List questions from elementary-functions

Published on 08 May 2023 - 12:31

77

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What is $\,\lim\limits_{x\to0}\frac{\ln\left(\frac{e^x}{x+1}\right)}{x^2}\;?$

Published on 15 May 2023 - 15:50

110

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can anyone find me or disprove existence of an elementary function such that $f(f(x))=\sin(x)$

Published on 18 May 2023 - 16:58

123

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Inverse function of $x \mapsto \coth x - 1/x$

Published on 21 May 2023 - 14:56

80

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if $f(x) = |3x - 1|$ so what is the sum of all $x$ such that $f(f(x)) = x$?

Published on 31 May 2023 - 20:05

242

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Prove that $e^{-ax} \leq (1 - x)^a + ax^2/2$ for $a > 1$, $0 \le x \le 1$

Published on 15 Jun 2023 - 19:31

153

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Coefficients of Chebyshev polynomials

Published on 26 Mar 2026 - 1:01

833

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How to approach this tricky log problem

Published on 28 Jun 2023 - 7:27

166

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Are there basic techniques for proving that no elementary antiderivative exists?

Published on 25 Mar 2026 - 16:06

82

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Can $\sin(\frac{n\pi}{m})$ with $n,m \in \mathbb{Z}$ always be represented using only algebraic functions?

Published on 19 Jul 2023 - 11:15

94

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How to solve the equation ${\log_{x} 9} + {\log_{2} x} = {\log_{2} (9+x)}$

Published on 21 Jul 2023 - 8:58

103

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how do you know when there is no antiderivative written in elementary functions?

Published on 25 Mar 2026 - 9:09

31

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A graph made of half circles

Published on 30 Jul 2023 - 12:43

315

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Need to simplify formula $ \pi \sim \frac{8}{n^2} \cdot \sum\limits_{i=0}^{n} \sqrt{i \cdot (n - i)} $

Published on 03 Aug 2023 - 0:45

48

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How to find the distance between two funtion inputs given two function outputs

Published on 04 Aug 2023 - 10:33

List Question

Determine all roots of $\sinh(z^2) = \dfrac{15}{8}$

What is $\,\lim\limits_{x\to0}\frac{\ln\left(\frac{e^x}{x+1}\right)}{x^2}\;?$

can anyone find me or disprove existence of an elementary function such that $f(f(x))=\sin(x)$

Inverse function of $x \mapsto \coth x - 1/x$

if $f(x) = |3x - 1|$ so what is the sum of all $x$ such that $f(f(x)) = x$?

Prove that $e^{-ax} \leq (1 - x)^a + ax^2/2$ for $a > 1$, $0 \le x \le 1$

Coefficients of Chebyshev polynomials

How to approach this tricky log problem

Are there basic techniques for proving that no elementary antiderivative exists?

Can $\sin(\frac{n\pi}{m})$ with $n,m \in \mathbb{Z}$ always be represented using only algebraic functions?

How to solve the equation ${\log_{x} 9} + {\log_{2} x} = {\log_{2} (9+x)}$

how do you know when there is no antiderivative written in elementary functions?

A graph made of half circles

Need to simplify formula $ \pi \sim \frac{8}{n^2} \cdot \sum\limits_{i=0}^{n} \sqrt{i \cdot (n - i)} $

How to find the distance between two funtion inputs given two function outputs

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