Limit of sqrt(x^2 + x) - x as x Approaches Infinity

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SUMMARY

The limit of the expression sqrt(x^2 + x) - x as x approaches infinity simplifies to 1. To evaluate this limit, one must rationalize the expression by multiplying by the conjugate, which is sqrt(x^2 + x) + x. This technique allows for the application of L'Hospital's rule effectively, leading to the conclusion that the limit is indeed 1.

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grothem
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lim sqrt(x^2 + x) - x as x approaches infinity

Not sure what I need to do. I tried to make it into a fraction so I could apply L'Hospital's rule but I didnt' get anywhere with that. Any ideas?
 
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[tex]1=\frac{\sqrt{x^{2}+x}+x}{\sqrt{x^{2}+x}+x}[/tex]
 
Yeah like arildno suggested you need to rationalize the expression by multiplying with what post #2 suggests!
 

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