Show that $f$ is periodic, where $int_x^x+af(t)dt=b$Differential Equation has a unique solution periodicHow do I show that all continuous periodic functions are bounded and uniform continuous?determine if a function is periodicCompute Limit Involving Integral and Periodic functionQuestion about a continuous periodic functionPeriodic solution: ODEIntegration of a Periodic FunctionProve that $F(x)=int_0^x f$ is periodicIs this function periodic function?Show that $lim_ntoinfty int_0^1f(x)g(nx)dx = 0$ $g$ periodic on $mathbbR$
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Show that $f$ is periodic, where $int_x^x+af(t)dt=b$
Differential Equation has a unique solution periodicHow do I show that all continuous periodic functions are bounded and uniform continuous?determine if a function is periodicCompute Limit Involving Integral and Periodic functionQuestion about a continuous periodic functionPeriodic solution: ODEIntegration of a Periodic FunctionProve that $F(x)=int_0^x f$ is periodicIs this function periodic function?Show that $lim_ntoinfty int_0^1f(x)g(nx)dx = 0$ $g$ periodic on $mathbbR$
$begingroup$
Let $f:mathbbRrightarrowmathbbR$ continuous, for which there is an $a>0$, $binmathbbR$ such that $int_x^x+af(t)dt=b$, any $xinmathbbR$. Show that $f$ is periodic. By $F(x)=int_0^xf(t)dt$, I get that $b=F(x+a)-F(x)$ (Leibniz-Newton theorem) and by differentiating, the period is $a$. Is this sufficient?
integration definite-integrals periodic-functions
asked 2 days ago
Jacob DeniculaJacob Denicula
554
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Jacob Denicula is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$
add a comment |
$begingroup$
Let $f:mathbbRrightarrowmathbbR$ continuous, for which there is an $a>0$, $binmathbbR$ such that $int_x^x+af(t)dt=b$, any $xinmathbbR$. Show that $f$ is periodic. By $F(x)=int_0^xf(t)dt$, I get that $b=F(x+a)-F(x)$ (Leibniz-Newton theorem) and by differentiating, the period is $a$. Is this sufficient?
integration definite-integrals periodic-functions
asked 2 days ago
Jacob DeniculaJacob Denicula
554
New contributor
Jacob Denicula is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Yeah. It's logical.
$endgroup$
– SinTan1729
2 days ago
add a comment |
$begingroup$
Let $f:mathbbRrightarrowmathbbR$ continuous, for which there is an $a>0$, $binmathbbR$ such that $int_x^x+af(t)dt=b$, any $xinmathbbR$. Show that $f$ is periodic. By $F(x)=int_0^xf(t)dt$, I get that $b=F(x+a)-F(x)$ (Leibniz-Newton theorem) and by differentiating, the period is $a$. Is this sufficient?
integration definite-integrals periodic-functions
asked 2 days ago
Jacob DeniculaJacob Denicula
554
New contributor
Jacob Denicula is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Let $f:mathbbRrightarrowmathbbR$ continuous, for which there is an $a>0$, $binmathbbR$ such that $int_x^x+af(t)dt=b$, any $xinmathbbR$. Show that $f$ is periodic. By $F(x)=int_0^xf(t)dt$, I get that $b=F(x+a)-F(x)$ (Leibniz-Newton theorem) and by differentiating, the period is $a$. Is this sufficient?
integration definite-integrals periodic-functions
integration definite-integrals periodic-functions
asked 2 days ago
Jacob DeniculaJacob Denicula
554
New contributor
Jacob Denicula is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Jacob DeniculaJacob Denicula
554
New contributor
Jacob Denicula is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Jacob DeniculaJacob Denicula
554
New contributor
Jacob Denicula is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Jacob DeniculaJacob Denicula
554
asked 2 days ago
Jacob DeniculaJacob Denicula
554
554
New contributor
Jacob Denicula is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Jacob Denicula is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Jacob Denicula is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
Yeah. It's logical.
$endgroup$
– SinTan1729
2 days ago
add a comment |
$begingroup$
Yeah. It's logical.
$endgroup$
– SinTan1729
2 days ago
$begingroup$
Yeah. It's logical.
$endgroup$
– SinTan1729
2 days ago
$begingroup$
Yeah. It's logical.
$endgroup$
– SinTan1729
2 days ago
add a comment |
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$begingroup$
Yeah. It's logical.
$endgroup$
– SinTan1729
2 days ago