Hello,

for the conjugate !

Now, multiply and divide by the conjugate :

You can apply l'Hospital's, but there are nicer methods :

LImit to infinity : , with superior values to 1. So with positive values.

Thus the limit is...

(you would have found the same with l'Hospital's)

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My point is that the limit would have been more friendly if it was (x²+x)^(1/2) - x.