Question

Behaviour of a function in two variables

score 110 · Answer 1 · 2018-03-16 17:26:59

110

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Behaviour of a function in two variables

Published on 16 Mar 2018 - 17:26

score 611 · Answer 2 · 2026-03-24 16:38:26

611

Views

A better way to prove this inequality

Published on 24 Mar 2026 - 16:38

score 92 · Answer 3 · 2018-03-17 11:05:08

92

Views

How many solution for the equation $x+y=m+6$

Published on 17 Mar 2018 - 11:05

score 121 · Answer 4 · 2026-03-25 05:41:58

121

Views

On an inequality inspired in the definition of strong primes and the Firoozbakht's conjecture

Published on 25 Mar 2026 - 5:41

score 33 · Answer 5 · 2018-03-18 02:37:37

33

Views

Prove/disprove $2|xx_0|-1<(x-x_0)^2$

Published on 18 Mar 2018 - 2:37

score 72 · Answer 6 · 2018-03-18 02:48:37

72

Views

Inequality for multi-dimensional holomorphic functions

Published on 18 Mar 2018 - 2:48

score 23 · Answer 7 · 2026-03-30 05:29:10

23

Views

How can I prove that for any $ \epsilon > 0$ exists: $\log_a(n) \le cn^\epsilon$?

Published on 30 Mar 2026 - 5:29

score 490 · Answer 8 · 2026-03-25 21:01:37

Show that there exist $k\in\{1,2,\cdots,n\}$ such that $\frac{1}{n}\sum_{i=1}^{n}\left(\{kx_{i}\}-\frac{1}{2}\right)^2>\frac{1}{12}-\frac{1}{6n}$

score 1.1k · Answer 9 · 2026-03-29 09:11:38

1.1k

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Prove that for every positive rational number $r$ where $r^2<2$, there must be another rational number $r+h$, such that $(r+h)^2<2$

Published on 29 Mar 2026 - 9:11

score 534 · Answer 10 · 2026-03-25 03:04:16

534

Views

Inequality $\frac{a}{\sqrt{bc}}\cdot\frac1{a+1}+\frac{b}{\sqrt{ca}}\cdot\frac1{b+1}+\frac{c}{\sqrt{ab}}\cdot\frac1{c+1}\leqslant\sqrt2.$

Published on 25 Mar 2026 - 3:04

score 139 · Answer 11 · 2018-03-19 01:56:29

139

Views

Inequality: $0<\alpha<1$, $(\sum_{i=1}^na_i)^{\alpha} \leq \sum_{i=1}^na_i^\alpha$

Published on 19 Mar 2018 - 1:56

score 122 · Answer 12 · 2026-03-30 05:29:15

122

Views

Prove or disprove that $(b-a)^2(\log(b)-\log(a))^{-2}\ge ab$ for all $a,b>0$

Published on 30 Mar 2026 - 5:29

score 180 · Answer 13 · 2026-03-25 00:24:27

180

Views

Exponentials inequality: $|e^x + e^y| \leq |x - y|$ for $x,y<0$.

Published on 25 Mar 2026 - 0:24

score 75 · Answer 14 · 2018-03-19 13:41:45

75

Views

If $|x| \le 2$, prove that $\frac{|x^2-4x+3|}{|x^2-2x+2|} \le 15$.

Published on 19 Mar 2018 - 13:41

score 639 · Answer 15 · 2018-03-19 18:35:08

639

Views

Inequality $\frac{a^3+b^3+c^3}{3}\geq\sqrt{\frac{a^4+b^4+c^4}{3}}$

Published on 19 Mar 2018 - 18:35

List Question

Behaviour of a function in two variables

A better way to prove this inequality

How many solution for the equation $x+y=m+6$

On an inequality inspired in the definition of strong primes and the Firoozbakht's conjecture

Prove/disprove $2|xx_0|-1<(x-x_0)^2$

Inequality for multi-dimensional holomorphic functions

How can I prove that for any $ \epsilon > 0$ exists: $\log_a(n) \le cn^\epsilon$?

Show that there exist $k\in\{1,2,\cdots,n\}$ such that $\frac{1}{n}\sum_{i=1}^{n}\left(\{kx_{i}\}-\frac{1}{2}\right)^2>\frac{1}{12}-\frac{1}{6n}$

Prove that for every positive rational number $r$ where $r^2<2$, there must be another rational number $r+h$, such that $(r+h)^2<2$

Inequality $\frac{a}{\sqrt{bc}}\cdot\frac1{a+1}+\frac{b}{\sqrt{ca}}\cdot\frac1{b+1}+\frac{c}{\sqrt{ab}}\cdot\frac1{c+1}\leqslant\sqrt2.$

Inequality: $0<\alpha<1$, $(\sum_{i=1}^na_i)^{\alpha} \leq \sum_{i=1}^na_i^\alpha$

Prove or disprove that $(b-a)^2(\log(b)-\log(a))^{-2}\ge ab$ for all $a,b>0$

Exponentials inequality: $|e^x + e^y| \leq |x - y|$ for $x,y<0$.

If $|x| \le 2$, prove that $\frac{|x^2-4x+3|}{|x^2-2x+2|} \le 15$.

Inequality $\frac{a^3+b^3+c^3}{3}\geq\sqrt{\frac{a^4+b^4+c^4}{3}}$

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