Solving Limit at Infinity Problem: x^(2/3) / (log^2(x))

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Discussion Overview

The discussion revolves around solving a limit problem as x approaches infinity, specifically the limit of the expression x^(2/3) / (x/(log^2(x))). Participants are exploring techniques for evaluating this limit, including the application of L'Hopital's Rule and simplification methods.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses confusion about how to apply L'Hopital's Rule to the limit problem and seeks guidance on techniques.
  • Another participant attempts to clarify the limit expression using LaTeX formatting, indicating the limit as x approaches infinity.
  • There are multiple attempts to present the limit in a clearer format, with some participants struggling with LaTeX syntax.
  • A participant suggests using L'Hopital's Rule after rewriting the limit expression, but does not confirm the correctness of this approach.
  • One participant requests additional resources for examples of simplifications involving fractional exponents, indicating a need for further clarification on the topic.
  • Another participant notes that the usual laws of exponents apply universally, regardless of whether the exponents are integers, fractions, or decimals.

Areas of Agreement / Disagreement

There is no clear consensus on the best approach to solve the limit problem, as participants express varying levels of understanding and confusion regarding the application of techniques like L'Hopital's Rule and simplification methods.

Contextual Notes

Participants demonstrate uncertainty regarding the correct application of mathematical techniques and the formatting of expressions, which may affect their ability to communicate effectively about the problem.

DanSlevin
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Hello, I am working on some limit problems and ran into one in which I am lost on how to proceed with:

The problem is:

lim
x -> infinity

x^(2/3)
x/(log^2(x))

I have a basic understanding of L'Hopital's Rule and attempted to apply it, but just ended up with a confusing mess. I'm assuming I'm supposed to simply first, but am not sure how to proceed. Any guidance as to the techniques to use here would be great. Thanks.
 
Last edited:
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Hard to read, I don't get very well what you mean.

This could be useful: http://www.mathhelpboards.com/forumdisplay.php?26-LaTeX-Help
 
DanSlevin said:
Hello, I am working on some limit problems and ran into one in which I am lost on how to proceed with:

The problem is:

lim
x -> infinity

x^(2/3)
x/(log^2(x))

I have a basic understanding of L'Hopital's Rule and attempted to apply it, but just ended up with a confusing mess. I'm assuming I'm supposed to simply first, but am not sure how to proceed. Any guidance as to the techniques to use here would be great. Thanks.

Is it this?

\[ \displaystyle \lim_{x \to \infty}\frac{x^{\frac{2}{3}}}{\frac{x}{(\log{x})^2}} \]
 
I'm sorry about that. I'm also having some trouble understanding the Latex syntax so hopefully this makes it a little clearer.

x2/3
________
x/log2(x)

as x approaches infinity.
 
DanSlevin said:
I'm sorry about that. I'm also having some trouble understanding the Latex syntax so hopefully this makes it a little clearer.

x2/3
________
x/log2(x)

as x approaches infinity.
$$\Large \lim_{x \to \infty}\frac{x^{\frac{2}{3}}}{\frac{x}{(\log{x})^2 }}$$

$$\Large \lim_{x \to \infty}\frac{(\log{x})^2 }{x^{\frac{1}{3}}}$$Now, try to use l'Hôpital's rule.
 
Last edited by a moderator:
Thank you for your reply and answer. Do you happen to have any sites I could look at that include examples of simplifications of this manner? I'm unfortunately unable to find any that show examples with fractional exponents and I'm a little confused as to some of the steps. Thanks again.
 
DanSlevin said:
Thank you for your reply and answer. Do you happen to have any sites I could look at that include examples of simplifications of this manner? I'm unfortunately unable to find any that show examples with fractional exponents and I'm a little confused as to some of the steps. Thanks again.

The usual laws of exponents apply for all exponents be they integer, common fractions or decimals.

CB
 

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