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Limits of functions - simple quick q.

When finding the limits of functions in the following format:

√x (√(x+1) - √(x-1))

I am able to obtain the correct limit by multiplying through by (x+1)^1/2 - (x-1)^1//2.

However if i try to apply the Calculus of Limits Theorem, the surely as x ---> infinity, both terms in the brackets, approx (x)^1/2 - and so they would cancel, giving the limit as 0.

Ofc this is not correct.

My question is, what is the exact reasoning for this - i guess this an incorrect use of the theorem - but in exactly what way?

Thanks alot anyone who can shed some light on this, greatly aprpeciated :smile: