Find the value of $f(x)$ with proof.












0












$begingroup$


The equation is:



$$lim_{x to 2} frac{f(x) - 1}{x - 2} = 3$$



Suppose f(x) is a function. Find (with proof) the value of lim x→2 f(x), or conclude that this limit diverges.



Our professor wrote in a hint stating: Use Arithmetic of Limits and contradiction. Why can't $lim_{xto2}
f(x) = 0$, for
instance?



It is a question from a previous midterm and noone ive spoken to has solved it,so i wanna ask you guys.






real-analysis







share|cite|improve this question











$endgroup$












  • $begingroup$
    Didn't you forget a "little" detail? What is $;f(x);$ , anyway?!
    $endgroup$
    – DonAntonio
    Jan 12 at 18:12










  • $begingroup$
    Its a function on x.
    $endgroup$
    – user569685
    Jan 12 at 18:16










  • $begingroup$
    Then perhaps the actual question is "what is the value of $;f(2);$ ..."?? Because the value of $;f(x);$ cannot be known from the given info.
    $endgroup$
    – DonAntonio
    Jan 12 at 18:16








  • 1




    $begingroup$
    @ThomasShelby I saw it...read my comment below such answer. Apparently the OP meant to ask what is the value of $;f(2);$ ...
    $endgroup$
    – DonAntonio
    Jan 12 at 18:17












  • $begingroup$
    Yes, you're right. I didn't read the question properly.@DonAntonio
    $endgroup$
    – Thomas Shelby
    Jan 12 at 18:19


















0












$begingroup$


The equation is:



$$lim_{x to 2} frac{f(x) - 1}{x - 2} = 3$$



Suppose f(x) is a function. Find (with proof) the value of lim x→2 f(x), or conclude that this limit diverges.



Our professor wrote in a hint stating: Use Arithmetic of Limits and contradiction. Why can't $lim_{xto2}
f(x) = 0$, for
instance?



It is a question from a previous midterm and noone ive spoken to has solved it,so i wanna ask you guys.






real-analysis







share|cite|improve this question











$endgroup$












  • $begingroup$
    Didn't you forget a "little" detail? What is $;f(x);$ , anyway?!
    $endgroup$
    – DonAntonio
    Jan 12 at 18:12










  • $begingroup$
    Its a function on x.
    $endgroup$
    – user569685
    Jan 12 at 18:16










  • $begingroup$
    Then perhaps the actual question is "what is the value of $;f(2);$ ..."?? Because the value of $;f(x);$ cannot be known from the given info.
    $endgroup$
    – DonAntonio
    Jan 12 at 18:16








  • 1




    $begingroup$
    @ThomasShelby I saw it...read my comment below such answer. Apparently the OP meant to ask what is the value of $;f(2);$ ...
    $endgroup$
    – DonAntonio
    Jan 12 at 18:17












  • $begingroup$
    Yes, you're right. I didn't read the question properly.@DonAntonio
    $endgroup$
    – Thomas Shelby
    Jan 12 at 18:19
















0












0








0





$begingroup$


The equation is:



$$lim_{x to 2} frac{f(x) - 1}{x - 2} = 3$$



Suppose f(x) is a function. Find (with proof) the value of lim x→2 f(x), or conclude that this limit diverges.



Our professor wrote in a hint stating: Use Arithmetic of Limits and contradiction. Why can't $lim_{xto2}
f(x) = 0$, for
instance?



It is a question from a previous midterm and noone ive spoken to has solved it,so i wanna ask you guys.






real-analysis







share|cite|improve this question











$endgroup$




The equation is:



$$lim_{x to 2} frac{f(x) - 1}{x - 2} = 3$$



Suppose f(x) is a function. Find (with proof) the value of lim x→2 f(x), or conclude that this limit diverges.



Our professor wrote in a hint stating: Use Arithmetic of Limits and contradiction. Why can't $lim_{xto2}
f(x) = 0$, for
instance?



