Question

Prove that $\int_{x}^{x+ (\ln x /x)} e^{t^2} dt > \frac{e^{x^2} \ln x}{2 x}$

score 54 · Answer 1 · 2018-04-09 21:48:50

54

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Prove that $\int_{x}^{x+ (\ln x /x)} e^{t^2} dt > \frac{e^{x^2} \ln x}{2 x}$

Published on 09 Apr 2018 - 21:48

score 116 · Answer 2 · 2026-03-30 13:03:59

116

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How I show this :$\sum_{k,j=0}^{n}\frac{a_k a_j}{k+j+1} \leq \pi \sum_{k=0}^{n}a_k^2$?

Published on 30 Mar 2026 - 13:03

score 62 · Answer 3 · 2018-04-10 03:27:04

62

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Concentration inequality involved the mean in RHS denominator

Published on 10 Apr 2018 - 3:27

score 3.3k · Answer 4 · 2026-03-26 02:45:50

3.3k

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What is the conditional expectation of $E(X|X<0)$ where $X$ is normally distributed with mean $0$?

Published on 26 Mar 2026 - 2:45

score 211 · Answer 5 · 2018-04-10 08:00:40

211

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Evaluate $\lim_{x \to \infty} e^{-x^2} \int_x^{x + \ln(x)/x} e^{t^2} dt $

Published on 10 Apr 2018 - 8:00

score 106 · Answer 6 · 2026-03-25 03:02:16

106

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Prove that $\|\mathbf{X}\|_\sigma \leq \sqrt{rank(X)} \|\mathbf{X}\|_F$

Published on 25 Mar 2026 - 3:02

score 72 · Answer 7 · 2018-04-10 13:37:49

If $n>2$, $a_2,\cdots,a_n\in\mathbb R^+$ and $a_2a_3\cdots a_n=1$, then $(1+a_2)^2(1+a_3)^3\cdots(1+a_n)^n>n^n$

score 45 · Answer 8 · 2026-03-26 04:49:23

45

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Inequality Word Problem Help Me Please

Published on 26 Mar 2026 - 4:49

score 75 · Answer 9 · 2018-04-10 16:07:35

75

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Generalization of the inequality $ab\leq \frac{1}{2}(a^2+b^2)$

Published on 10 Apr 2018 - 16:07

score 114 · Answer 10 · 2026-03-25 20:07:39

114

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Show that $x^3 - 2 x^2 +\log(1+x)(x(3x+4) -2(1+x)^2 \log(1+x))$ is positive

Published on 25 Mar 2026 - 20:07

score 333 · Answer 11 · 2026-03-25 23:52:30

333

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Prove: $(a+b) \sqrt {ab}+(a+c) \sqrt {ac}+(b+c)\sqrt {bc}≥ \frac {(a+b+c)^2}{2}$

Published on 25 Mar 2026 - 23:52

score 64 · Answer 12 · 2026-03-25 02:59:47

64

Views

Evaluating whether or not a particular sequence is monotone.

Published on 25 Mar 2026 - 2:59

score 459 · Answer 13 · 2026-03-24 19:08:58

459

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Conditions on coefficients of positive semidefinite matrix with certain symmetries

Published on 24 Mar 2026 - 19:08

score 590 · Answer 14 · 2026-03-25 03:07:01

590

Views

Evaluating Inequality with absolute value and a square root: $|x| \leq \sqrt{2}$

Published on 25 Mar 2026 - 3:07

score 670 · Answer 15 · 2026-03-22 05:56:56

670

Views

prove this inequality by $abc=1$

Published on 22 Mar 2026 - 5:56

List Question

Prove that $\int_{x}^{x+ (\ln x /x)} e^{t^2} dt > \frac{e^{x^2} \ln x}{2 x}$

How I show this :$\sum_{k,j=0}^{n}\frac{a_k a_j}{k+j+1} \leq \pi \sum_{k=0}^{n}a_k^2$?

Concentration inequality involved the mean in RHS denominator

What is the conditional expectation of $E(X|X<0)$ where $X$ is normally distributed with mean $0$?

Evaluate $\lim_{x \to \infty} e^{-x^2} \int_x^{x + \ln(x)/x} e^{t^2} dt $

Prove that $\|\mathbf{X}\|_\sigma \leq \sqrt{rank(X)} \|\mathbf{X}\|_F$

If $n>2$, $a_2,\cdots,a_n\in\mathbb R^+$ and $a_2a_3\cdots a_n=1$, then $(1+a_2)^2(1+a_3)^3\cdots(1+a_n)^n>n^n$

Inequality Word Problem Help Me Please

Generalization of the inequality $ab\leq \frac{1}{2}(a^2+b^2)$

Show that $x^3 - 2 x^2 +\log(1+x)(x(3x+4) -2(1+x)^2 \log(1+x))$ is positive

Prove: $(a+b) \sqrt {ab}+(a+c) \sqrt {ac}+(b+c)\sqrt {bc}≥ \frac {(a+b+c)^2}{2}$

Evaluating whether or not a particular sequence is monotone.

Conditions on coefficients of positive semidefinite matrix with certain symmetries

Evaluating Inequality with absolute value and a square root: $|x| \leq \sqrt{2}$

prove this inequality by $abc=1$

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