Question

Proving a function $\frac{1}{2y}\int_{x-y}^{x+y} f(t) dt=f(x)$ is a linear polynomial

score 173 · Answer 1 · 2019-05-17 03:29:06

173

Views

Proving a function $\frac{1}{2y}\int_{x-y}^{x+y} f(t) dt=f(x)$ is a linear polynomial

Published on 17 May 2019 - 3:29

score 5.4k · Answer 2 · 2019-05-18 20:08:05

5.4k

Views

Showing $a^2 + b^2 > 2ab$ without using the fact that $(a-b)^2 = a^2 + b^2 -2ab$?

Published on 18 May 2019 - 20:08

score 34 · Answer 3 · 2019-05-19 19:33:38

34

Views

what's the best way to prove the equivalences of such formulas?

Published on 19 May 2019 - 19:33

score 237 · Answer 4 · 2019-05-22 13:26:17

237

Views

Show that a linear map on a finite dimensional complex vector space always have an eigenvalue.

Published on 22 May 2019 - 13:26

score 116 · Answer 5 · 2019-05-25 19:03:22

116

Views

If $\bigcap\limits_\alpha K_\alpha=\emptyset,$ then there exists $\alpha_1,\dots,\alpha_n$ such that $\bigcap\limits_{k=1}^n K_{\alpha_k}=\emptyset$

Published on 25 May 2019 - 19:03

score 117 · Answer 6 · 2026-03-26 14:35:05

Proving that $\gamma(ω^{β}n+η)=\gamma(ω^{β})+\omega^{β}(ω^{β}(n-1)+η)$, where $n∈ℕ$ , $η<\omega^{β}$ is not a successor ordinal, and $\beta>0$.

score 112 · Answer 7 · 2019-05-31 16:29:28

112

Views

Showing $\cos(x)-\cos(2x)+\cos(3x)$ has no period smaller than $2\pi$ without calculus?

Published on 31 May 2019 - 16:29

score 377 · Answer 8 · 2019-06-01 20:31:53

377

Views

Proving the circumradius (R) for an equilateral triangle

Published on 01 Jun 2019 - 20:31

score 199 · Answer 9 · 2019-06-02 23:51:47

199

Views

prove $ g(x) = x^{5} - x$ is surjective.

Published on 02 Jun 2019 - 23:51

score 216 · Answer 10 · 2019-06-04 00:18:51

216

Views

Is this a correct alternative proof to "Prove there is no rational $r$ satisfying $2^r=3$"

Published on 04 Jun 2019 - 0:18

score 190 · Answer 11 · 2019-06-04 07:31:59

190

Views

The cardinality of $P(\mathbb Z_+)$ is the same as $\mathbb R$ using decimal expansion.

Published on 04 Jun 2019 - 7:31

score 463 · Answer 12 · 2026-03-20 04:26:33

463

Views

For $a,b,c,d > 0$ and $abcd = 1$, show that $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} + \frac{12}{a + b + c + d} \geq 7$

Published on 20 Mar 2026 - 4:26

score 105 · Answer 13 · 2026-03-26 20:16:53

105

Views

Another way to calculate the integral $ \int_{0}^{1} (x-x^{2})^{3/2} dx $

Published on 26 Mar 2026 - 20:16

score 101 · Answer 14 · 2026-03-27 01:04:17

101

Views

Calculate the maximum value of $\frac{ab}{ab + a + b} + \frac{2ca}{ca + c + a} + \frac{3bc}{bc + b + c}$ where $3a + 4b + 5c = 12$

Published on 27 Mar 2026 - 1:04

score 1.3k · Answer 15 · 2026-03-27 04:34:12

1.3k

Views

New bound for Am-Gm of 2 variables

Published on 27 Mar 2026 - 4:34

List Question

Proving a function $\frac{1}{2y}\int_{x-y}^{x+y} f(t) dt=f(x)$ is a linear polynomial

Showing $a^2 + b^2 > 2ab$ without using the fact that $(a-b)^2 = a^2 + b^2 -2ab$?

what's the best way to prove the equivalences of such formulas?

Show that a linear map on a finite dimensional complex vector space always have an eigenvalue.

If $\bigcap\limits_\alpha K_\alpha=\emptyset,$ then there exists $\alpha_1,\dots,\alpha_n$ such that $\bigcap\limits_{k=1}^n K_{\alpha_k}=\emptyset$

Proving that $\gamma(ω^{β}n+η)=\gamma(ω^{β})+\omega^{β}(ω^{β}(n-1)+η)$, where $n∈ℕ$ , $η<\omega^{β}$ is not a successor ordinal, and $\beta>0$.

Showing $\cos(x)-\cos(2x)+\cos(3x)$ has no period smaller than $2\pi$ without calculus?

Proving the circumradius (R) for an equilateral triangle

prove $ g(x) = x^{5} - x$ is surjective.

Is this a correct alternative proof to "Prove there is no rational $r$ satisfying $2^r=3$"

The cardinality of $P(\mathbb Z_+)$ is the same as $\mathbb R$ using decimal expansion.

For $a,b,c,d > 0$ and $abcd = 1$, show that $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} + \frac{12}{a + b + c + d} \geq 7$

Another way to calculate the integral $ \int_{0}^{1} (x-x^{2})^{3/2} dx $

Calculate the maximum value of $\frac{ab}{ab + a + b} + \frac{2ca}{ca + c + a} + \frac{3bc}{bc + b + c}$ where $3a + 4b + 5c = 12$

New bound for Am-Gm of 2 variables

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