Question

Convex continuous piecewise linear function form

score 109 · Answer 1 · 2020-11-18 11:34:47

109

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Convex continuous piecewise linear function form

Published on 18 Nov 2020 - 11:34

score 26 · Answer 2 · 2020-11-19 22:10:26

26

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Deriving the expectation $E\left[\left | \sum_{i=1}^N X_{i} e^{j \varphi_i} \right |\right]$

Published on 19 Nov 2020 - 22:10

score 112 · Answer 3 · 2020-11-22 14:06:53

112

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Prove that $|a|\leq \max\{|b|,|c|\}$ if $b\leq a \leq c$

Published on 22 Nov 2020 - 14:06

score 61 · Answer 4 · 2020-11-22 15:19:36

61

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Absolute values in limits

Published on 22 Nov 2020 - 15:19

score 241 · Answer 5 · 2020-11-25 05:06:52

241

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Solving $|2x-3|+7 \le 3x-3|x-7|$

Published on 25 Nov 2020 - 5:06

score 52 · Answer 6 · 2020-11-25 11:22:05

Let $a,b$ be real numbers. Suppose that inequality $|(ax+by)(ay+bx)|\leqslant x^2+y^2$ holds for any real $x,y$. Prove that $a^2+b^2\leqslant2$

score 46 · Answer 7 · 2020-11-25 14:04:20

46

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Absolute value proof, $|a|\leq\max\{|x|,|y|\}$

Published on 25 Nov 2020 - 14:04

score 74 · Answer 8 · 2020-11-26 14:04:01

74

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Show $\frac{1}{\lvert a - b \rvert} < \frac{2}{\lvert a \rvert}$

Published on 26 Nov 2020 - 14:04

score 329 · Answer 9 · 2026-02-23 08:53:19

329

Views

Oscillatory integral with absolute value

Published on 23 Feb 2026 - 8:53

score 58 · Answer 10 · 2020-11-27 02:30:05

58

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Simplifying $ \frac{2x-x\lvert x-1\rvert+x\lvert x\rvert+5}{\lvert x\rvert+1}$

Published on 27 Nov 2020 - 2:30

score 79 · Answer 11 · 2020-11-27 17:30:59

79

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Finding the anti-derivative of complex absolute value

Published on 27 Nov 2020 - 17:30

score 41 · Answer 12 · 2020-11-29 11:36:26

41

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For every $a, b, x \in \mathbb{R}$ such that $a \le x \le b$, we have $|x| \le \max\{|a| , |b|\}$

Published on 29 Nov 2020 - 11:36

score 159 · Answer 13 · 2026-03-30 00:24:36

159

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$y(x)=\lambda \int_{-1}^1 (1-|x-t|)y(t)dt$ to differential equation

Published on 30 Mar 2026 - 0:24

score 43 · Answer 14 · 2020-11-29 15:15:28

43

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Proving $2|c_1|^2|c_2|^2 \leq c_1c_2^* + c_1^*c_2$ for $|c_1|,|c_2|\leq 1$

Published on 29 Nov 2020 - 15:15

score 38 · Answer 15 · 2020-11-29 15:50:56

38

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Maximum value of $|\overrightarrow{a}-2\overrightarrow{b}|^2+|\overrightarrow{b}-2\overrightarrow{c}|^2+|\overrightarrow{c}-2\overrightarrow{a}|^2$

Published on 29 Nov 2020 - 15:50

List Question

Convex continuous piecewise linear function form

Deriving the expectation $E\left[\left | \sum_{i=1}^N X_{i} e^{j \varphi_i} \right |\right]$

Prove that $|a|\leq \max\{|b|,|c|\}$ if $b\leq a \leq c$

Absolute values in limits

Solving $|2x-3|+7 \le 3x-3|x-7|$

Let $a,b$ be real numbers. Suppose that inequality $|(ax+by)(ay+bx)|\leqslant x^2+y^2$ holds for any real $x,y$. Prove that $a^2+b^2\leqslant2$

Absolute value proof, $|a|\leq\max\{|x|,|y|\}$

Show $\frac{1}{\lvert a - b \rvert} < \frac{2}{\lvert a \rvert}$

Oscillatory integral with absolute value

Simplifying $ \frac{2x-x\lvert x-1\rvert+x\lvert x\rvert+5}{\lvert x\rvert+1}$

Finding the anti-derivative of complex absolute value

For every $a, b, x \in \mathbb{R}$ such that $a \le x \le b$, we have $|x| \le \max\{|a| , |b|\}$

$y(x)=\lambda \int_{-1}^1 (1-|x-t|)y(t)dt$ to differential equation

Proving $2|c_1|^2|c_2|^2 \leq c_1c_2^* + c_1^*c_2$ for $|c_1|,|c_2|\leq 1$

Maximum value of $|\overrightarrow{a}-2\overrightarrow{b}|^2+|\overrightarrow{b}-2\overrightarrow{c}|^2+|\overrightarrow{c}-2\overrightarrow{a}|^2$

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