List questions from exponential-function

Published on 02 Apr 2026 - 0:30

467

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Proving the existence of number such that $\lim_{h\to 0}(x^h-1)/h=1$

Published on 15 Jun 2020 - 8:03

32

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Will $ -a e^{2x} + b e^{x} - cx + d$ always have a root for positive $a,c$?

Published on 15 Jun 2020 - 18:26

562

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Exponential distribution - With Half life

Published on 16 Jun 2020 - 19:07

49

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Solving the equation: $ (x - 1)e^x + x + 2 = 0$

Published on 16 Jun 2020 - 22:18

39

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Exponential convergence of interconnected systems

Published on 17 Jun 2020 - 7:58

162

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Complex conjugations

Published on 17 Jun 2020 - 12:57

42

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Solve $\log_3(3^x+3)\log_3(3^{x+1}+19)=12$

Published on 17 Jun 2020 - 14:35

54

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Inverting the function $f(x)=x\cdot C^x$

Published on 29 Mar 2026 - 9:18

132

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Indefinite integral of bilinear form inside exponential

Published on 26 Mar 2026 - 12:35

81

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Prove the convergence of the integral $\int_{0}^{\infty}\frac{x^n}{\Gamma\Big(\operatorname{W}(x)\Big)}dx$

Published on 26 Mar 2026 - 2:57

801

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A very interesting question: intersection point of $x^y=y^x$

Published on 23 Feb 2026 - 3:59

64

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Why is $(1 - \frac{\ln n}{n})^n$ approximated by $e^{-\ln n}$ for $n \rightarrow \infty$?

Published on 01 Apr 2026 - 13:08

54

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Expression for a double product of exponential functions

Published on 30 Mar 2026 - 15:02

119

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How to show $\sum_{k=0}^{\infty} \frac{1}{k!} \left( \int_{1}^{x} \frac{1}{t} \ dt \right)^k =x$?

Published on 29 Mar 2026 - 10:49

List Question

Is $e-1/e$ rational?

Proving the existence of number such that $\lim_{h\to 0}(x^h-1)/h=1$

Will $ -a e^{2x} + b e^{x} - cx + d$ always have a root for positive $a,c$?

Exponential distribution - With Half life

Solving the equation: $ (x - 1)e^x + x + 2 = 0$

Exponential convergence of interconnected systems

Complex conjugations

Solve $\log_3(3^x+3)\log_3(3^{x+1}+19)=12$

Inverting the function $f(x)=x\cdot C^x$

Indefinite integral of bilinear form inside exponential

Prove the convergence of the integral $\int_{0}^{\infty}\frac{x^n}{\Gamma\Big(\operatorname{W}(x)\Big)}dx$

A very interesting question: intersection point of $x^y=y^x$

Why is $(1 - \frac{\ln n}{n})^n$ approximated by $e^{-\ln n}$ for $n \rightarrow \infty$?

Expression for a double product of exponential functions

How to show $\sum_{k=0}^{\infty} \frac{1}{k!} \left( \int_{1}^{x} \frac{1}{t} \ dt \right)^k =x$?

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