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iamMJae
 one year ago
How do I start with questions that look like this?:
iamMJae
 one year ago
How do I start with questions that look like this?:

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iamMJae
 one year ago
Best ResponseYou've already chosen the best response.3\[Construct~an~f(x)~such~that~\lim_{x \rightarrow 3} f(x)=\infty~but~\lim_{x \rightarrow 3} (x3)f(x)=0.\]

iamMJae
 one year ago
Best ResponseYou've already chosen the best response.3I ended up with \[f(x)=\frac{ x+3 }{ (x3)^2 }\] It's almost right except it diverges and even if it could be correct, how do I go about my "solution" because I just guessed at it and it was somehow close.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the infinite limit is an asymptote, that's why (x3) is in the denominator. I think you should be fine if you don't square it. Multiplying by (x3) makes a hole at (3, 0).

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0isn't squaring a must for both side limits to be +infinity ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you're right. I missed that

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0looks very tricky haha i still don't see how we can get 0 for the limit f(x)*(x3)

iamMJae
 one year ago
Best ResponseYou've already chosen the best response.3Sorry, yes, I was wrong. The square makes it not diverge.

iamMJae
 one year ago
Best ResponseYou've already chosen the best response.3@ganeshie8 It's not "limit f(x)*(x3)" but limit (x3)f(x)... If that makes any difference.

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Maybe it's a typo and it should really say: \[\lim_{x \rightarrow 3} (x3)f(x)=1\]

iamMJae
 one year ago
Best ResponseYou've already chosen the best response.3@Empty It says 0 but if it was, what would be the function?

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Oh even then I can't find a simple answer because I had thought it would have been either \[f(x) = \frac{1}{x3} \]or \[f(x) = \frac{1}{x3} \] but both would not work either. Weird, I will be amazed if there is a solution to this question! :D

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0Below function fits the given spec but im pretty sure this is not what you want \[f(x)=\dfrac{1}{\sqrt{x3}}\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0f:R>R so that we don't have to wry about x<=3 part that is not part of the domain of f(x)

amoodarya
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{\sqrt[3]{x3}}\]

Empty
 one year ago
Best ResponseYou've already chosen the best response.0I don't think any of these work exactly, unfortunately because of twosided limits not existing.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0two sided limit is not the definition of a limit for boundary points

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.03 is a boundary point for f(x) = 1/sqrt(x3), so we are fine

amoodarya
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{\sqrt[3]{x3}}\\ \lim_{x \rightarrow 3}\frac{1}{\sqrt[3]{x3}}=+\infty\\lim_{x \rightarrow 3}(x3)\frac{1}{\sqrt[3]{x3}}=0\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0wow! thats really clever!!

amoodarya
 one year ago
Best ResponseYou've already chosen the best response.1\[f(x)=\lnx3\] this function also work

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0both work like charm! xD

amoodarya
 one year ago
Best ResponseYou've already chosen the best response.1I think ,we can't find f(x) R>R easily !

phi
 one year ago
Best ResponseYou've already chosen the best response.1in general, if you have a function f(x) > infinity then let g(x)= 1/f(x) goes to zero i.e. let f(x)= 1/g(x) next, (x3) f(x) = (x3)/g(x) goes to 0 for this to be true, we want g(x) to "go to zero *slower* * than (x3) goes to zero. in which case (x3) "wins"

phi
 one year ago
Best ResponseYou've already chosen the best response.1as amood suggests, a log function grows very slowly we could also use sqrt, which grows more slowly than (x3) for example \[ \lim_{x\rightarrow 3}\frac{1}{\sqrt{x3}} = \infty \\ \lim_{x\rightarrow 3}\frac{(x3)}{\sqrt{x3}} =0 \]
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