Finding the limit without L'Hospital?How to evaluate this limit without using L'Hospital's rule?Finding the limit without L'Hospital's rule.Limit using l'hospitalFinding $lim_xto -2fracx+2sqrt-x-1-1;$ without L'HospitalEvaluating $lim_xto 0fracsin^2x2x^2$ without L'HospitalHint on finding limit without application of L'Hospital's rule (mathematical analysis)How to solve this limit without L'Hospital?Solving the following limit without L'Hospital Rule: $lim_xto1left(x-1right)tanleft(fracpi x2right)$?$lim_x to 2 fraccosleft(fracpixright)x-2$ without using De L'HospitalFinding Limit related to third derivative without L'Hospital
Non-trivial topology where only open sets are closed
If I can solve Sudoku, can I solve the Travelling Salesman Problem (TSP)? If so, how?
Why did it take so long to abandon sail after steamships were demonstrated?
Describing a chess game in a novel
et qui - how do you really understand that kind of phraseology?
I got the following comment from a reputed math journal. What does it mean?
How do you talk to someone whose loved one is dying?
Why does a Star of David appear at a rally with Francisco Franco?
Why do newer 737s use two different styles of split winglets?
Why do tuner card drivers fail to build after kernel update to 4.4.0-143-generic?
Are Roman Catholic priests ever addressed as pastor
Does .bashrc contain syntax errors?
Happy pi day, everyone!
Professor being mistaken for a grad student
Have the tides ever turned twice on any open problem?
Adventure Game (text based) in C++
Does multi-classing into Fighter give you heavy armor proficiency?
Custom alignment for GeoMarkers
Bacteria contamination inside a thermos bottle
How difficult is it to simply disable/disengage the MCAS on Boeing 737 Max 8 & 9 Aircraft?
Bach's Toccata and Fugue in D minor breaks the "no parallel octaves" rule?
How can we have a quark condensate without a quark potential?
What are substitutions for coconut in curry?
A single argument pattern definition applies to multiple-argument patterns?
Finding the limit without L'Hospital?
How to evaluate this limit without using L'Hospital's rule?Finding the limit without L'Hospital's rule.Limit using l'hospitalFinding $lim_xto -2fracx+2sqrt-x-1-1;$ without L'HospitalEvaluating $lim_xto 0fracsin^2x2x^2$ without L'HospitalHint on finding limit without application of L'Hospital's rule (mathematical analysis)How to solve this limit without L'Hospital?Solving the following limit without L'Hospital Rule: $lim_xto1left(x-1right)tanleft(fracpi x2right)$?$lim_x to 2 fraccosleft(fracpixright)x-2$ without using De L'HospitalFinding Limit related to third derivative without L'Hospital
$begingroup$
How to evaluate the limit without using the L'Hospital's rule? I have tried using L'Hospital's rule and got the value as 1.
limit x approaches 0 ((1+2x)-(1+3x)^(2/3))/(x^2)
limits-without-lhopital
edited Mar 12 at 11:35
Bernard
123k741116
asked Mar 12 at 11:19
yalamyalam
61
New contributor
yalam 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 |
$begingroup$
How to evaluate the limit without using the L'Hospital's rule? I have tried using L'Hospital's rule and got the value as 1.
limit x approaches 0 ((1+2x)-(1+3x)^(2/3))/(x^2)
limits-without-lhopital
edited Mar 12 at 11:35
Bernard
123k741116
asked Mar 12 at 11:19
yalamyalam
61
New contributor
yalam is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
2
$begingroup$
Which limit? Please write the problem with MathJax.
$endgroup$
– Matti P.
Mar 12 at 11:19
$begingroup$
Is this $$lim_x to 0frac1+2x-(1+3x)^2/3x^2$$?
$endgroup$
– Dr. Sonnhard Graubner
Mar 12 at 11:25
$begingroup$
Yes! the problem is correct.
$endgroup$
– yalam
Mar 12 at 11:29
$begingroup$
Use Taylor's formula at order $2$ for $(1+3x)^3/2$.
