Question

If $|f(x) − f(y)| ≤ |\sin x − \sin y|,\text{for all} ~~x, y \in\mathbb{R}$ then $\text{Show that} ~f \text{is} 2\pi−\text{periodic}~?$

score 195 · Answer 1 · 2026-04-01 06:32:15

195

Views

If $|f(x) − f(y)| ≤ |\sin x − \sin y|,\text{for all} ~~x, y \in\mathbb{R}$ then $\text{Show that} ~f \text{is} 2\pi−\text{periodic}~?$

Published on 01 Apr 2026 - 6:32

score 49 · Answer 2 · 2020-11-13 15:13:51

49

Views

Are there any functions that satisfy these properties?

Published on 13 Nov 2020 - 15:13

score 656 · Answer 3 · 2026-03-26 11:05:19

656

Views

Are piecewise functions continuous?

Published on 26 Mar 2026 - 11:05

score 134 · Answer 4 · 2020-11-19 16:16:39

134

Views

Finding the period of a linear combination of sines and cosines

Published on 19 Nov 2020 - 16:16

score 118 · Answer 5 · 2020-11-19 19:32:57

118

Views

If $f$ is a function such that $f'(x)$ exists for all $x\in\mathbb{R}$. Then $f'$ has period $2\pi $.

Published on 19 Nov 2020 - 19:32

score 53 · Answer 6 · 2020-11-22 10:01:14

53

Views

Prove that, if $\frac{\tau_i}{\tau_j}\in\Bbb Q\space j\ne i,\space i,j\in\{1,\ldots,n\},$ the function $f(x)=\sum_{k=1}^nf_k(x)$

Published on 22 Nov 2020 - 10:01

score 61 · Answer 7 · 2020-11-25 21:34:01

61

Views

Show that $f$ is periodic from an integral property

Published on 25 Nov 2020 - 21:34

score 24 · Answer 8 · 2020-11-26 19:56:25

24

Views

Notation when describing properties of a periodic function

Published on 26 Nov 2020 - 19:56

score 113 · Answer 9 · 2020-11-28 16:42:59

113

Views

How to prove $\lim\limits_{n\to\infty}\int^\pi_0 \pi f(nx)g(x)\ \mathrm {d}x = \int^\pi_0 f(x)\ \mathrm {d}x \int^\pi_0 g(x)\ \mathrm {d}x$

Published on 28 Nov 2020 - 16:42

score 56 · Answer 10 · 2020-11-29 19:55:49

56

Views

Period of a discrete sine function?

Published on 29 Nov 2020 - 19:55

score 71 · Answer 11 · 2026-02-23 16:56:59

71

Views

convergence sequence of xor bit operation

Published on 23 Feb 2026 - 16:56

score 53 · Answer 12 · 2020-12-04 20:58:43

53

Views

Prove that exist a $C^1$ function $\omega(\lambda)$ such that $\omega(0)=\tau$ and $x'=f(x,\lambda)$

Published on 04 Dec 2020 - 20:58

score 181 · Answer 13 · 2026-02-23 22:23:14

181

Views

Draw a graph of periodic extension of a piecewise given function

Published on 23 Feb 2026 - 22:23

score 101 · Answer 14 · 2026-03-27 16:39:15

101

Views

Schwartz functions after periodization has period 1

Published on 27 Mar 2026 - 16:39

score 24 · Answer 15 · 2020-12-07 11:11:12

24

Views

changing argument of integrand of a periodic function inside an integral

Published on 07 Dec 2020 - 11:11

List Question

If $|f(x) − f(y)| ≤ |\sin x − \sin y|,\text{for all} ~~x, y \in\mathbb{R}$ then $\text{Show that} ~f \text{is} 2\pi−\text{periodic}~?$

Are there any functions that satisfy these properties?

Are piecewise functions continuous?

Finding the period of a linear combination of sines and cosines

If $f$ is a function such that $f'(x)$ exists for all $x\in\mathbb{R}$. Then $f'$ has period $2\pi $.

Prove that, if $\frac{\tau_i}{\tau_j}\in\Bbb Q\space j\ne i,\space i,j\in\{1,\ldots,n\},$ the function $f(x)=\sum_{k=1}^nf_k(x)$

Show that $f$ is periodic from an integral property

Notation when describing properties of a periodic function

How to prove $\lim\limits_{n\to\infty}\int^\pi_0 \pi f(nx)g(x)\ \mathrm {d}x = \int^\pi_0 f(x)\ \mathrm {d}x \int^\pi_0 g(x)\ \mathrm {d}x$

Period of a discrete sine function?

convergence sequence of xor bit operation

Prove that exist a $C^1$ function $\omega(\lambda)$ such that $\omega(0)=\tau$ and $x'=f(x,\lambda)$

Draw a graph of periodic extension of a piecewise given function

Schwartz functions after periodization has period 1

changing argument of integrand of a periodic function inside an integral

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