Question

Evaluating $\int_0^{100}{e^{\{x\}}}dx$ on Desmos

score 115 · Answer 1 · 2023-09-13 09:27:18

115

Views

Evaluating $\int_0^{100}{e^{\{x\}}}dx$ on Desmos

Published on 13 Sep 2023 - 9:27

score 142 · Answer 2 · 2023-09-28 12:55:16

142

Views

Prove or disprove: the sequence $a_n = \{ \alpha n \}$ (fractional part) converges if and only if $\alpha \in \mathbb{Z}$

Published on 28 Sep 2023 - 12:55

score 102 · Answer 3 · 2023-10-27 13:53:31

102

Views

A characterization of the floor function

Published on 27 Oct 2023 - 13:53

score 133 · Answer 4 · 2023-11-03 13:04:18

133

Views

Solution Verification Solve the equation $\frac{38-11x}{6}=\{\frac{2x+1}{6}\}+\{\frac{x+17}{3}\}$ in the set of real numbers

Published on 03 Nov 2023 - 13:04

score 50 · Answer 5 · 2023-11-20 22:39:10

50

Views

On an identity involving fractional parts

Published on 20 Nov 2023 - 22:39

score 117 · Answer 6 · 2023-12-06 12:07:47

117

Views

Solving $\lfloor 2022 x \rfloor+\{2023 x\}=2023$

Published on 06 Dec 2023 - 12:07

score 405 · Answer 7 · 2023-12-19 17:44:06

405

Views

A curious property of the fractional part

Published on 19 Dec 2023 - 17:44

score 293 · Answer 8 · 2023-12-21 10:43:32

293

Views

Distribution of the fractional parts of $n/1, n/2,\ldots, n/n$ as $n$ tends to infinity

Published on 21 Dec 2023 - 10:43

score 54 · Answer 9 · 2023-12-21 15:15:29

54

Views

Solution verification | Determine the positive rational number $x$ with the property that $x=3^{[\frac{3x-1}{2}-[\frac{3x}{2}]]-1}$

Published on 21 Dec 2023 - 15:15

score 172 · Answer 10 · 2024-01-28 15:36:25

172

Views

What is $\int\limits_0^1\left\{\frac{1}{x\left\{\frac{1}{x}\right\}}\right\}dx$?

Published on 28 Jan 2024 - 15:36

score 139 · Answer 11 · 2024-02-04 17:26:04

139

Views

Does $\displaystyle\lim\limits_{a\to\infty}\frac{1}{a}\int\limits_{-\infty}^{a}\{e^x\}dx=\frac{1}{2}$?

Published on 04 Feb 2024 - 17:26

score 115 · Answer 12 · 2024-02-04 18:54:42

115

Views

Solutions to $\left\{x^n\right\}=\{x\}^n$

Published on 04 Feb 2024 - 18:54

score 534 · Answer 13 · 2024-02-05 22:45:10

534

Views

Does $\lim\limits_{n\to\infty}\int\limits_{0}^{1}\{x+\frac{1}{2}\{x+\frac{1}{3}\{x+...\frac{1}{n}\}\}\}dx$ converge?

Published on 05 Feb 2024 - 22:45

score 92 · Answer 14 · 2024-02-07 13:10:55

Solution-verification || Solve the equation $\{ \frac {3x + 5}{x + 2} \}+ \big \lfloor \frac{3x + 2}{x + 1} \big \rfloor = \frac{25}{9}$

score 47 · Answer 15 · 2024-02-08 00:37:07

47

Views

For what sequences $a_n$ does $\lim\limits_{n\to\infty}\int\limits_{0}^{1}\{x+a_1\{x+a_2\{x+...a_n\}\}\}dx$ converge?

Published on 08 Feb 2024 - 0:37

List Question

Evaluating $\int_0^{100}{e^{\{x\}}}dx$ on Desmos

Prove or disprove: the sequence $a_n = \{ \alpha n \}$ (fractional part) converges if and only if $\alpha \in \mathbb{Z}$

A characterization of the floor function

Solution Verification Solve the equation $\frac{38-11x}{6}=\{\frac{2x+1}{6}\}+\{\frac{x+17}{3}\}$ in the set of real numbers

On an identity involving fractional parts

Solving $\lfloor 2022 x \rfloor+\{2023 x\}=2023$

A curious property of the fractional part

Distribution of the fractional parts of $n/1, n/2,\ldots, n/n$ as $n$ tends to infinity

Solution verification | Determine the positive rational number $x$ with the property that $x=3^{[\frac{3x-1}{2}-[\frac{3x}{2}]]-1}$

What is $\int\limits_0^1\left\{\frac{1}{x\left\{\frac{1}{x}\right\}}\right\}dx$?

Does $\displaystyle\lim\limits_{a\to\infty}\frac{1}{a}\int\limits_{-\infty}^{a}\{e^x\}dx=\frac{1}{2}$?

Solutions to $\left\{x^n\right\}=\{x\}^n$

Does $\lim\limits_{n\to\infty}\int\limits_{0}^{1}\{x+\frac{1}{2}\{x+\frac{1}{3}\{x+...\frac{1}{n}\}\}\}dx$ converge?

Solution-verification || Solve the equation $\{ \frac {3x + 5}{x + 2} \}+ \big \lfloor \frac{3x + 2}{x + 1} \big \rfloor = \frac{25}{9}$

For what sequences $a_n$ does $\lim\limits_{n\to\infty}\int\limits_{0}^{1}\{x+a_1\{x+a_2\{x+...a_n\}\}\}dx$ converge?

Trending Questions

Popular # Hahtags

Popular Questions