$endgroup$
– Bernard
Mar 12 at 11:38
add a comment |
$begingroup$
How to evaluate the limit without using the L'Hospital's rule? I have tried using L'Hospital's rule and got the value as 1.
limit x approaches 0 ((1+2x)-(1+3x)^(2/3))/(x^2)
limits-without-lhopital
edited Mar 12 at 11:35
Bernard
123k741116
asked Mar 12 at 11:19
yalamyalam
61
New contributor
yalam is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
How to evaluate the limit without using the L'Hospital's rule? I have tried using L'Hospital's rule and got the value as 1.
limit x approaches 0 ((1+2x)-(1+3x)^(2/3))/(x^2)
limits-without-lhopital
limits-without-lhopital
edited Mar 12 at 11:35
Bernard
123k741116
asked Mar 12 at 11:19
yalamyalam
61
New contributor
yalam is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Mar 12 at 11:35
Bernard
123k741116
asked Mar 12 at 11:19
yalamyalam
61
New contributor
yalam is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Mar 12 at 11:35
Bernard
123k741116
edited Mar 12 at 11:35
Bernard
123k741116
edited Mar 12 at 11:35
Bernard
123k741116
123k741116
asked Mar 12 at 11:19
yalamyalam
61
New contributor
yalam is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 12 at 11:19
yalamyalam
61
asked Mar 12 at 11:19
yalamyalam
61
61
New contributor
yalam is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
yalam is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
yalam is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
$begingroup$
Which limit? Please write the problem with MathJax.
$endgroup$
– Matti P.
Mar 12 at 11:19
$begingroup$
Is this $$lim_x to 0frac1+2x-(1+3x)^2/3x^2$$?
$endgroup$
– Dr. Sonnhard Graubner
Mar 12 at 11:25
$begingroup$
Yes! the problem is correct.
$endgroup$
– yalam
Mar 12 at 11:29
$begingroup$
Use Taylor's formula at order $2$ for $(1+3x)^3/2$.
$endgroup$
– Bernard
Mar 12 at 11:38
add a comment |
2
$begingroup$
Which limit? Please write the problem with MathJax.
$endgroup$
– Matti P.
Mar 12 at 11:19
$begingroup$
Is this $$lim_x to 0frac1+2x-(1+3x)^2/3x^2$$?
$endgroup$
– Dr. Sonnhard Graubner
Mar 12 at 11:25
$begingroup$
Yes! the problem is correct.
$endgroup$
– yalam
Mar 12 at 11:29
$begingroup$
Use Taylor's formula at order $2$ for $(1+3x)^3/2$.
$endgroup$
– Bernard
Mar 12 at 11:38
2
2
$begingroup$
Which limit? Please write the problem with MathJax.
$endgroup$
– Matti P.
Mar 12 at 11:19
$begingroup$
Which limit? Please write the problem with MathJax.
$endgroup$
– Matti P.
Mar 12 at 11:19
$begingroup$
Is this $$lim_x to 0frac1+2x-(1+3x)^2/3x^2$$?
$endgroup$
– Dr. Sonnhard Graubner
Mar 12 at 11:25
$begingroup$
Is this $$lim_x to 0frac1+2x-(1+3x)^2/3x^2$$?
$endgroup$
– Dr. Sonnhard Graubner
Mar 12 at 11:25
$begingroup$
Yes! the problem is correct.
$endgroup$
– yalam
Mar 12 at 11:29
$begingroup$
Yes! the problem is correct.
$endgroup$
– yalam
Mar 12 at 11:29
$begingroup$
Use Taylor's formula at order $2$ for $(1+3x)^3/2$.
$endgroup$
– Bernard
Mar 12 at 11:38
$begingroup$
Use Taylor's formula at order $2$ for $(1+3x)^3/2$.
