What Went Wrong in Evaluating the Limit Using L'Hospital's Rule?

  • Context: Undergrad 
  • Thread starter Thread starter SpockTock
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Discussion Overview

The discussion revolves around evaluating the limit as x approaches infinity of the expression xln((x+3)/(x)). Participants explore the use of L'Hospital's Rule and alternative methods for solving the limit, while addressing discrepancies between their results and graphical representations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant claims that the limit evaluates to negative infinity using L'Hospital's Rule, but questions arise due to a conflicting graphical result of three.
  • Another participant requests to see the work done by the first participant to understand the error.
  • A suggestion is made to rewrite the limit in a different form that avoids L'Hospital's Rule, indicating that the rule may not be necessary for this problem.
  • Another approach is introduced using the power series expansion for ln, suggesting that this could provide a clearer path to the limit.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct evaluation of the limit, with multiple competing methods and interpretations presented without resolution.

Contextual Notes

There are unresolved assumptions regarding the application of L'Hospital's Rule and the conditions under which the alternative methods are valid. The discussion does not clarify the specific steps leading to the conflicting results.

Who May Find This Useful

This discussion may be of interest to students and practitioners in mathematics or related fields who are exploring limit evaluation techniques and the application of L'Hospital's Rule.

SpockTock
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I came across the problem lim as x approaches infinity of xln((x+3)/(x)). This is an indeterminate limit so L'Hospitals rule must be used to evaluate it. I solved it to come out to negative infinity, but the graph says it's three. What did I do wrong in solving it?
 
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Can I see what you've done?
 
write
x log((x+3)/x)=3 [log(1+3/x)-log(1)]/(3/x)
then you won't need L'Hospital's Rule which would work despite being unneeded. As far as what the mistake was how would anyone know?
 
You can also use the power series for ln: ln(1 + 3/x) = 3/x +O(1/x2)
 

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