 2026-03-31 07:50:32

98

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Solve $| \frac{2+z}{2-z} | < 1$

Published on 31 Mar 2026 - 7:50

score 32 · Answer 2 · 2026-03-31 12:20:52

32

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Negative square roots of Reals in inequalities

Published on 31 Mar 2026 - 12:20

score 76 · Answer 3 · 2018-07-25 01:31:08

76

Views

For $\frac{1}{a^2+x^2}, \exists K>0$ such that $|f(x)|+|f'(x)| \leq \frac{K}{1+x^2} \; \forall x \in \mathbb{R}$

Published on 25 Jul 2018 - 1:31

score 238 · Answer 4 · 2018-07-25 07:07:11

238

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the maximum value of $\frac{\sin A}{A}+\frac{\sin B}{B}+\frac{\sin C}{C}$

Published on 25 Jul 2018 - 7:07

score 204 · Answer 5 · 2026-03-26 09:39:48

204

Views

Control some function by the average of its extreme values on an interval

Published on 26 Mar 2026 - 9:39

score 73 · Answer 6 · 2018-07-25 14:50:12

73

Views

Verifying that $\left[\int_a^b(x-p)\,dx\right]^2\le(b-a)\int_a^b(x-p)^2\,dx$ without Cauchy-Schwarz

Published on 25 Jul 2018 - 14:50

score 59 · Answer 7 · 2026-03-29 12:38:35

59

Views

Elementary proof on vector algebra

Published on 29 Mar 2026 - 12:38

score 197 · Answer 8 · 2026-03-25 17:42:22

197

Views

Proving $\frac{1}{\sin(A/2)}+\frac{1}{\sin(B/2)}+\frac{1}{\sin(C/2)}\ge 6$, where $A$, $B$, $C$ are angles of a triangle

Published on 25 Mar 2026 - 17:42

score 42 · Answer 9 · 2026-03-25 19:10:06

42

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Compare $\|h\|^k$ and $\sum_{i_1, \ldots, i_k} h_{i_1}\cdots h_{i_k}$ when $h \ll 0$

Published on 25 Mar 2026 - 19:10

score 463 · Answer 10 · 2018-07-26 06:42:40

463

Views

How to prove $e^t-1 > (e-1) t^2$.

Published on 26 Jul 2018 - 6:42

score 507 · Answer 11 · 2026-03-26 01:17:26

507

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Finding the minimum value of $\log _d a + \log _bd + \log _ac + \log _c b$

Published on 26 Mar 2026 - 1:17

score 66 · Answer 12 · 2026-03-25 22:06:37

66

Views

Find analytic solution: for what $n_0$, $\forall n > n_0$ : $n \cdot p ^{n-1} \leq \delta$ holds?

Published on 25 Mar 2026 - 22:06

score 2.1k · Answer 13 · 2026-03-25 22:26:34

2.1k

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Between any two powers of $5$ there are either two or three powers of $2$

Published on 25 Mar 2026 - 22:26

score 206 · Answer 14 · 2026-03-25 00:04:25

206

Views

Prove that $\sqrt{1-x^2} + \sqrt{1-y^2} + \sqrt{1-z^2}\geq 4\sqrt{\frac{3-(x^2+y^2+z^2)}{5+x^2+y^2+z^2}}$.

Published on 25 Mar 2026 - 0:04

score 58 · Answer 15 · 2018-07-27 06:58:54

58

Views

$|a^{2x}+a^{x+2}-1|\ge 1$ equation for positive a

Published on 27 Jul 2018 - 6:58

List Question

Solve $| \frac{2+z}{2-z} | < 1$

Negative square roots of Reals in inequalities

For $\frac{1}{a^2+x^2}, \exists K>0$ such that $|f(x)|+|f'(x)| \leq \frac{K}{1+x^2} \; \forall x \in \mathbb{R}$

the maximum value of $\frac{\sin A}{A}+\frac{\sin B}{B}+\frac{\sin C}{C}$

Control some function by the average of its extreme values on an interval

Verifying that $\left[\int_a^b(x-p)\,dx\right]^2\le(b-a)\int_a^b(x-p)^2\,dx$ without Cauchy-Schwarz

Elementary proof on vector algebra

Proving $\frac{1}{\sin(A/2)}+\frac{1}{\sin(B/2)}+\frac{1}{\sin(C/2)}\ge 6$, where $A$, $B$, $C$ are angles of a triangle

Compare $\|h\|^k$ and $\sum_{i_1, \ldots, i_k} h_{i_1}\cdots h_{i_k}$ when $h \ll 0$

How to prove $e^t-1 > (e-1) t^2$.

Finding the minimum value of $\log _d a + \log _bd + \log _ac + \log _c b$

Find analytic solution: for what $n_0$, $\forall n > n_0$ : $n \cdot p ^{n-1} \leq \delta$ holds?

Between any two powers of $5$ there are either two or three powers of $2$

Prove that $\sqrt{1-x^2} + \sqrt{1-y^2} + \sqrt{1-z^2}\geq 4\sqrt{\frac{3-(x^2+y^2+z^2)}{5+x^2+y^2+z^2}}$.

$|a^{2x}+a^{x+2}-1|\ge 1$ equation for positive a

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