Why $lim_{xto0^+}{frac bxleft[frac xaright]}=0$?, where $[x] = sup{n in N, n leq x}$
0
$begingroup$
I ask this question here, and I was told that using squezze theorem I could solve it, but using this idea in this limit I end with.
$frac{b}{a} leq lim_{xto0^+}{frac bxleft[frac xaright]} leq infty$
Why?
calculus limits fractions
edited Dec 14 '18 at 16:00
Matt Samuel
38.5k63768
asked Dec 14 '18 at 15:55
Maria GuthierMaria Guthier
887
$endgroup$
add a comment |
0
$begingroup$
I ask this question here, and I was told that using squezze theorem I could solve it, but using this idea in this limit I end with.
$frac{b}{a} leq lim_{xto0^+}{frac bxleft[frac xaright]} leq infty$
Why?
calculus limits fractions
edited Dec 14 '18 at 16:00
Matt Samuel
38.5k63768
asked Dec 14 '18 at 15:55
Maria GuthierMaria Guthier
887
$endgroup$
$begingroup$
Been attempting to fix your title, I see you've been helping. Seems better to me now.
$endgroup$
– Matt Samuel
Dec 14 '18 at 16:00
$begingroup$
Yeah, first edit don't work out, but I appreciate your help.
$endgroup$
– Maria Guthier
Dec 14 '18 at 16:01
add a comment |
0
0
0
$begingroup$
I ask this question here, and I was told that using squezze theorem I could solve it, but using this idea in this limit I end with.
$frac{b}{a} leq lim_{xto0^+}{frac bxleft[frac xaright]} leq infty$
Why?
calculus limits fractions
edited Dec 14 '18 at 16:00
Matt Samuel
38.5k63768
asked Dec 14 '18 at 15:55
Maria GuthierMaria Guthier
887
$endgroup$
I ask this question here, and I was told that using squezze theorem I could solve it, but using this idea in this limit I end with.
$frac{b}{a} leq lim_{xto0^+}{frac bxleft[frac xaright]} leq infty$
Why?
calculus limits fractions
calculus limits fractions
edited Dec 14 '18 at 16:00
Matt Samuel
38.5k63768
asked Dec 14 '18 at 15:55
Maria GuthierMaria Guthier
887
edited Dec 14 '18 at 16:00
Matt Samuel
38.5k63768
asked Dec 14 '18 at 15:55
Maria GuthierMaria Guthier
887
edited Dec 14 '18 at 16:00
Matt Samuel
38.5k63768
edited Dec 14 '18 at 16:00
Matt Samuel
38.5k63768
edited Dec 14 '18 at 16:00
Matt Samuel
38.5k63768
38.5k63768
asked Dec 14 '18 at 15:55
Maria GuthierMaria Guthier
887
asked Dec 14 '18 at 15:55
Maria GuthierMaria Guthier
887
asked Dec 14 '18 at 15:55
Maria GuthierMaria Guthier
887
887
$begingroup$
Been attempting to fix your title, I see you've been helping. Seems better to me now.
$endgroup$
– Matt Samuel
Dec 14 '18 at 16:00
$begingroup$
Yeah, first edit don't work out, but I appreciate your help.
$endgroup$
– Maria Guthier
Dec 14 '18 at 16:01
add a comment |
$begingroup$
Been attempting to fix your title, I see you've been helping. Seems better to me now.
$endgroup$
– Matt Samuel
Dec 14 '18 at 16:00
$begingroup$
Yeah, first edit don't work out, but I appreciate your help.
$endgroup$
– Maria Guthier
Dec 14 '18 at 16:01
$begingroup$
Been attempting to fix your title, I see you've been helping. Seems better to me now.
$endgroup$
– Matt Samuel
Dec 14 '18 at 16:00
$begingroup$
Been attempting to fix your title, I see you've been helping. Seems better to me now.
$endgroup$
– Matt Samuel
Dec 14 '18 at 16:00
$begingroup$
Yeah, first edit don't work out, but I appreciate your help.
$endgroup$
– Maria Guthier
Dec 14 '18 at 16:01
$begingroup$
Yeah, first edit don't work out, but I appreciate your help.
$endgroup$
– Maria Guthier
Dec 14 '18 at 16:01
add a comment |
1 Answer
1
active
oldest
votes
2
$begingroup$
Hint: $x-1leq left [ x right ]leq x$
answered Dec 14 '18 at 15:58
John11John11
1,0321821
$endgroup$
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
});
}
});
draft saved
draft discarded
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%2f3039534%2fwhy-lim-x-to0-frac-bx-left-frac-xa-right-0-where-x-sup-n-in%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
2
$begingroup$
Hint: $x-1leq left [ x right ]leq x$
answered Dec 14 '18 at 15:58
John11John11
1,0321821
$endgroup$
add a comment |
2
$begingroup$
Hint: $x-1leq left [ x right ]leq x$
answered Dec 14 '18 at 15:58
John11John11
1,0321821
$endgroup$
add a comment |
2
2
2
$begingroup$
Hint: $x-1leq left [ x right ]leq x$
answered Dec 14 '18 at 15:58
John11John11
1,0321821
$endgroup$
Hint: $x-1leq left [ x right ]leq x$
answered Dec 14 '18 at 15:58
John11John11
1,0321821
answered Dec 14 '18 at 15:58
John11John11
1,0321821
answered Dec 14 '18 at 15:58
John11John11
1,0321821
answered Dec 14 '18 at 15:58
John11John11
1,0321821
1,0321821
add a comment |
add a comment |
draft saved
draft discarded
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.
draft saved
draft discarded
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%2f3039534%2fwhy-lim-x-to0-frac-bx-left-frac-xa-right-0-where-x-sup-n-in%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
$begingroup$
Been attempting to fix your title, I see you've been helping. Seems better to me now.
$endgroup$
– Matt Samuel
Dec 14 '18 at 16:00
$begingroup$
Yeah, first edit don't work out, but I appreciate your help.
$endgroup$
– Maria Guthier
Dec 14 '18 at 16:01