It is a question from a previous midterm and noone ive spoken to has solved it,so i wanna ask you guys.






real-analysis




real-analysis






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 12 at 18:26







user569685

















asked Jan 12 at 18:05









user569685user569685

102




102












  • $begingroup$
    Didn't you forget a "little" detail? What is $;f(x);$ , anyway?!
    $endgroup$
    – DonAntonio
    Jan 12 at 18:12










  • $begingroup$
    Its a function on x.
    $endgroup$
    – user569685
    Jan 12 at 18:16










  • $begingroup$
    Then perhaps the actual question is "what is the value of $;f(2);$ ..."?? Because the value of $;f(x);$ cannot be known from the given info.
    $endgroup$
    – DonAntonio
    Jan 12 at 18:16








  • 1




    $begingroup$
    @ThomasShelby I saw it...read my comment below such answer. Apparently the OP meant to ask what is the value of $;f(2);$ ...
    $endgroup$
    – DonAntonio
    Jan 12 at 18:17












  • $begingroup$
    Yes, you're right. I didn't read the question properly.@DonAntonio
    $endgroup$
    – Thomas Shelby
    Jan 12 at 18:19




















  • $begingroup$
    Didn't you forget a "little" detail? What is $;f(x);$ , anyway?!
    $endgroup$
    – DonAntonio
    Jan 12 at 18:12










  • $begingroup$
    Its a function on x.
    $endgroup$
    – user569685
    Jan 12 at 18:16










  • $begingroup$
    Then perhaps the actual question is "what is the value of $;f(2);$ ..."?? Because the value of $;f(x);$ cannot be known from the given info.
    $endgroup$
    – DonAntonio
    Jan 12 at 18:16








  • 1




    $begingroup$
    @ThomasShelby I saw it...read my comment below such answer. Apparently the OP meant to ask what is the value of $;f(2);$ ...
    $endgroup$
    – DonAntonio
    Jan 12 at 18:17












  • $begingroup$
    Yes, you're right. I didn't read the question properly.@DonAntonio
    $endgroup$
    – Thomas Shelby
    Jan 12 at 18:19


















$begingroup$
Didn't you forget a "little" detail? What is $;f(x);$ , anyway?!
$endgroup$
– DonAntonio
Jan 12 at 18:12




$begingroup$
Didn't you forget a "little" detail? What is $;f(x);$ , anyway?!
$endgroup$
– DonAntonio
Jan 12 at 18:12












$begingroup$
Its a function on x.
$endgroup$
– user569685
Jan 12 at 18:16




$begingroup$
Its a function on x.
$endgroup$
– user569685
Jan 12 at 18:16












$begingroup$
Then perhaps the actual question is "what is the value of $;f(2);$ ..."?? Because the value of $;f(x);$ cannot be known from the given info.
$endgroup$
– DonAntonio
Jan 12 at 18:16






$begingroup$
Then perhaps the actual question is "what is the value of $;f(2);$ ..."?? Because the value of $;f(x);$ cannot be known from the given info.
$endgroup$
– DonAntonio
Jan 12 at 18:16






1




1




$begingroup$
@ThomasShelby I saw it...read my comment below such answer. Apparently the OP meant to ask what is the value of $;f(2);$ ...
$endgroup$
– DonAntonio
Jan 12 at 18:17






$begingroup$
@ThomasShelby I saw it...read my comment below such answer. Apparently the OP meant to ask what is the value of $;f(2);$ ...
$endgroup$
– DonAntonio
Jan 12 at 18:17














$begingroup$
Yes, you're right. I didn't read the question properly.@DonAntonio
$endgroup$
– Thomas Shelby
Jan 12 at 18:19






$begingroup$
Yes, you're right. I didn't read the question properly.@DonAntonio
$endgroup$
– Thomas Shelby
Jan 12 at 18:19












