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

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In summary, the rule for finding limits works for 0/0 or infinity/infinity, as long as the limit exists. This also applies to -infinity/infinity and can be used with l'Hopital's rule or l'Hospital's rule. However, some sources may misspell the name of the rule.
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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.
 
  • #3
Are you talking about l'Hopital, or l'Hospital's rule? If so, that is a weird spelling in the title!
 
  • #4
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
 
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Related to Does l'Hopital's rule apply to -infinity/infinity?

What is L'ptsle's rule?

L'ptsle's rule is a mathematical formula used to solve for an unknown variable in a proportion. It is also known as the cross multiplication method.

How do I use L'ptsle's rule?

To use L'ptsle's rule, you must first set up a proportion with two ratios. Then, cross multiply the numerator of one ratio with the denominator of the other ratio. Finally, set the two cross products equal to each other and solve for the unknown variable.

When should I use L'ptsle's rule?

L'ptsle's rule is commonly used when solving for an unknown variable in a proportion. It can also be used to solve for an unknown value in a ratio or to find the missing term in a geometric sequence.

What are the limitations of L'ptsle's rule?

L'ptsle's rule can only be used for proportions with two ratios. It cannot be used for proportions with more than two ratios or for equations with variables on both sides.

Who invented L'ptsle's rule?

L'ptsle's rule was named after the French mathematician Etienne L'ptsle, who developed the formula in the 19th century. However, the method of cross multiplication has been used since ancient times by mathematicians such as Euclid and Archimedes.

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