$endgroup$
– Bernard
Mar 12 at 11:38
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
$(1+3x)^frac23 ≈ 1 + (2/3)(3x) + 0.5(2/3)(-1/3)(3x)^2$
So, $1 + 2x - (1+3x)^frac23 ≈ x^2$
Hence desired limit is $1$
edited Mar 13 at 9:10
YuiTo Cheng
2,0532637
answered Mar 12 at 11:41
Prakhar NeemaPrakhar Neema
1074
New contributor
Prakhar Neema is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Thank you for your suggestion. I am still looking for a method without the T-series expansion or differentiation.
$endgroup$
– yalam
Mar 12 at 11:45
$begingroup$
What about binomial series?
$endgroup$
– user361424
yesterday
add a comment |
$begingroup$
Rationalize the numerator using $a-b=dfraca^3-b^3a^2+ab+b^2$ for $ane b$
to find
$$lim_xto0dfrac(1+2x)^3-(1+3x)^2x^2cdotlim_xto0dfrac1(1+2x)^2+(1+2x)(1+3x)^2/3+(1+3x)^4/3==?$$
answered 21 hours ago
lab bhattacharjeelab bhattacharjee
227k15158275
$endgroup$
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
);
);
yalam 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%2f3144971%2ffinding-the-limit-without-lhospital%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$(1+3x)^frac23 ≈ 1 + (2/3)(3x) + 0.5(2/3)(-1/3)(3x)^2$
So, $1 + 2x - (1+3x)^frac23 ≈ x^2$
Hence desired limit is $1$
edited Mar 13 at 9:10
YuiTo Cheng
2,0532637
answered Mar 12 at 11:41
Prakhar NeemaPrakhar Neema
1074
New contributor
Prakhar Neema is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Thank you for your suggestion. I am still looking for a method without the T-series expansion or differentiation.
$endgroup$
– yalam
Mar 12 at 11:45
$begingroup$
What about binomial series?
$endgroup$
– user361424
yesterday
add a comment |
$begingroup$
$(1+3x)^frac23 ≈ 1 + (2/3)(3x) + 0.5(2/3)(-1/3)(3x)^2$
So, $1 + 2x - (1+3x)^frac23 ≈ x^2$
Hence desired limit is $1$
edited Mar 13 at 9:10
YuiTo Cheng
2,0532637
answered Mar 12 at 11:41
Prakhar NeemaPrakhar Neema
1074
New contributor
Prakhar Neema is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Thank you for your suggestion. I am still looking for a method without the T-series expansion or differentiation.
$endgroup$
– yalam
Mar 12 at 11:45
$begingroup$
What about binomial series?
$endgroup$
– user361424
yesterday
add a comment |
$begingroup$
$(1+3x)^frac23 ≈ 1 + (2/3)(3x) + 0.5(2/3)(-1/3)(3x)^2$
So, $1 + 2x - (1+3x)^frac23 ≈ x^2$
Hence desired limit is $1$
edited Mar 13 at 9:10
YuiTo Cheng
2,0532637
answered Mar 12 at 11:41
Prakhar NeemaPrakhar Neema
1074
New contributor
Prakhar Neema is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$(1+3x)^frac23 ≈ 1 + (2/3)(3x) + 0.5(2/3)(-1/3)(3x)^2$
So, $1 + 2x - (1+3x)^frac23 ≈ x^2$
Hence desired limit is $1$
edited Mar 13 at 9:10
YuiTo Cheng
2,0532637
answered Mar 12 at 11:41
Prakhar NeemaPrakhar Neema
1074
New contributor
Prakhar Neema is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Mar 13 at 9:10
YuiTo Cheng
2,0532637
edited Mar 13 at 9:10
YuiTo Cheng
2,0532637
edited Mar 13 at 9:10
YuiTo Cheng
2,0532637
2,0532637
answered Mar 12 at 11:41
Prakhar NeemaPrakhar Neema
1074
New contributor
Prakhar Neema is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Mar 12 at 11:41
Prakhar NeemaPrakhar Neema
1074
answered Mar 12 at 11:41
Prakhar NeemaPrakhar Neema
1074
1074
New contributor
Prakhar Neema is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Prakhar Neema is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Prakhar Neema is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
Thank you for your suggestion. I am still looking for a method without the T-series expansion or differentiation.
