JEE Math Practice Question

Let f : R $$\to$$ R be defined as $$f(x) = \left\{ {\begin{matrix} {{{{x^3}} \over {{{(1 - \cos 2x)}^2}}}{{\log }_e}\left( {{{1 + 2x{e^{ - 2x}}} \over {{{(1 - x{e^{ - x}})}^2}}}} \right),} & {x \ne 0} \\ {\alpha ,} & {x = 0} \\ \end{matrix} } \right.$$ If f is continuous at x = 0, then $$\alpha$$ is equal to :

1. A.1
2. B.3
3. C.0
4. D.2