Mixing
Is $sup_{xin mathbb R} sqrt{|x|} sin x = + infty$?
$begingroup$
The graph of $sqrt{|x|} sin x$ seems like staying around the $x$-axis, but $lim_{xto infty} sqrt{|x|} = +infty$ and $sin x$ is bounded.
real-analysis analysis proof-explanation intuition
asked Feb 1 at 5:47
user398843user398843
708316
$endgroup$
add a comment |
$begingroup$
The graph of $sqrt{|x|} sin x$ seems like staying around the $x$-axis, but $lim_{xto infty} sqrt{|x|} = +infty$ and $sin x$ is bounded.
real-analysis analysis proof-explanation intuition
asked Feb 1 at 5:47
user398843user398843
708316
$endgroup$
$begingroup$
Perhaps a more interesting question is if you restrict $x$ to be an integer.
$endgroup$
– MathematicsStudent1122
Feb 1 at 5:53
add a comment |
$begingroup$
The graph of $sqrt{|x|} sin x$ seems like staying around the $x$-axis, but $lim_{xto infty} sqrt{|x|} = +infty$ and $sin x$ is bounded.
real-analysis analysis proof-explanation intuition
asked Feb 1 at 5:47
user398843user398843
708316
$endgroup$
The graph of $sqrt{|x|} sin x$ seems like staying around the $x$-axis, but $lim_{xto infty} sqrt{|x|} = +infty$ and $sin x$ is bounded.
real-analysis analysis proof-explanation intuition
real-analysis analysis proof-explanation intuition
asked Feb 1 at 5:47
user398843user398843
708316
asked Feb 1 at 5:47
user398843user398843
708316
asked Feb 1 at 5:47
user398843user398843
708316
asked Feb 1 at 5:47
user398843user398843
708316
asked Feb 1 at 5:47
user398843user398843
708316
708316
$begingroup$
Perhaps a more interesting question is if you restrict $x$ to be an integer.
$endgroup$
– MathematicsStudent1122
Feb 1 at 5:53
add a comment |
$begingroup$
Perhaps a more interesting question is if you restrict $x$ to be an integer.
$endgroup$
– MathematicsStudent1122
Feb 1 at 5:53
$begingroup$
Perhaps a more interesting question is if you restrict $x$ to be an integer.
$endgroup$
– MathematicsStudent1122
Feb 1 at 5:53
$begingroup$
Perhaps a more interesting question is if you restrict $x$ to be an integer.
$endgroup$
– MathematicsStudent1122
Feb 1 at 5:53
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Let $x = frac{pi}2 +2npi$,
Then, $$sqrt{|x|} sin x=sqrt{frac{pi}2+2npi}$$
Now, let $nto infty$ to get your result.
answered Feb 1 at 5:52
Siong Thye GohSiong Thye Goh
104k1468120
$endgroup$
add a comment |
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
});
}
});
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%2f3095867%2fis-sup-x-in-mathbb-r-sqrtx-sin-x-infty%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Let $x = frac{pi}2 +2npi$,
Then, $$sqrt{|x|} sin x=sqrt{frac{pi}2+2npi}$$
Now, let $nto infty$ to get your result.
answered Feb 1 at 5:52
Siong Thye GohSiong Thye Goh
104k1468120
$endgroup$
add a comment |
$begingroup$
Let $x = frac{pi}2 +2npi$,
Then, $$sqrt{|x|} sin x=sqrt{frac{pi}2+2npi}$$
Now, let $nto infty$ to get your result.
answered Feb 1 at 5:52
Siong Thye GohSiong Thye Goh
104k1468120
$endgroup$
add a comment |
$begingroup$
Let $x = frac{pi}2 +2npi$,
Then, $$sqrt{|x|} sin x=sqrt{frac{pi}2+2npi}$$
Now, let $nto infty$ to get your result.
answered Feb 1 at 5:52
Siong Thye GohSiong Thye Goh
104k1468120
$endgroup$
Let $x = frac{pi}2 +2npi$,
Then, $$sqrt{|x|} sin x=sqrt{frac{pi}2+2npi}$$
Now, let $nto infty$ to get your result.
answered Feb 1 at 5:52
Siong Thye GohSiong Thye Goh
104k1468120
answered Feb 1 at 5:52
Siong Thye GohSiong Thye Goh
104k1468120
answered Feb 1 at 5:52
Siong Thye GohSiong Thye Goh
104k1468120
answered Feb 1 at 5:52
Siong Thye GohSiong Thye Goh
104k1468120
104k1468120
add a comment |
add a comment |
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%2f3095867%2fis-sup-x-in-mathbb-r-sqrtx-sin-x-infty%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
$begingroup$
Perhaps a more interesting question is if you restrict $x$ to be an integer.
$endgroup$
– MathematicsStudent1122
Feb 1 at 5:53