Evaluate the intermediate difference with L'Hospital's rule

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Homework Help Overview

The problem involves evaluating the limit of the expression (x - sqrt(x^2 - 1)) as x approaches infinity, which falls under the topic of calculus, specifically limits and the application of L'Hospital's rule.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to eliminate the radical in the expression to facilitate the use of L'Hospital's rule, expressing uncertainty about the approach. Some participants engage in a side discussion regarding the spelling and pronunciation of L'Hospital's rule.

Discussion Status

The discussion is ongoing, with the original poster seeking guidance on how to manipulate the expression for L'Hospital's rule. There is no consensus on the approach yet, as the focus has shifted to a clarification of terminology.

Contextual Notes

There is a mention of differing spellings of L'Hospital's rule in various sources, which may indicate a broader discussion about terminology in mathematical contexts.

Painguy
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Homework Statement



limit (x-sqrt(x^2 -1)) x-> inf

Homework Equations





The Attempt at a Solution



What I had in mind was to somehow get rid of the radical so I can factor out an x then use L'Hospital's rule with the resulting intermediate product. I'm not sure how to approach the problem however.
 
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L'hopital, not L'hospital. LOL.
 
operationsres said:
L'hopital, not L'hospital. LOL.

http://mathworld.wolfram.com/LHospitalsRule.html

My book spells it as L'hospital, and so does Wolfram Alpha.

Wikipedia says, "In calculus, l'Hôpital's rule pronounced: [lopiˈtal] (also sometimes spelled l'Hospital's rule with silent "s" and identical pronunciation)"
 
Nice!
 

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