1 Answer
1






active

oldest

votes


















3












$begingroup$

Hint



We know that
$$
lim_{xto 2}(f(x)-1)=left(lim_{xto 2}frac{f(x)-1}{x-2}right)timeslim_{xto2}(x-2)tag{0}
$$
by the product rule for limits and
$$
lim_{xto2}f(x)=lim_{xto 2}(f(x)-1)+lim_{xto2}1tag{1}.
$$
You have enough information to compute all the limits.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Yes, the limits can be computed, apparently (if the OP did give all the relevant info...), yet the question seems to be what is the value of $;f;$ ...perhaps when $;x=2;$ or something like that.
    $endgroup$
    – DonAntonio
    Jan 12 at 18:15










  • $begingroup$
    @user569685 Great! Why then in the world didn't you write this in your question?!
    $endgroup$
    – DonAntonio
    Jan 12 at 18:25













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%2f3071204%2ffind-the-value-of-fx-with-proof%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









3












$begingroup$

Hint



We know that
$$
lim_{xto 2}(f(x)-1)=left(lim_{xto 2}frac{f(x)-1}{x-2}right)timeslim_{xto2}(x-2)tag{0}
$$
by the product rule for limits and
$$
lim_{xto2}f(x)=lim_{xto 2}(f(x)-1)+lim_{xto2}1tag{1}.
$$
You have enough information to compute all the limits.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Yes, the limits can be computed, apparently (if the OP did give all the relevant info...), yet the question seems to be what is the value of $;f;$ ...perhaps when $;x=2;$ or something like that.
    $endgroup$
    – DonAntonio
    Jan 12 at 18:15










  • $begingroup$
    @user569685 Great! Why then in the world didn't you write this in your question?!
    $endgroup$
    – DonAntonio
    Jan 12 at 18:25


















3












$begingroup$

Hint



We know that
$$
lim_{xto 2}(f(x)-1)=left(lim_{xto 2}frac{f(x)-1}{x-2}right)timeslim_{xto2}(x-2)tag{0}
$$
by the product rule for limits and
$$
lim_{xto2}f(x)=lim_{xto 2}(f(x)-1)+lim_{xto2}1tag{1}.
$$
You have enough information to compute all the limits.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Yes, the limits can be computed, apparently (if the OP did give all the relevant info...), yet the question seems to be what is the value of $;f;$ ...perhaps when $;x=2;$ or something like that.
    $endgroup$
    – DonAntonio
    Jan 12 at 18:15










  • $begingroup$
    @user569685 Great! Why then in the world didn't you write this in your question?!
    $endgroup$
    – DonAntonio
    Jan 12 at 18:25
















3












3








3





$begingroup$

Hint



We know that
$$
lim_{xto 2}(f(x)-1)=left(lim_{xto 2}frac{f(x)-1}{x-2}right)timeslim_{xto2}(x-2)tag{0}
$$
by the product rule for limits and
$$
lim_{xto2}f(x)=lim_{xto 2}(f(x)-1)+lim_{xto2}1tag{1}.
$$
You have enough information to compute all the limits.






share|cite|improve this answer









$endgroup$



Hint



We know that
$$
lim_{xto 2}(f(x)-1)=left(lim_{xto 2}frac{f(x)-1}{x-2}right)timeslim_{xto2}(x-2)tag{0}
$$
by the product rule for limits and
$$
lim_{xto2}f(x)=lim_{xto 2}(f(x)-1)+lim_{xto2}1tag{1}.
$$
You have enough information to compute all the limits.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Jan 12 at 18:08









Foobaz JohnFoobaz John

21.9k41352




21.9k41352












  • $begingroup$
    Yes, the limits can be computed, apparently (if the OP did give all the relevant info...), yet the question seems to be what is the value of $;f;$ ...perhaps when $;x=2;$ or something like that.
    $endgroup$
    – DonAntonio
    Jan 12 at 18:15










