Question

How is e to the hyperbola what pi is to the circle?

score 270 · Answer 1 · 2021-11-05 09:27:37

270

Views

How is e to the hyperbola what pi is to the circle?

Published on 05 Nov 2021 - 9:27

score 2.6k · Answer 2 · 2021-11-26 19:39:05

2.6k

Views

Why does $\ln(1)+\ln(2)+\ln(3)=\ln(1+2+3)$?

Published on 26 Nov 2021 - 19:39

score 518 · Answer 3 · 2021-11-28 17:22:55

518

Views

Calculate and prove the limit $\lim\limits_{n\to\infty }(1+\frac{1}{a_n})^{a_n}$ Given $a_n$ is an increasing monotone sequence of integers

Published on 28 Nov 2021 - 17:22

score 564 · Answer 4 · 2021-12-03 16:51:53

564

Views

Prove that $(1+\frac{1}{n})^n$ is a Cauchy sequence

Published on 03 Dec 2021 - 16:51

score 54 · Answer 5 · 2021-12-13 20:07:15

54

Views

Can $\frac{e^{r(n+1)}-1}{e^r-1}$ be simplified?

Published on 13 Dec 2021 - 20:07

score 30 · Answer 6 · 2022-01-19 17:01:47

30

Views

What is the maximum $b$ for which $\log_b(x) = \log_b(\log_b(x))$ has real solutions? And would there be 1 or 2 solutions?

Published on 19 Jan 2022 - 17:01

score 20 · Answer 7 · 2022-02-12 20:29:54

20

Views

Limit of a modified Euler's number expression

Published on 12 Feb 2022 - 20:29

score 198 · Answer 8 · 2022-03-18 13:09:18

198

Views

Estimate: $\pi \to e \to \log(2) \to G$ by sampling uniform distribution

Published on 18 Mar 2022 - 13:09

score 804 · Answer 9 · 2022-05-02 09:22:35

804

Views

Smooth zoom formula

Published on 02 May 2022 - 9:22

score 51 · Answer 10 · 2022-05-23 18:19:01

51

Views

How to calculate the average number of turns until going bust for a simplified blackjack style game?

Published on 23 May 2022 - 18:19

score 31 · Answer 11 · 2022-05-24 21:37:31

31

Views

How do you do this transformation of two Euler's number formula?

Published on 24 May 2022 - 21:37

score 86 · Answer 12 · 2022-05-30 13:56:42

86

Views

How to solve $sin(x) = n$ for all $n\in{\mathbb{R}}$?

Published on 30 May 2022 - 13:56

score 138 · Answer 13 · 2022-06-21 05:36:04

138

Views

There's this infinite geometric mean, or the infinity'th term of a sequence of finite means. I know what it converges to, but how do I prove it?

Published on 21 Jun 2022 - 5:36

score 102 · Answer 14 · 2022-06-27 11:42:39

102

Views

Simpler approach when calculating $\lim_{x\to0} \frac{e^{2x} - e^x}{4^x - 2^x}$?

Published on 27 Jun 2022 - 11:42

score 76 · Answer 15 · 2022-08-06 01:09:35

76

Views

How could Euler's constant e be used in math tables and approximations before e was known?

Published on 06 Aug 2022 - 1:09

List Question

How is e to the hyperbola what pi is to the circle?

Why does $\ln(1)+\ln(2)+\ln(3)=\ln(1+2+3)$?

Calculate and prove the limit $\lim\limits_{n\to\infty }(1+\frac{1}{a_n})^{a_n}$ Given $a_n$ is an increasing monotone sequence of integers

Prove that $(1+\frac{1}{n})^n$ is a Cauchy sequence

Can $\frac{e^{r(n+1)}-1}{e^r-1}$ be simplified?

What is the maximum $b$ for which $\log_b(x) = \log_b(\log_b(x))$ has real solutions? And would there be 1 or 2 solutions?

Limit of a modified Euler's number expression

Estimate: $\pi \to e \to \log(2) \to G$ by sampling uniform distribution

Smooth zoom formula

How to calculate the average number of turns until going bust for a simplified blackjack style game?

How do you do this transformation of two Euler's number formula?

How to solve $sin(x) = n$ for all $n\in{\mathbb{R}}$?

There's this infinite geometric mean, or the infinity'th term of a sequence of finite means. I know what it converges to, but how do I prove it?

Simpler approach when calculating $\lim_{x\to0} \frac{e^{2x} - e^x}{4^x - 2^x}$?

How could Euler's constant e be used in math tables and approximations before e was known?

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