lim as x -> infinity of (sqrt(x - 6) - sqrt(x))

I answered 0 but I wasn't really sure. I thought it may have been 6 or maybe infinity. The usual method I use is dividing everything by x raised to the highest power in the denominator then simplifying. But since the denominator is x^0 this didn't work...

>I just had a test on
>this and this was the
>one problem I couldn't get:
>
>lim as x -> infinity of (sqrt(x - 6) - sqrt(x))
>
>The usual method
>I use is dividing everything
>by x raised to the
>highest power in the denominator
>then simplifying.

You do not have denominator here. But honestly I am bewildered by the implication that there may be a usual method for computing limits. In the very least there is a couple dozens usual methods. You just have to learn them all. No single method will serve you in all circumstances.

>But since
>the denominator is x^0 this
>didn't work...

Right. I may give two advices:

1. Get into the habit of consulting your textbook.
2. Divide and multiply your expression by the sum (sqrt(x - 6) + sqrt(x))