Advance Calculus Limit question The Next CEO of Stack OverflowLimit finding of an indeterminate formI need compute a rational limit that involves rootsComplex Limit Without L'hopital'sLimit of $x^2e^x $as $x$ approaches negative infinity without using L'hopital's ruleSolving limit of radicals without L'Hopital $lim_xto 64 dfracsqrt x - 8sqrt[3] x - 4 $Solve a limit without L'Hopital: $ lim_xto0 fracln(cos5x)ln(cos7x)$Limit question - L'Hopital's rule doesn't seem to workHow can I solve this limit without L'Hopital rule?Find a limit of a function W/OUT l'Hopital's rule.Compute $lim_x rightarrow 4 frac(2x^2 - 7x -4)(-x^2 + 8x - 16)$
Why did the Drakh emissary look so blurred in S04:E11 "Lines of Communication"?
Upgrading From a 9 Speed Sora Derailleur?
How to pronounce fünf in 45
Can you teleport closer to a creature you are Frightened of?
How badly should I try to prevent a user from XSSing themselves?
What is the difference between 'contrib' and 'non-free' packages repositories?
How dangerous is XSS
Why was Sir Cadogan fired?
Do I need to write [sic] when including a quotation with a number less than 10 that isn't written out?
Incomplete cube
Is it "common practice in Fourier transform spectroscopy to multiply the measured interferogram by an apodizing function"? If so, why?
How to coordinate airplane tickets?
Prodigo = pro + ago?
Creating a script with console commands
Why do we say “un seul M” and not “une seule M” even though M is a “consonne”?
Is it okay to majorly distort historical facts while writing a fiction story?
Is it OK to decorate a log book cover?
That's an odd coin - I wonder why
Can this transistor (2N2222) take 6 V on emitter-base? Am I reading the datasheet incorrectly?
How can I prove that a state of equilibrium is unstable?
pgfplots: How to draw a tangent graph below two others?
Can I cast Thunderwave and be at the center of its bottom face, but not be affected by it?
Another proof that dividing by 0 does not exist -- is it right?
logical reads on global temp table, but not on session-level temp table
Advance Calculus Limit question
The Next CEO of Stack OverflowLimit finding of an indeterminate formI need compute a rational limit that involves rootsComplex Limit Without L'hopital'sLimit of $x^2e^x $as $x$ approaches negative infinity without using L'hopital's ruleSolving limit of radicals without L'Hopital $lim_xto 64 dfracsqrt x - 8sqrt[3] x - 4 $Solve a limit without L'Hopital: $ lim_xto0 fracln(cos5x)ln(cos7x)$Limit question - L'Hopital's rule doesn't seem to workHow can I solve this limit without L'Hopital rule?Find a limit of a function W/OUT l'Hopital's rule.Compute $lim_x rightarrow 4 frac(2x^2 - 7x -4)(-x^2 + 8x - 16)$
$begingroup$
I'm trying to compute this limit without the use of L'Hopital's rule:
$$lim_x to 0^+ frac4^-1/x+4^1/x4^-1/x-4^1/x$$
I've been trying to multiply by the lcd and doing other creative stuff... anyone have any suggestions on theorems or techniques?
calculus limits limits-without-lhopital
edited 6 hours ago
Foobaz John
22.9k41552
asked 6 hours ago
Kevin CalderonKevin Calderon
563
$endgroup$
add a comment |
$begingroup$
I'm trying to compute this limit without the use of L'Hopital's rule:
$$lim_x to 0^+ frac4^-1/x+4^1/x4^-1/x-4^1/x$$
I've been trying to multiply by the lcd and doing other creative stuff... anyone have any suggestions on theorems or techniques?
calculus limits limits-without-lhopital
edited 6 hours ago
Foobaz John
22.9k41552
asked 6 hours ago
Kevin CalderonKevin Calderon
563
$endgroup$
add a comment |
$begingroup$
I'm trying to compute this limit without the use of L'Hopital's rule:
$$lim_x to 0^+ frac4^-1/x+4^1/x4^-1/x-4^1/x$$
I've been trying to multiply by the lcd and doing other creative stuff... anyone have any suggestions on theorems or techniques?
calculus limits limits-without-lhopital
edited 6 hours ago
Foobaz John
22.9k41552
asked 6 hours ago
Kevin CalderonKevin Calderon
563
$endgroup$
I'm trying to compute this limit without the use of L'Hopital's rule:
$$lim_x to 0^+ frac4^-1/x+4^1/x4^-1/x-4^1/x$$
I've been trying to multiply by the lcd and doing other creative stuff... anyone have any suggestions on theorems or techniques?
