List questions from periodic-functions

Published on 16 Nov 2022 - 18:29

182

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Prove that $\cos\sqrt x$ is not a periodic function.

Published on 22 Nov 2022 - 10:46

158

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How to find the period of $f(x)= (\sin x)(\cos x)$?

Published on 24 Nov 2022 - 18:51

178

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Prove that the function $f(x)=\cos x^2$ is not a periodic one .

Published on 29 Nov 2022 - 9:27

102

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Let $f: \mathbb{R}\rightarrow \mathbb{R} $ that verifies for all $x_1,x_2$: $|f(x_1)-f(x_2)| \leq 5|cos(x_1)-cos(x_2)|$ so $f(x)$ is periodic

Published on 04 Dec 2022 - 21:34

68

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Fourier series converging to a function which doesn't satisfy Dirichlet's conditions

Published on 13 Dec 2022 - 12:39

24

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Fundemental period of $x(t) = \sum_{k=-\infty}^{\infty}\operatorname{rect}(\frac{t+k}{2c})$

Published on 15 Dec 2022 - 14:57

93

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Is there a closed form, or a series approximation, for $ f(x)=\int_{1}^{x} \left(\cos\left( \frac{\pi r}{t}\right)+\cos(\pi t)\right)^{N}dt $?

Published on 23 Dec 2022 - 23:28

191

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When is the period of a periodic function not defined? Examples?

Published on 30 Dec 2022 - 11:03

53

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Prove this function is periodic.

Published on 30 Dec 2022 - 14:39

55

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If $n,k$ are odd numbers, proof that all solutions of the ODE $x^{''}+x^k+x^n=0$ are periodic.

Published on 31 Dec 2022 - 14:20

93

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Residues at poles of periodic functions

Published on 04 Jan 2023 - 19:18

81

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How do you go from a discrete sum of waves $u(x)=\sum_{i=1}^n a_i e^{ikx}$ to a continuous integral $u(x)=\int_{-\infty}^{+\infty} A(k) e^{ikx} dk$

Published on 06 Jan 2023 - 11:18

85

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Prove all solutions to $ x^{\prime}=A(t) x, \quad x(0)=x_0 $ are $T$-periodic.

Published on 29 Mar 2026 - 22:29

42

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Overlap between two periodic intervals

Published on 29 Mar 2026 - 15:23

List Question

Riemann sum of a periodic function

Prove that $\cos\sqrt x$ is not a periodic function.

How to find the period of $f(x)= (\sin x)(\cos x)$?

Prove that the function $f(x)=\cos x^2$ is not a periodic one .

Let $f: \mathbb{R}\rightarrow \mathbb{R} $ that verifies for all $x_1,x_2$: $|f(x_1)-f(x_2)| \leq 5|cos(x_1)-cos(x_2)|$ so $f(x)$ is periodic

Fourier series converging to a function which doesn't satisfy Dirichlet's conditions

Fundemental period of $x(t) = \sum_{k=-\infty}^{\infty}\operatorname{rect}(\frac{t+k}{2c})$

Is there a closed form, or a series approximation, for $ f(x)=\int_{1}^{x} \left(\cos\left( \frac{\pi r}{t}\right)+\cos(\pi t)\right)^{N}dt $?

When is the period of a periodic function not defined? Examples?

Prove this function is periodic.

If $n,k$ are odd numbers, proof that all solutions of the ODE $x^{''}+x^k+x^n=0$ are periodic.

Residues at poles of periodic functions

How do you go from a discrete sum of waves $u(x)=\sum_{i=1}^n a_i e^{ikx}$ to a continuous integral $u(x)=\int_{-\infty}^{+\infty} A(k) e^{ikx} dk$

Prove all solutions to $ x^{\prime}=A(t) x, \quad x(0)=x_0 $ are $T$-periodic.

Overlap between two periodic intervals

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