Ans: option A (-1/8)
f(0) = limx->0 (2-√(x+4))/(sin(2x))
Since we have an indeterminate form of type 0/0, we can apply the l'Hopital's rule:
f(0) = limx->0 (-1/2)*(1/√(x+4))/(2cos(2x))
now, putting x=0 -->
f(0) = (-1/2)*(1/2)*(1/2)
f(0)= (-1/8)
option(A) - 1/8