Evaluate the intermediate difference with L'Hospital's rule

[Painguy]

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.

 

[operationsres]

L'hopital, not L'hospital. LOL.

 

[Painguy]

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)"

 

[operationsres]

Nice!