List questions from elementary-functions

Published on 25 Feb 2022 - 10:11

732

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Examples of non-elementary integrals, but whose definite integral IS solvable with power series.

Published on 27 Feb 2022 - 2:50

70

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Are there any bounded elementary functions which are not Riemann integrable?

Published on 16 Mar 2022 - 0:31

76

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Are the functions here well defined?

Published on 29 Mar 2022 - 5:53

36

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Is Sqrt(x) not well defined?

Published on 16 Apr 2022 - 19:06

32

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What is the right exponent $x=x(p, q)$ such that both $a^p\le (a+b)^x$ and $b^q\le (a+b)^x$?

Published on 27 Apr 2022 - 16:00

36

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Elementary function that $f(0)=1$ and $f(x)=0$ for all $x>0$.

Published on 08 May 2022 - 18:07

52

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Finding functions $f, g, h : \mathbb R_{> 0} \to \mathbb R_{> 0} $

Published on 16 May 2022 - 19:51

178

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Closed / explicit form of a recursively defined real function involving a square root?

Published on 30 May 2022 - 17:27

19

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Differentiable function that has minimum when all the variables are equal

Published on 01 Jun 2022 - 1:59

47

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Proof that if p: $\mathcal{P} \rightarrow \mathcal{P}$ is a monotonic function, than there exist a set $Z$ such that $P(Z) = Z$

Published on 03 Jun 2022 - 2:14

51

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Elementary real function that is increasing and positive?

Published on 10 Jun 2022 - 16:19

28

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Property for a continuous function with the same value

Published on 13 Jun 2022 - 13:16

115

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$\sqrt[3]{10-x}+\sqrt[3]{30-x}=\sqrt[3]{15-x}+\sqrt[3]{25-x}$

Published on 15 Jun 2022 - 18:16

71

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Proof that the inverse of $f(x)={10}^x$ is $f^{-1}\left(x\right)={\mathrm{log} x\ }$.

Published on 16 Jun 2022 - 19:49

List Question

When is it necessary to define a new function?

Examples of non-elementary integrals, but whose definite integral IS solvable with power series.

Are there any bounded elementary functions which are not Riemann integrable?

Are the functions here well defined?

Is Sqrt(x) not well defined?

What is the right exponent $x=x(p, q)$ such that both $a^p\le (a+b)^x$ and $b^q\le (a+b)^x$?

Elementary function that $f(0)=1$ and $f(x)=0$ for all $x>0$.

Finding functions $f, g, h : \mathbb R_{> 0} \to \mathbb R_{> 0} $

Closed / explicit form of a recursively defined real function involving a square root?

Differentiable function that has minimum when all the variables are equal

Proof that if p: $\mathcal{P} \rightarrow \mathcal{P}$ is a monotonic function, than there exist a set $Z$ such that $P(Z) = Z$

Elementary real function that is increasing and positive?

Property for a continuous function with the same value

$\sqrt[3]{10-x}+\sqrt[3]{30-x}=\sqrt[3]{15-x}+\sqrt[3]{25-x}$

Proof that the inverse of $f(x)={10}^x$ is $f^{-1}\left(x\right)={\mathrm{log} x\ }$.

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