I'm not any sort of an expert at limits, but this looks so I'm going to take a shot at it.

First since we know that

Thus

Next we have . We know that since the tangent line to y = f(x) at x = 0 is 2y = x. Thus the limit is of the form and we may apply L'Hopital's rule:

(Because near x = 0.)

Thus

-Dan