Counterexample of $lim_xrightarrow inftyf(x,t(x))neq 1$ where $lim_xrightarrow infty t(x)=2$. Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Pointwise convergence implies uniform convergenceIf a sequence of continuous functions converges pointwise to a continuous function on $ [a,b] $, it converges uniformlyConvergence of monotone $f_n:[0, infty) rightarrow [0,1]$ to continuous, monotone $g$ is uniformProve that $lim_n rightarrow infty int_0^1 f_n(x)dx ne int_0^1lim_n rightarrow inftyf_n(x) dx$Limits: $lim_nrightarrowinftyfracnx1+n^2x^2$ on $I=[0,1]$Can you help me with finding x values where series is convergent and not convergentIf $lim_k rightarrow infty g_k(x)=g(x) text, and lim_k rightarrow infty g_k^'(x)=f(x) text a.e.$ show $g^'(x)=f(x) text a.e.$Given f such that $ f(0)=0, lim_xto infty f(x) = 1$, is $f_n(x)=f(x+e^n)$ uniformly convergent?Example of a sequence of functions where the limit cannot be interchangedCounterexample: Interchange Limit and Integral
Error "illegal generic type for instanceof" when using local classes
Why is "Consequences inflicted." not a sentence?
What's the meaning of 間時肆拾貳 at a car parking sign
Overriding an object in memory with placement new
How to find all the available tools in mac terminal?
What exactly is a "Meth" in Altered Carbon?
How do I keep my slimes from escaping their pens?
Withdrew £2800, but only £2000 shows as withdrawn on online banking; what are my obligations?
What causes the vertical darker bands in my photo?
Can I cast Passwall to drop an enemy into a 20-foot pit?
51k Euros annually for a family of 4 in Berlin: Is it enough?
Can a non-EU citizen traveling with me come with me through the EU passport line?
Single word antonym of "flightless"
Why are there no cargo aircraft with "flying wing" design?
Why was the term "discrete" used in discrete logarithm?
How to tell that you are a giant?
Sci-Fi book where patients in a coma ward all live in a subconscious world linked together
List of Python versions
Do I really need recursive chmod to restrict access to a folder?
Why am I getting the error "non-boolean type specified in a context where a condition is expected" for this request?
Echoing a tail command produces unexpected output?
Generate an RGB colour grid
Seeking colloquialism for “just because”
Denied boarding although I have proper visa and documentation. To whom should I make a complaint?
Counterexample of $lim_xrightarrow inftyf(x,t(x))neq 1$ where $lim_xrightarrow infty t(x)=2$.
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Pointwise convergence implies uniform convergenceIf a sequence of continuous functions converges pointwise to a continuous function on $ [a,b] $, it converges uniformlyConvergence of monotone $f_n:[0, infty) rightarrow [0,1]$ to continuous, monotone $g$ is uniformProve that $lim_n rightarrow infty int_0^1 f_n(x)dx ne int_0^1lim_n rightarrow inftyf_n(x) dx$Limits: $lim_nrightarrowinftyfracnx1+n^2x^2$ on $I=[0,1]$Can you help me with finding x values where series is convergent and not convergentIf $lim_k rightarrow infty g_k(x)=g(x) text, and lim_k rightarrow infty g_k^'(x)=f(x) text a.e.$ show $g^'(x)=f(x) text a.e.$Given f such that $ f(0)=0, lim_xto infty f(x) = 1$, is $f_n(x)=f(x+e^n)$ uniformly convergent?Example of a sequence of functions where the limit cannot be interchangedCounterexample: Interchange Limit and Integral
$begingroup$
Given $lim_xrightarrow infty f(x,t)=1$ for any fixed t in $(1,3)$, in general $lim_xrightarrow infty f(x,t(x))neq 1$ where $lim_xrightarrowinftyt(x)=2$ and $t(x)in (1,3)$ unless we have uniform convergence. However, I cannot find a good counterexample. Any suggestion is highly appreciated. Thank you very much.
convergence examples-counterexamples uniform-convergence
edited Mar 26 at 17:15
Mostafa Ayaz
18.1k31040
asked Mar 26 at 16:34
EthanabcEthanabc
1527
$endgroup$
add a comment |
$begingroup$
Given $lim_xrightarrow infty f(x,t)=1$ for any fixed t in $(1,3)$, in general $lim_xrightarrow infty f(x,t(x))neq 1$ where $lim_xrightarrowinftyt(x)=2$ and $t(x)in (1,3)$ unless we have uniform convergence. However, I cannot find a good counterexample. Any suggestion is highly appreciated. Thank you very much.
convergence examples-counterexamples uniform-convergence
edited Mar 26 at 17:15
Mostafa Ayaz
18.1k31040
asked Mar 26 at 16:34
EthanabcEthanabc
1527
$endgroup$
add a comment |
$begingroup$
Given $lim_xrightarrow infty f(x,t)=1$ for any fixed t in $(1,3)$, in general $lim_xrightarrow infty f(x,t(x))neq 1$ where $lim_xrightarrowinftyt(x)=2$ and $t(x)in (1,3)$ unless we have uniform convergence. However, I cannot find a good counterexample. Any suggestion is highly appreciated. Thank you very much.
convergence examples-counterexamples uniform-convergence
edited Mar 26 at 17:15
Mostafa Ayaz
18.1k31040
asked Mar 26 at 16:34
EthanabcEthanabc
1527
$endgroup$
Given $lim_xrightarrow infty f(x,t)=1$ for any fixed t in $(1,3)$, in general $lim_xrightarrow infty f(x,t(x))neq 1$ where $lim_xrightarrowinftyt(x)=2$ and $t(x)in (1,3)$ unless we have uniform convergence. However, I cannot find a good counterexample. Any suggestion is highly appreciated. Thank you very much.
