Let
$$L = \lim_{x \rightarrow 0}\frac{a - \sqrt{a^2 - x^2} - \frac{x^4}{4}}{x^4}, a>0$$. If L is finite, then

A

a = 2

B

a = 1

C

$$L = \frac{1}{64}$$

D

$$L = \frac{1}{32}$$