  • $begingroup$
    @user569685 Great! Why then in the world didn't you write this in your question?!
    $endgroup$
    – DonAntonio
    Jan 12 at 18:25




















  • $begingroup$
    Yes, the limits can be computed, apparently (if the OP did give all the relevant info...), yet the question seems to be what is the value of $;f;$ ...perhaps when $;x=2;$ or something like that.
    $endgroup$
    – DonAntonio
    Jan 12 at 18:15










  • $begingroup$
    @user569685 Great! Why then in the world didn't you write this in your question?!
    $endgroup$
    – DonAntonio
    Jan 12 at 18:25


















$begingroup$
Yes, the limits can be computed, apparently (if the OP did give all the relevant info...), yet the question seems to be what is the value of $;f;$ ...perhaps when $;x=2;$ or something like that.
$endgroup$
– DonAntonio
Jan 12 at 18:15




$begingroup$
Yes, the limits can be computed, apparently (if the OP did give all the relevant info...), yet the question seems to be what is the value of $;f;$ ...perhaps when $;x=2;$ or something like that.
$endgroup$
– DonAntonio
Jan 12 at 18:15












$begingroup$
@user569685 Great! Why then in the world didn't you write this in your question?!
$endgroup$
– DonAntonio
Jan 12 at 18:25






$begingroup$
@user569685 Great! Why then in the world didn't you write this in your question?!
$endgroup$
– DonAntonio
Jan 12 at 18:25




















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%2f3071204%2ffind-the-value-of-fx-with-proof%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

Mario Kart Wii

Image
Please consider supporting The Cutting Room Floor on Patreon. Thanks for all your support! Mario Kart Wii From The Cutting Room Floor Jump to: navigation, search Mario Kart Wii Developer : Nintendo Publisher : Nintendo Platform : Wii Released in JP : April 10, 2008 Released in US : April 27, 2008 Released in EU : April 11, 2008 Released in AU : April 24, 2008 Released in KR : April 30, 2009 This game has unused animations. This game has unused areas. This game has unused code. This game has unused objects. This game has unused modes / minigames. This game has unused graphics. This game has unused models. This game has unused items. This game has unused music. This game has regional differences. This game has a notes page This game has a prerelease article Mario Kart Wii is the sixth game in the series (not counting Arcade editions), which intro
Read more

What does “Dominus providebit” mean?

Image
5 Does "Dominus providebit" mean "The Lord will provide" or "The Lord provides"? I once had a bit of an argument with a guy who studied Latin over that. It's an inscription that appears on the rim of some old Swiss coins that I have. meaning latin-to-english-translation grammar-identification share | improve this question edited Jan 18 at 15:27 V2Blast 105 4 asked Jan 17 at 22:49 Donald K. Donald K. 26 1
Read more

Antonio Litta Visconti Arese

Image
Antonio Litta Visconti Arese I duca Litta, VII marchese di Gambolò In carica 1797 – 1820 Predecessore Pompeo Litta Visconti Arese Successore Alfonso Litta Visconti Arese Trattamento Sua grazia Altri titoli Duca Litta Conte del Regno napoleonico d'Italia Patrizio milanese Don Nascita Milano, 2 maggio 1748 Morte Milano, 14 agosto 1820 Dinastia Litta Visconti Arese Padre Pompeo Litta Visconti Arese Madre Maria Elisabetta Visconti Borromeo Consorte Barbara Barbiano di Belgioioso Religione cattolicesimo Antonio Litta Visconti Arese , I duca Litta, VII marchese di Gambolò (Milano, 2 maggio 1748 – Milano, 14 agosto 1820), è stato un nobile e politico italiano. Composizione "Il pastore svizzero" di Pietro Morlacchi, con dedica Indice 1 Biografia 2 Onorificenze 3 Araldica 4 Albero genealogico 5 Note 6 Altri progetti Biografia | Antonio Litta Visco
Read more