calculus limits limits-without-lhopital
calculus limits limits-without-lhopital
edited 6 hours ago
Foobaz John
22.9k41552
asked 6 hours ago
Kevin CalderonKevin Calderon
563
edited 6 hours ago
Foobaz John
22.9k41552
asked 6 hours ago
Kevin CalderonKevin Calderon
563
edited 6 hours ago
Foobaz John
22.9k41552
edited 6 hours ago
Foobaz John
22.9k41552
edited 6 hours ago
Foobaz John
22.9k41552
22.9k41552
asked 6 hours ago
Kevin CalderonKevin Calderon
563
asked 6 hours ago
Kevin CalderonKevin Calderon
563
asked 6 hours ago
Kevin CalderonKevin Calderon
563
563
add a comment |
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Write the limit as
$$
lim_xto 0+frac1+4^-2/x-1+4^-2/x
$$
and use the fact that
$$
lim_xto 0+frac-2x=-infty.
$$
to find that the limit equals $-1$.
answered 6 hours ago
Foobaz JohnFoobaz John
22.9k41552
$endgroup$
add a comment |
$begingroup$
A substitution can be helpful, as it transforms the expression into a rational function:
- Set $y=4^frac1x$ and consider $y to +infty$
begineqnarray* frac4^-1/x+4^1/x4^-1/x-4^1/x
& stackrely=4^frac1x= & fracfrac1y+yfrac1y-y \
& = & fracfrac1y^2+1frac1y^2-1 \
& stackrely to +inftylongrightarrow & frac0+10-1 = -1
endeqnarray*
answered 2 hours ago
trancelocationtrancelocation
13.5k1827
$endgroup$
add a comment |
$begingroup$
$$lim_xto 0^+dfrac4^-1/x+4^1/x4^-1/x-4^1/x=lim_xto 0^+dfrac4^-2/x+14^-2/x-1$$
Clearly as $xto 0^+$, $2/xto infty$. Since the power of $4$ is $-2/x$, it must go to $0$. Effectively we have $frac0+10-1=-1$. Hence the required limit is $-1$.
answered 1 hour ago
Paras KhoslaParas Khosla
2,758423
$endgroup$
add a comment |
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%2f3171288%2fadvance-calculus-limit-question%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Write the limit as
$$
lim_xto 0+frac1+4^-2/x-1+4^-2/x
$$
and use the fact that
$$
lim_xto 0+frac-2x=-infty.
$$
to find that the limit equals $-1$.
answered 6 hours ago
Foobaz JohnFoobaz John
22.9k41552
$endgroup$
add a comment |
$begingroup$
Write the limit as
$$
lim_xto 0+frac1+4^-2/x-1+4^-2/x
$$
and use the fact that
$$
lim_xto 0+frac-2x=-infty.
$$
to find that the limit equals $-1$.
answered 6 hours ago
Foobaz JohnFoobaz John
22.9k41552
$endgroup$
add a comment |
$begingroup$
Write the limit as
$$
lim_xto 0+frac1+4^-2/x-1+4^-2/x
$$
and use the fact that
$$
lim_xto 0+frac-2x=-infty.
$$
to find that the limit equals $-1$.
answered 6 hours ago
Foobaz JohnFoobaz John
22.9k41552
$endgroup$
Write the limit as
$$
lim_xto 0+frac1+4^-2/x-1+4^-2/x
$$
and use the fact that
$$
lim_xto 0+frac-2x=-infty.
$$
to find that the limit equals $-1$.
