List questions from absolute-value

Published on 20 Feb 2021 - 19:11

86

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Prove that $a ≤ x ≤ b ⇒ |x| ≤ |a|+|b|$

Published on 23 Feb 2021 - 3:13

53

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Derivatives of general absolute value functions

Published on 24 Feb 2021 - 11:35

38

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Justify if True or False $\forall x\in\mathbb{R}\left(-|x|\le x\le |x|\right)$.

Published on 25 Feb 2021 - 17:29

56

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For each $\epsilon>0$ there is a polynomial $p\colon\mathbb{C}\to\mathbb{C}$ such that $|p(x)-|x||<\epsilon$ for all $x\in[-r,r]$.

Published on 04 Apr 2026 - 8:43

124

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Computing integral $\int_0^1 |x-a| \, {\rm d} x$

Published on 28 Feb 2021 - 12:44

42

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Solving equation in one unknown with absolute value

Published on 02 Mar 2021 - 1:17

63

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Absolute Value Inequality Implication

Published on 05 Mar 2021 - 0:11

48

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Show that the maximum of $f(x)= \sqrt{x^{2}+a} - |x| $ on $[-1,1]$ for some real $a>0$ is $\sqrt{a}$.

Published on 05 Mar 2021 - 15:34

440

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Absolute value of sum of absolute values

Published on 05 Mar 2021 - 16:19

28

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Adding "C" to an absolute value equation

Published on 05 Mar 2021 - 16:28

30

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Question about continuity and absolute value

Published on 06 Mar 2021 - 13:32

27

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How to turn $|a_n| < 1 + |L|$ into $L -1 < a_n < L + 1$?

Published on 07 Mar 2021 - 13:29

97

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Does this norm inequality hold?

Published on 09 Mar 2021 - 10:16

51

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What is the domain of k? $2|x-2|-3|x-3|=k$

Published on 10 Mar 2021 - 8:52

List Question

Pointwise maximum: translation and scaling

Prove that $a ≤ x ≤ b ⇒ |x| ≤ |a|+|b|$

Derivatives of general absolute value functions

Justify if True or False $\forall x\in\mathbb{R}\left(-|x|\le x\le |x|\right)$.

For each $\epsilon>0$ there is a polynomial $p\colon\mathbb{C}\to\mathbb{C}$ such that $|p(x)-|x||<\epsilon$ for all $x\in[-r,r]$.

Computing integral $\int_0^1 |x-a| \, {\rm d} x$

Solving equation in one unknown with absolute value

Absolute Value Inequality Implication

Show that the maximum of $f(x)= \sqrt{x^{2}+a} - |x| $ on $[-1,1]$ for some real $a>0$ is $\sqrt{a}$.

Absolute value of sum of absolute values

Adding "C" to an absolute value equation

Question about continuity and absolute value

How to turn $|a_n| < 1 + |L|$ into $L -1 < a_n < L + 1$?

Does this norm inequality hold?

What is the domain of k? $2|x-2|-3|x-3|=k$

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