C an we conclude that $lim_{xto0+}(f*g)(x)= lim_{xto0+}f(x)* lim_{xto0+}g(x)?$












0












$begingroup$


Let $f,g:(0,1)to(0,1)$ be two continuous functions such that $lim_{xto0+}f(x)$ and $lim_{xto0+}g(x)$ exists. If $*:[0,1]times[0,1]to[0,1]$ be continuous then can we conclude that $lim_{xto0+}(f(x)*g(x))= lim_{xto0+}f(x)* lim_{xto0+}g(x)?$



I think that will be true but I couldn’t conclude this using proper logic.



Please help me.










share|cite|improve this question











$endgroup$












  • $begingroup$
    The notation doesn't make sense. If $*$ is a function defined on $[0,1]$, what is $f*g$ supposed to be?
    $endgroup$
    – Git Gud
    Jan 17 at 14:42










  • $begingroup$
    Modified it properly
    $endgroup$
    – Jave
    Jan 17 at 14:43










  • $begingroup$
    Still not clear. On the LHS is the function $xmapsto *left(g(x)right)cdot f(x)$? Or perhaps you mean that $*$ is a function from $[0,1]^2$ to $[0,1]$ and you're using infix notation.
    $endgroup$
    – Git Gud
    Jan 17 at 14:46












  • $begingroup$
    Yes yes I am sorry
    $endgroup$
    – Jave
    Jan 17 at 14:48










  • $begingroup$
    Do you know multivariable calculus? Can you prove that $xmapsto (f(x), g(x))$ is continuous? Do you know that the composition of continuous functions is continuous?
    $endgroup$
    – Git Gud
    Jan 17 at 14:57
















0












$begingroup$


Let $f,g:(0,1)to(0,1)$ be two continuous functions such that $lim_{xto0+}f(x)$ and $lim_{xto0+}g(x)$ exists. If $*:[0,1]times[0,1]to[0,1]$ be continuous then can we conclude that $lim_{xto0+}(f(x)*g(x))= lim_{xto0+}f(x)* lim_{xto0+}g(x)?$



I think that will be true but I couldn’t conclude this using proper logic.



Please help me.










share|cite|improve this question











$endgroup$












  • $begingroup$
    The notation doesn't make sense. If $*$ is a function defined on $[0,1]$, what is $f*g$ supposed to be?
    $endgroup$
    – Git Gud
    Jan 17 at 14:42










  • $begingroup$
    Modified it properly
    $endgroup$
    – Jave
    Jan 17 at 14:43










  • $begingroup$
    Still not clear. On the LHS is the function $xmapsto *left(g(x)right)cdot f(x)$? Or perhaps you mean that $*$ is a function from $[0,1]^2$ to $[0,1]$ and you're using infix notation.
    $endgroup$
    – Git Gud
    Jan 17 at 14:46












  • $begingroup$
    Yes yes I am sorry
    $endgroup$
    – Jave
    Jan 17 at 14:48










  • $begingroup$
    Do you know multivariable calculus? Can you prove that $xmapsto (f(x), g(x))$ is continuous? Do you know that the composition of continuous functions is continuous?
    $endgroup$
    – Git Gud
    Jan 17 at 14:57














0












0








0





$begingroup$


Let $f,g:(0,1)to(0,1)$ be two continuous functions such that $lim_{xto0+}f(x)$ and $lim_{xto0+}g(x)$ exists. If $*:[0,1]times[0,1]to[0,1]$ be continuous then can we conclude that $lim_{xto0+}(f(x)*g(x))= lim_{xto0+}f(x)* lim_{xto0+}g(x)?$



I think that will be true but I couldn’t conclude this using proper logic.



Please help me.










share|cite|improve this question











$endgroup$




Let $f,g:(0,1)to(0,1)$ be two continuous functions such that $lim_{xto0+}f(x)$ and $lim_{xto0+}g(x)$ exists. If $*:[0,1]times[0,1]to[0,1]$ be continuous then can we conclude that $lim_{xto0+}(f(x)*g(x))= lim_{xto0+}f(x)* lim_{xto0+}g(x)?$



I think that will be true but I couldn’t conclude this using proper logic.