answered 6 hours ago
Foobaz JohnFoobaz John
22.9k41552
answered 6 hours ago
Foobaz JohnFoobaz John
22.9k41552
answered 6 hours ago
Foobaz JohnFoobaz John
22.9k41552
answered 6 hours ago
Foobaz JohnFoobaz John
22.9k41552
22.9k41552
add a comment |
add a comment |
$begingroup$
A substitution can be helpful, as it transforms the expression into a rational function:
- Set $y=4^frac1x$ and consider $y to +infty$
begineqnarray* frac4^-1/x+4^1/x4^-1/x-4^1/x
& stackrely=4^frac1x= & fracfrac1y+yfrac1y-y \
& = & fracfrac1y^2+1frac1y^2-1 \
& stackrely to +inftylongrightarrow & frac0+10-1 = -1
endeqnarray*
answered 2 hours ago
trancelocationtrancelocation
13.5k1827
$endgroup$
add a comment |
$begingroup$
A substitution can be helpful, as it transforms the expression into a rational function:
- Set $y=4^frac1x$ and consider $y to +infty$
begineqnarray* frac4^-1/x+4^1/x4^-1/x-4^1/x
& stackrely=4^frac1x= & fracfrac1y+yfrac1y-y \
& = & fracfrac1y^2+1frac1y^2-1 \
& stackrely to +inftylongrightarrow & frac0+10-1 = -1
endeqnarray*
answered 2 hours ago
trancelocationtrancelocation
13.5k1827
$endgroup$
add a comment |
$begingroup$
A substitution can be helpful, as it transforms the expression into a rational function:
- Set $y=4^frac1x$ and consider $y to +infty$
begineqnarray* frac4^-1/x+4^1/x4^-1/x-4^1/x
& stackrely=4^frac1x= & fracfrac1y+yfrac1y-y \
& = & fracfrac1y^2+1frac1y^2-1 \
& stackrely to +inftylongrightarrow & frac0+10-1 = -1
endeqnarray*
answered 2 hours ago
trancelocationtrancelocation
13.5k1827
$endgroup$
A substitution can be helpful, as it transforms the expression into a rational function:
- Set $y=4^frac1x$ and consider $y to +infty$
begineqnarray* frac4^-1/x+4^1/x4^-1/x-4^1/x
& stackrely=4^frac1x= & fracfrac1y+yfrac1y-y \
& = & fracfrac1y^2+1frac1y^2-1 \
& stackrely to +inftylongrightarrow & frac0+10-1 = -1
endeqnarray*
answered 2 hours ago
trancelocationtrancelocation
13.5k1827
answered 2 hours ago
trancelocationtrancelocation
13.5k1827
answered 2 hours ago
trancelocationtrancelocation
13.5k1827
answered 2 hours ago
trancelocationtrancelocation
13.5k1827
13.5k1827
add a comment |
add a comment |
$begingroup$
$$lim_xto 0^+dfrac4^-1/x+4^1/x4^-1/x-4^1/x=lim_xto 0^+dfrac4^-2/x+14^-2/x-1$$
Clearly as $xto 0^+$, $2/xto infty$. Since the power of $4$ is $-2/x$, it must go to $0$. Effectively we have $frac0+10-1=-1$. Hence the required limit is $-1$.
answered 1 hour ago
Paras KhoslaParas Khosla
2,758423
$endgroup$
add a comment |
$begingroup$
$$lim_xto 0^+dfrac4^-1/x+4^1/x4^-1/x-4^1/x=lim_xto 0^+dfrac4^-2/x+14^-2/x-1$$
Clearly as $xto 0^+$, $2/xto infty$. Since the power of $4$ is $-2/x$, it must go to $0$. Effectively we have $frac0+10-1=-1$. Hence the required limit is $-1$.
answered 1 hour ago
Paras KhoslaParas Khosla
2,758423
$endgroup$
add a comment |
$begingroup$
$$lim_xto 0^+dfrac4^-1/x+4^1/x4^-1/x-4^1/x=lim_xto 0^+dfrac4^-2/x+14^-2/x-1$$
Clearly as $xto 0^+$, $2/xto infty$. Since the power of $4$ is $-2/x$, it must go to $0$. Effectively we have $frac0+10-1=-1$. Hence the required limit is $-1$.
answered 1 hour ago
Paras KhoslaParas Khosla
2,758423
$endgroup$
$$lim_xto 0^+dfrac4^-1/x+4^1/x4^-1/x-4^1/x=lim_xto 0^+dfrac4^-2/x+14^-2/x-1$$
Clearly as $xto 0^+$, $2/xto infty$. Since the power of $4$ is $-2/x$, it must go to $0$. Effectively we have $frac0+10-1=-1$. Hence the required limit is $-1$.
answered 1 hour ago
Paras KhoslaParas Khosla
2,758423
answered 1 hour ago
Paras KhoslaParas Khosla
2,758423
answered 1 hour ago
Paras KhoslaParas Khosla
2,758423
answered 1 hour ago
Paras KhoslaParas Khosla
2,758423
2,758423
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%2f3171288%2fadvance-calculus-limit-question%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
