Question

What is the limit as x approaches infinity of `sqrt(x)`?

Answer 1

There is no upper limit.

You can prove this by considering that:

If `x` goes up you always need a greater number, that, if squared, will give you `x`.

Or, the other way around:
Suppose there is a limit to `root 2 x`. Lets call this limit `N`

Then the largest `x` we could have would be `N^2`, which is not even near `oo`

(Of course there is a lower limit to both `x` and `root 2 x`.
they both can't be negative)