Please help me.







continuity






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 17 at 14:48







Jave

















asked Jan 17 at 14:39









JaveJave

472114




472114












  • $begingroup$
    The notation doesn't make sense. If $*$ is a function defined on $[0,1]$, what is $f*g$ supposed to be?
    $endgroup$
    – Git Gud
    Jan 17 at 14:42










  • $begingroup$
    Modified it properly
    $endgroup$
    – Jave
    Jan 17 at 14:43










  • $begingroup$
    Still not clear. On the LHS is the function $xmapsto *left(g(x)right)cdot f(x)$? Or perhaps you mean that $*$ is a function from $[0,1]^2$ to $[0,1]$ and you're using infix notation.
    $endgroup$
    – Git Gud
    Jan 17 at 14:46












  • $begingroup$
    Yes yes I am sorry
    $endgroup$
    – Jave
    Jan 17 at 14:48










  • $begingroup$
    Do you know multivariable calculus? Can you prove that $xmapsto (f(x), g(x))$ is continuous? Do you know that the composition of continuous functions is continuous?
    $endgroup$
    – Git Gud
    Jan 17 at 14:57


















  • $begingroup$
    The notation doesn't make sense. If $*$ is a function defined on $[0,1]$, what is $f*g$ supposed to be?
    $endgroup$
    – Git Gud
    Jan 17 at 14:42










  • $begingroup$
    Modified it properly
    $endgroup$
    – Jave
    Jan 17 at 14:43










  • $begingroup$
    Still not clear. On the LHS is the function $xmapsto *left(g(x)right)cdot f(x)$? Or perhaps you mean that $*$ is a function from $[0,1]^2$ to $[0,1]$ and you're using infix notation.
    $endgroup$
    – Git Gud
    Jan 17 at 14:46












  • $begingroup$
    Yes yes I am sorry
    $endgroup$
    – Jave
    Jan 17 at 14:48










  • $begingroup$
    Do you know multivariable calculus? Can you prove that $xmapsto (f(x), g(x))$ is continuous? Do you know that the composition of continuous functions is continuous?
    $endgroup$
    – Git Gud
    Jan 17 at 14:57
















$begingroup$
The notation doesn't make sense. If $*$ is a function defined on $[0,1]$, what is $f*g$ supposed to be?
$endgroup$
– Git Gud
Jan 17 at 14:42




$begingroup$
The notation doesn't make sense. If $*$ is a function defined on $[0,1]$, what is $f*g$ supposed to be?
$endgroup$
– Git Gud
Jan 17 at 14:42












$begingroup$
Modified it properly
$endgroup$
– Jave
Jan 17 at 14:43




$begingroup$
Modified it properly
$endgroup$
– Jave
Jan 17 at 14:43












$begingroup$
Still not clear. On the LHS is the function $xmapsto *left(g(x)right)cdot f(x)$? Or perhaps you mean that $*$ is a function from $[0,1]^2$ to $[0,1]$ and you're using infix notation.
$endgroup$
– Git Gud
Jan 17 at 14:46






$begingroup$
Still not clear. On the LHS is the function $xmapsto *left(g(x)right)cdot f(x)$? Or perhaps you mean that $*$ is a function from $[0,1]^2$ to $[0,1]$ and you're using infix notation.
$endgroup$
– Git Gud
Jan 17 at 14:46














$begingroup$
Yes yes I am sorry
$endgroup$
– Jave
Jan 17 at 14:48




$begingroup$
Yes yes I am sorry
$endgroup$
– Jave
Jan 17 at 14:48












$begingroup$
Do you know multivariable calculus? Can you prove that $xmapsto (f(x), g(x))$ is continuous? Do you know that the composition of continuous functions is continuous?
$endgroup$
– Git Gud
Jan 17 at 14:57




$begingroup$
Do you know multivariable calculus? Can you prove that $xmapsto (f(x), g(x))$ is continuous? Do you know that the composition of continuous functions is continuous?
$endgroup$
– Git Gud
Jan 17 at 14:57










0






active

oldest

votes











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


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3077062%2fc-an-we-conclude-that-lim-x-to0fgx-lim-x-to0fx-lim-x-to0g%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























0






active

oldest

votes








0






active

oldest

votes









active

oldest

votes






active

oldest

votes
















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














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3077062%2fc-an-we-conclude-that-lim-x-to0fgx-lim-x-to0fx-lim-x-to0g%23new-answer', 'question_page');
}
);

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







Popular posts from this blog

Can a sorcerer learn a 5th-level spell early by creating spell slots using the Font of Magic feature?

Does disintegrating a polymorphed enemy still kill it after the 2018 errata?

A Topological Invariant for $pi_3(U(n))$