Question

What is the limit of `sqrt(2-T) - (sqrt 2)/T` as T approaches 0?

Answer 1

I think the lateral limits are different:

Explanation:

As `T->0` we get that `sqrt(2-x)->sqrt(2)`
but the term `-sqrt(2)/x`, depending upon the side you are approaching zero, should tend to `-oo` from the right and `+oo` from the left.

Graphically:
graph{sqrt(2-x)-sqrt(2)/x [-10, 10, -5, 5]}