Question

Integral inequality $e^{\int _0^1f\left(x\right)dx-1\:}\le \frac{1}{4}\int _0^1\left(x+1\right)e^{f\left(x\right)}dx$

score 104 · Answer 1 · 2026-05-10 12:17:51

104

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Integral inequality $e^{\int _0^1f\left(x\right)dx-1\:}\le \frac{1}{4}\int _0^1\left(x+1\right)e^{f\left(x\right)}dx$

Published on 10 May 2026 - 12:17

score 127 · Answer 2 · 2026-04-14 17:45:11

127

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Does there exist a function $f$ from $R^2$ to $R$ and constant $c_0>0$ such that for all $x,y\in R^2$, $|f(x)-f(y)| \ge c_0|x-y|^2$?

Published on 14 Apr 2026 - 17:45

score 118 · Answer 3 · 2026-04-18 08:25:43

118

Views

$\frac{2x}{1}-\frac{(2x)^2}{2}+\frac{(2x)^3}{3}-...$ Alembert (Ratio test) or Leibniz?

Published on 18 Apr 2026 - 8:25

score 166 · Answer 4 · 2026-04-11 21:52:58

166

Views

Recurrence relation for integral

Published on 11 Apr 2026 - 21:52

score 56 · Answer 5 · 2026-03-25 17:37:35

56

Views

If $a$ is complex and $n$ is a positive integer, prove that the series converges when $a$ is a positive integer.

Published on 25 Mar 2026 - 17:37

score 298 · Answer 6 · 2026-04-18 08:12:39

298

Views

sequence $x_{n+1}=x_n+e^{-2018x_n}$

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score 89 · Answer 7 · 2026-04-11 07:58:58

89

Views

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score 211 · Answer 8 · 2026-04-16 17:12:38

211

Views

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score 29 · Answer 9 · 2026-04-24 11:20:27

29

Views

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score 339 · Answer 10 · 2026-04-12 19:49:19

339

Views

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score 94 · Answer 11 · 2026-04-13 21:03:16

94

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score 66 · Answer 12 · 2026-05-11 01:05:41

66

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score 134 · Answer 13 · 2026-05-11 17:28:33

134

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score 682 · Answer 14 · 2026-04-12 15:07:45

682

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score 454 · Answer 15 · 2026-05-11 09:59:09

454

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List Question

Integral inequality $e^{\int _0^1f\left(x\right)dx-1\:}\le \frac{1}{4}\int _0^1\left(x+1\right)e^{f\left(x\right)}dx$

Does there exist a function $f$ from $R^2$ to $R$ and constant $c_0>0$ such that for all $x,y\in R^2$, $|f(x)-f(y)| \ge c_0|x-y|^2$?

$\frac{2x}{1}-\frac{(2x)^2}{2}+\frac{(2x)^3}{3}-...$ Alembert (Ratio test) or Leibniz?

Recurrence relation for integral

If $a$ is complex and $n$ is a positive integer, prove that the series converges when $a$ is a positive integer.

sequence $x_{n+1}=x_n+e^{-2018x_n}$

how to define bounded linear operator from $L^2+L^\infty\rightarrow L^2$

Differential equation solved by $y(x) = c_1e^x + c_2xe^x + c_3x^2e^x + c_4\cos(x) + c_5\sin(x)$

Estimating an integral under strong regularity conditions

Show that $e+\pi$ is not integer.

Cesaro means $\to \infty$

Real Analysis. Integration. Confused

How to use Banach's fixed point theorem?

Constructing a function using the Schroeder-Bernstein Theorem

Implications of the Borel-Cantelli Lemma

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