The limit of the right hand side as x goes to zero can be found using L'Hopital's Rule. (verify conditions)
So the limit as x tends to 0 of
Note that the limit of is 1, so you're left with
, whose limit is 0.
But remember that we just measured the limit of equal to 0, which means the limit of y, your original expression, is 1. Verify numerically and graphically.