Correct.
Here is the problem:
The limit of the denominator is obviously zero, which means that this equation must be converted to find its limit. This can be done my multiplying by the conjugate of the numerator.
The h cancels out, leaving:
This is equal to:
Substituting for h, is equal to 1
Thus, the answer is:
It's because both the numerator and denominator are 0. The form is indeterminate. The form where is not.
Also, all your x's should be h's.
And one last minor point: When you say "the h cancels out" you mean that the two expressions after the limit are equal except when h=0. This is ok by a limit theorem which says that you get the same limit as long as the two functions agree everywhere except possibly at the number you're approaching.