The correct option is B a=2,L=164
L=limx→0a−√a2−x2−x2/4x4
Applying L-Hospital's rule, L=limx→02x−x√a2−x28x3√a2−x2
=limx→0x√a2−x2(2√a2−x2−1)8x3√a2−x2
=limx→0(2√a2−x2−1)8x2
As x→0, denominator tends to 0, so the numerator also tends to 0.
⇒limx→02√a2−x2−1=0
⇒a=2
So, L=limx→02−√4−x2−x2/4x4
Applying L-Hospital's rule, =limx→0(2√4−x2−1)8x2
Again ,applying L-Hospital's rule, =limx→02x(4−x2)−3/216x=164
Hence, option 'A' is correct.