convergence examples-counterexamples uniform-convergence
convergence examples-counterexamples uniform-convergence
edited Mar 26 at 17:15
Mostafa Ayaz
18.1k31040
asked Mar 26 at 16:34
EthanabcEthanabc
1527
edited Mar 26 at 17:15
Mostafa Ayaz
18.1k31040
asked Mar 26 at 16:34
EthanabcEthanabc
1527
edited Mar 26 at 17:15
Mostafa Ayaz
18.1k31040
edited Mar 26 at 17:15
Mostafa Ayaz
18.1k31040
edited Mar 26 at 17:15
Mostafa Ayaz
18.1k31040
18.1k31040
asked Mar 26 at 16:34
EthanabcEthanabc
1527
asked Mar 26 at 16:34
EthanabcEthanabc
1527
asked Mar 26 at 16:34
EthanabcEthanabc
1527
1527
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
What about this one?$$f(x,t)=begincases1+tanpiover 4tover x&,quad tne 2\1&,quad t=2endcases$$and $t(x)=2-e^-x$.
answered Mar 26 at 17:13
Mostafa AyazMostafa Ayaz
18.1k31040
$endgroup$
$begingroup$
Based on your idea, I can now generate many counterexamples. Thank you very much!
$endgroup$
– Ethanabc
Mar 26 at 17:30
$begingroup$
Your welcome. Yes, there are infinitely many other counter examples. Good luck!
$endgroup$
– Mostafa Ayaz
Mar 26 at 17:31
add a comment |
Your Answer
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%2f3163436%2fcounterexample-of-lim-x-rightarrow-inftyfx-tx-neq-1-where-lim-x-rig%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
$begingroup$
What about this one?$$f(x,t)=begincases1+tanpiover 4tover x&,quad tne 2\1&,quad t=2endcases$$and $t(x)=2-e^-x$.
answered Mar 26 at 17:13
Mostafa AyazMostafa Ayaz
18.1k31040
$endgroup$
$begingroup$
Based on your idea, I can now generate many counterexamples. Thank you very much!
$endgroup$
– Ethanabc
Mar 26 at 17:30
$begingroup$
Your welcome. Yes, there are infinitely many other counter examples. Good luck!
$endgroup$
– Mostafa Ayaz
Mar 26 at 17:31
add a comment |
$begingroup$
What about this one?$$f(x,t)=begincases1+tanpiover 4tover x&,quad tne 2\1&,quad t=2endcases$$and $t(x)=2-e^-x$.
answered Mar 26 at 17:13
Mostafa AyazMostafa Ayaz
18.1k31040
$endgroup$
$begingroup$
Based on your idea, I can now generate many counterexamples. Thank you very much!
$endgroup$
– Ethanabc
Mar 26 at 17:30
$begingroup$
Your welcome. Yes, there are infinitely many other counter examples. Good luck!
$endgroup$
– Mostafa Ayaz
Mar 26 at 17:31
add a comment |
$begingroup$
What about this one?$$f(x,t)=begincases1+tanpiover 4tover x&,quad tne 2\1&,quad t=2endcases$$and $t(x)=2-e^-x$.
answered Mar 26 at 17:13
Mostafa AyazMostafa Ayaz
18.1k31040
$endgroup$
What about this one?$$f(x,t)=begincases1+tanpiover 4tover x&,quad tne 2\1&,quad t=2endcases$$and $t(x)=2-e^-x$.
answered Mar 26 at 17:13
Mostafa AyazMostafa Ayaz
18.1k31040
answered Mar 26 at 17:13
Mostafa AyazMostafa Ayaz
18.1k31040
answered Mar 26 at 17:13
Mostafa AyazMostafa Ayaz
18.1k31040
answered Mar 26 at 17:13
Mostafa AyazMostafa Ayaz
18.1k31040
18.1k31040
$begingroup$
Based on your idea, I can now generate many counterexamples. Thank you very much!
$endgroup$
– Ethanabc
Mar 26 at 17:30
$begingroup$
Your welcome. Yes, there are infinitely many other counter examples. Good luck!
$endgroup$
– Mostafa Ayaz
Mar 26 at 17:31
add a comment |
$begingroup$
Based on your idea, I can now generate many counterexamples. Thank you very much!
$endgroup$
– Ethanabc
Mar 26 at 17:30
$begingroup$
Your welcome. Yes, there are infinitely many other counter examples. Good luck!
$endgroup$
– Mostafa Ayaz
Mar 26 at 17:31
$begingroup$
Based on your idea, I can now generate many counterexamples. Thank you very much!
$endgroup$
– Ethanabc
Mar 26 at 17:30
$begingroup$
Based on your idea, I can now generate many counterexamples. Thank you very much!
$endgroup$
– Ethanabc
Mar 26 at 17:30
$begingroup$
Your welcome. Yes, there are infinitely many other counter examples. Good luck!
$endgroup$
– Mostafa Ayaz
Mar 26 at 17:31
$begingroup$
Your welcome. Yes, there are infinitely many other counter examples. Good luck!
$endgroup$
– Mostafa Ayaz
Mar 26 at 17:31
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%2f3163436%2fcounterexample-of-lim-x-rightarrow-inftyfx-tx-neq-1-where-lim-x-rig%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
