Does l'Hopital's rule apply to -infinity/infinity?

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Homework Help Overview

The discussion revolves around the application of l'Hôpital's rule, particularly in the context of limits that approach -infinity/infinity. Participants are exploring whether this form is valid under the rule's conditions.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants question the applicability of l'Hôpital's rule to -infinity/infinity, referencing sources that suggest it does not apply. Others argue that it should work based on the properties of limits.

Discussion Status

The discussion is ongoing, with differing opinions on the validity of applying l'Hôpital's rule to -infinity/infinity. Some participants provide reasoning to support their views, while others focus on clarifying terminology related to the rule.

Contextual Notes

There is mention of potential confusion regarding the spelling of l'Hôpital's rule, which may affect the clarity of the discussion.

theoritician
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It works for 0/0 or infinity/infinity

Does it work for -infinity/infinity? wiki suggests no.

Books give examples for lim xln(x) and does it and appplies this rule. HOwever it's really -infinity/infinity!
 
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Of course it works for -infinity/infinity! Thats because (if and only if the limit exists) [tex]\lim_{x\to a} - f(x) = - \lim_{x\to a} f(x)[/tex]. The second part is one of the cases you know it works.
 
Are you talking about l'Hopital, or l'Hospital's rule? If so, that is a weird spelling in the title!
 
cristo said:
Are you talking about l'Hopital, or l'Hospital's rule? If so, that is a weird spelling in the title!
LOL! Damn ... I've never seen it butchered that badly. Good laugh, thanks :-] no offense either :p
 
Last edited:

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