$endgroup$
– yalam
Mar 12 at 11:45
$begingroup$
What about binomial series?
$endgroup$
– user361424
yesterday
add a comment |
$begingroup$
Thank you for your suggestion. I am still looking for a method without the T-series expansion or differentiation.
$endgroup$
– yalam
Mar 12 at 11:45
$begingroup$
What about binomial series?
$endgroup$
– user361424
yesterday
$begingroup$
Thank you for your suggestion. I am still looking for a method without the T-series expansion or differentiation.
$endgroup$
– yalam
Mar 12 at 11:45
$begingroup$
Thank you for your suggestion. I am still looking for a method without the T-series expansion or differentiation.
$endgroup$
– yalam
Mar 12 at 11:45
$begingroup$
What about binomial series?
$endgroup$
– user361424
yesterday
$begingroup$
What about binomial series?
$endgroup$
– user361424
yesterday
add a comment |
$begingroup$
Rationalize the numerator using $a-b=dfraca^3-b^3a^2+ab+b^2$ for $ane b$
to find
$$lim_xto0dfrac(1+2x)^3-(1+3x)^2x^2cdotlim_xto0dfrac1(1+2x)^2+(1+2x)(1+3x)^2/3+(1+3x)^4/3==?$$
answered 21 hours ago
lab bhattacharjeelab bhattacharjee
227k15158275
$endgroup$
add a comment |
$begingroup$
Rationalize the numerator using $a-b=dfraca^3-b^3a^2+ab+b^2$ for $ane b$
to find
$$lim_xto0dfrac(1+2x)^3-(1+3x)^2x^2cdotlim_xto0dfrac1(1+2x)^2+(1+2x)(1+3x)^2/3+(1+3x)^4/3==?$$
answered 21 hours ago
lab bhattacharjeelab bhattacharjee
227k15158275
$endgroup$
add a comment |
$begingroup$
Rationalize the numerator using $a-b=dfraca^3-b^3a^2+ab+b^2$ for $ane b$
to find
$$lim_xto0dfrac(1+2x)^3-(1+3x)^2x^2cdotlim_xto0dfrac1(1+2x)^2+(1+2x)(1+3x)^2/3+(1+3x)^4/3==?$$
answered 21 hours ago
lab bhattacharjeelab bhattacharjee
227k15158275
$endgroup$
Rationalize the numerator using $a-b=dfraca^3-b^3a^2+ab+b^2$ for $ane b$
to find
$$lim_xto0dfrac(1+2x)^3-(1+3x)^2x^2cdotlim_xto0dfrac1(1+2x)^2+(1+2x)(1+3x)^2/3+(1+3x)^4/3==?$$
answered 21 hours ago
lab bhattacharjeelab bhattacharjee
227k15158275
answered 21 hours ago
lab bhattacharjeelab bhattacharjee
227k15158275
answered 21 hours ago
lab bhattacharjeelab bhattacharjee
227k15158275
answered 21 hours ago
lab bhattacharjeelab bhattacharjee
227k15158275
227k15158275
add a comment |
add a comment |
yalam is a new contributor. Be nice, and check out our Code of Conduct.
yalam is a new contributor. Be nice, and check out our Code of Conduct.
yalam is a new contributor. Be nice, and check out our Code of Conduct.
yalam 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%2f3144971%2ffinding-the-limit-without-lhospital%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
2
$begingroup$
Which limit? Please write the problem with MathJax.
$endgroup$
– Matti P.
Mar 12 at 11:19
$begingroup$
Is this $$lim_x to 0frac1+2x-(1+3x)^2/3x^2$$?
$endgroup$
– Dr. Sonnhard Graubner
Mar 12 at 11:25
$begingroup$
Yes! the problem is correct.
$endgroup$
– yalam
Mar 12 at 11:29
$begingroup$
Use Taylor's formula at order $2$ for $(1+3x)^3/2$.
$endgroup$
– Bernard
Mar 12 at 11:38