Mixing
Comparing two infinitely large functions
$begingroup$
I have $ f(x)=frac{x*arctgx}{sqrt{4x+3}} $
And $ g(x)=sqrt x - {x}^{1/3} $
Limits of both functions are infinity, so these functions are infinitely large .
I need to write equivalent functions for both as $ C{x}^{n} $ and find out order of growth/smallness of functions and then compare f(x) and g(x).
I don't no how to write equivalent for f(x) and what are common ideas of tasks like this, in my lecture copybook I didn't find anything/
calculus limits functions
edited Jan 16 at 9:10
MaoWao
3,318617
asked Jan 16 at 8:48
TovarischTovarisch
297
$endgroup$
add a comment |
$begingroup$
I have $ f(x)=frac{x*arctgx}{sqrt{4x+3}} $
And $ g(x)=sqrt x - {x}^{1/3} $
Limits of both functions are infinity, so these functions are infinitely large .
I need to write equivalent functions for both as $ C{x}^{n} $ and find out order of growth/smallness of functions and then compare f(x) and g(x).
I don't no how to write equivalent for f(x) and what are common ideas of tasks like this, in my lecture copybook I didn't find anything/
calculus limits functions
edited Jan 16 at 9:10
MaoWao
3,318617
asked Jan 16 at 8:48
TovarischTovarisch
297
$endgroup$
add a comment |
$begingroup$
I have $ f(x)=frac{x*arctgx}{sqrt{4x+3}} $
And $ g(x)=sqrt x - {x}^{1/3} $
Limits of both functions are infinity, so these functions are infinitely large .
I need to write equivalent functions for both as $ C{x}^{n} $ and find out order of growth/smallness of functions and then compare f(x) and g(x).
I don't no how to write equivalent for f(x) and what are common ideas of tasks like this, in my lecture copybook I didn't find anything/
calculus limits functions
edited Jan 16 at 9:10
MaoWao
3,318617
asked Jan 16 at 8:48
TovarischTovarisch
297
$endgroup$
I have $ f(x)=frac{x*arctgx}{sqrt{4x+3}} $
And $ g(x)=sqrt x - {x}^{1/3} $
Limits of both functions are infinity, so these functions are infinitely large .
I need to write equivalent functions for both as $ C{x}^{n} $ and find out order of growth/smallness of functions and then compare f(x) and g(x).
I don't no how to write equivalent for f(x) and what are common ideas of tasks like this, in my lecture copybook I didn't find anything/
calculus limits functions
calculus limits functions
edited Jan 16 at 9:10
MaoWao
3,318617
asked Jan 16 at 8:48
TovarischTovarisch
297
edited Jan 16 at 9:10
MaoWao
3,318617
asked Jan 16 at 8:48
TovarischTovarisch
297
edited Jan 16 at 9:10
MaoWao
3,318617
edited Jan 16 at 9:10
MaoWao
3,318617
edited Jan 16 at 9:10
MaoWao
3,318617
3,318617
asked Jan 16 at 8:48
TovarischTovarisch
297
asked Jan 16 at 8:48
TovarischTovarisch
297
asked Jan 16 at 8:48
TovarischTovarisch
297
297
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$f(x)=x^{1/2} frac {arctan (x)} {sqrt {4+frac 3 x}}$ and $g(x)=x^{1/2} (1-x^{frac 1 3 -frac 1 2})$. So both functions behave like $x^{1/2}$ when $x to infty$ and $lim frac {f(x)} {g(x)}=frac {pi} 4$ as $x to infty$.
answered Jan 16 at 8:53
Kavi Rama MurthyKavi Rama Murthy
61.7k42262
$endgroup$
$begingroup$
I guess you forgot a square root in the denominator of $f(x)$. Then the limit will be $pi/4$.
$endgroup$
– Toffomat
Jan 16 at 9:30
$begingroup$
@Toffomat Right. Thanks for pointing out.
