Limf (x) = a (x → x0), if f (x) > 0, is there a > 0?

Limf (x) = a (x → x0), if f (x) > 0, is there a > 0?

A can be equal to 0
For example: F (x) = (x-1) ^ 2 / lgx
Another example: F (x) = | X-1 | (x ≠ 1)