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 $mathbbR$
Multi tool use
If the Captain's screens are out, does he switch seats with the co-pilot?
Do Bugbears' arms literally get longer when it's their turn?
Low budget alien movie about the Earth being cooked
Accountant/ lawyer will not return my call
Force user to remove USB token
Why does Captain Marvel assume the people on this planet know this?
Why does Deadpool say "You're welcome, Canada," after shooting Ryan Reynolds in the end credits?
Do items de-spawn in Diablo?
Word for a person who has no opinion about whether god exists
Latest web browser compatible with Windows 98
Subset counting for even numbers
In the late 1940’s to early 1950’s what technology was available that could melt a LOT of ice?
What are some noteworthy "mic-drop" moments in math?
Unreachable code, but reachable with exception
Is there any way to damage Intellect Devourer(s) when already within a creature's skull?
Why don't MCU characters ever seem to have language issues?
Peter's Strange Word
infinitive telling the purpose
What is the likely impact of grounding an entire aircraft series?
Should QA ask requirements to developers?
A three room house but a three headED dog
Best approach to update all entries in a list that is paginated?
Logic. Truth of a negation
Can someone explain what is being said here in color publishing in the American Mathematical Monthly?
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
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.
$endgroup$
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 |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Jacob Denicula is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3142171%2fshow-that-f-is-periodic-where-int-xxaftdt-b%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Jacob Denicula is a new contributor. Be nice, and check out our Code of Conduct.
Jacob Denicula is a new contributor. Be nice, and check out our Code of Conduct.
Jacob Denicula is a new contributor. Be nice, and check out our Code of Conduct.
Jacob Denicula is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3142171%2fshow-that-f-is-periodic-where-int-xxaftdt-b%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
oVdVUjixs0v6lMT8C8PBpDTEtCEIZ2DPJvVOg49fJHZWGqC7nEtR0Er9HL8l9SNzb7 jGeIcccCgKeNJ
$begingroup$
Yeah. It's logical.
$endgroup$
– SinTan1729
2 days ago