$endgroup$
– Kavi Rama Murthy
Jan 16 at 9:32
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%2f3075487%2fcomparing-two-infinitely-large-functions%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
$begingroup$
$f(x)=x^{1/2} frac {arctan (x)} {sqrt {4+frac 3 x}}$ and $g(x)=x^{1/2} (1-x^{frac 1 3 -frac 1 2})$. So both functions behave like $x^{1/2}$ when $x to infty$ and $lim frac {f(x)} {g(x)}=frac {pi} 4$ as $x to infty$.
answered Jan 16 at 8:53
Kavi Rama MurthyKavi Rama Murthy
61.7k42262
$endgroup$
$begingroup$
I guess you forgot a square root in the denominator of $f(x)$. Then the limit will be $pi/4$.
$endgroup$
– Toffomat
Jan 16 at 9:30
$begingroup$
@Toffomat Right. Thanks for pointing out.
$endgroup$
– Kavi Rama Murthy
Jan 16 at 9:32
add a comment |
$begingroup$
$f(x)=x^{1/2} frac {arctan (x)} {sqrt {4+frac 3 x}}$ and $g(x)=x^{1/2} (1-x^{frac 1 3 -frac 1 2})$. So both functions behave like $x^{1/2}$ when $x to infty$ and $lim frac {f(x)} {g(x)}=frac {pi} 4$ as $x to infty$.
answered Jan 16 at 8:53
Kavi Rama MurthyKavi Rama Murthy
61.7k42262
$endgroup$
$begingroup$
I guess you forgot a square root in the denominator of $f(x)$. Then the limit will be $pi/4$.
$endgroup$
– Toffomat
Jan 16 at 9:30
$begingroup$
@Toffomat Right. Thanks for pointing out.
$endgroup$
– Kavi Rama Murthy
Jan 16 at 9:32
add a comment |
$begingroup$
$f(x)=x^{1/2} frac {arctan (x)} {sqrt {4+frac 3 x}}$ and $g(x)=x^{1/2} (1-x^{frac 1 3 -frac 1 2})$. So both functions behave like $x^{1/2}$ when $x to infty$ and $lim frac {f(x)} {g(x)}=frac {pi} 4$ as $x to infty$.
answered Jan 16 at 8:53
Kavi Rama MurthyKavi Rama Murthy
61.7k42262
$endgroup$
$f(x)=x^{1/2} frac {arctan (x)} {sqrt {4+frac 3 x}}$ and $g(x)=x^{1/2} (1-x^{frac 1 3 -frac 1 2})$. So both functions behave like $x^{1/2}$ when $x to infty$ and $lim frac {f(x)} {g(x)}=frac {pi} 4$ as $x to infty$.
answered Jan 16 at 8:53
Kavi Rama MurthyKavi Rama Murthy
61.7k42262
edited Jan 16 at 9:31
answered Jan 16 at 8:53
Kavi Rama MurthyKavi Rama Murthy
61.7k42262
answered Jan 16 at 8:53
Kavi Rama MurthyKavi Rama Murthy
61.7k42262
answered Jan 16 at 8:53
Kavi Rama MurthyKavi Rama Murthy
61.7k42262
61.7k42262
$begingroup$
I guess you forgot a square root in the denominator of $f(x)$. Then the limit will be $pi/4$.
$endgroup$
– Toffomat
Jan 16 at 9:30
$begingroup$
@Toffomat Right. Thanks for pointing out.
$endgroup$
– Kavi Rama Murthy
Jan 16 at 9:32
add a comment |
$begingroup$
I guess you forgot a square root in the denominator of $f(x)$. Then the limit will be $pi/4$.
$endgroup$
– Toffomat
Jan 16 at 9:30
$begingroup$
@Toffomat Right. Thanks for pointing out.
$endgroup$
– Kavi Rama Murthy
Jan 16 at 9:32
$begingroup$
I guess you forgot a square root in the denominator of $f(x)$. Then the limit will be $pi/4$.
$endgroup$
– Toffomat
Jan 16 at 9:30
$begingroup$
I guess you forgot a square root in the denominator of $f(x)$. Then the limit will be $pi/4$.
$endgroup$
– Toffomat
Jan 16 at 9:30
$begingroup$
@Toffomat Right. Thanks for pointing out.
$endgroup$
– Kavi Rama Murthy
Jan 16 at 9:32
$begingroup$
@Toffomat Right. Thanks for pointing out.
$endgroup$
– Kavi Rama Murthy
Jan 16 at 9:32
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%2f3075487%2fcomparing-two-infinitely-large-functions%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
